tag:blogger.com,1999:blog-48039359336701757512024-03-14T04:38:01.030-07:00VTU Engineering PhysicsRAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.comBlogger29125tag:blogger.com,1999:blog-4803935933670175751.post-64316842230979150512014-02-17T04:48:00.003-08:002014-02-17T04:48:58.827-08:00First/Second Semester B.E. Degree Examination, June 2014 Engineering Physics-Model question paper for VTU examination<div dir="ltr" style="text-align: left;" trbidi="on">
<div id="yui_3_13_0_ym1_1_1392649169696_2526" style="margin-bottom: 0in;">
<span id="yui_3_13_0_ym1_1_1392649169696_2525" style="font-size: medium;">USN
10PHY12/22
</span>
</div>
<div align="CENTER" id="yui_3_13_0_ym1_1_1392649169696_2649" style="margin-bottom: 0in;">
<br />
</div>
<div align="CENTER" id="yui_3_13_0_ym1_1_1392649169696_2655" style="margin-bottom: 0in;">
<span id="yui_3_13_0_ym1_1_1392649169696_2657" style="font-size: medium;">First/Second
Semester B.E. Degree Examination, June 2014</span></div>
<div align="CENTER" id="yui_3_13_0_ym1_1_1392649169696_2520" style="margin-bottom: 0in;">
<span id="yui_3_13_0_ym1_1_1392649169696_2519" style="font-size: medium;"><b id="yui_3_13_0_ym1_1_1392649169696_2518">Engineering
Physics</b></span></div>
<div align="CENTER" style="margin-bottom: 0in;">
Time: 3 hrs.
Max. Marks:100</div>
<div align="CENTER" style="margin-bottom: 0in;">
<br />
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2658" style="margin-bottom: 0in;">
Note: 1. Answer any FIVE
full questions, choosing atleast two from each part.</div>
<div style="margin-bottom: 0in;">
2. Answer all
objective type questions only in OMR sheet page 5 of the answer
booklet.</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2659" style="margin-bottom: 0in;">
3. Answer to
objective type questions on sheets other than OMR will not be valued.</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2660" style="margin-bottom: 0in;">
4. Physical
constants: h = 6.626×10<sup>-34</sup> Js, c = 3×10<sup>8</sup> m/s,
m<sub>e</sub> = 9.1×10<sup>-31</sup> kg,
</div>
<div style="margin-bottom: 0in;">
k = 1.38×10<sup>-23</sup> J/K, ε<sub>0</sub> =
8.854×10<sup>-12</sup> F/m</div>
<div style="margin-bottom: 0in;">
</div>
<div align="CENTER" id="yui_3_13_0_ym1_1_1392649169696_2661" style="margin-bottom: 0in;">
<b>PART-A</b></div>
<div id="yui_3_13_0_ym1_1_1392649169696_2662" style="margin-bottom: 0in;">
<b>1 </b>a. i) The law
which describes the blackbody radiation completely is
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2663" style="margin-bottom: 0in;">
A) Planck’s law<sub>
</sub>B) Stefan’s law C) Wien’s law D) Rayleigh-Jean’s
law<sub> </sub>
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2664" style="margin-bottom: 0in;">
ii) Photoelectric
effect establishes
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2665" style="margin-bottom: 0in;">
A) wave nature of light
B) particle nature of light C) dual nature of light D)
None of these<sub> </sub>
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2666" style="margin-bottom: 0in;">
ii) Experimental
evidence for the existence of matter waves was first provided by</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2667" style="margin-bottom: 0in;">
A) de-Broglie B) Davisson and Germer C) G.P.Thomson
D) Max Planck</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2718" style="margin-bottom: 0in;">
iv) If the group
velocity of the de-Broglie waves associated with a particle is 3×10<sup>4</sup>
m/sec, the velocity of the particle is
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2719" style="margin-bottom: 0in;">
A) 3×10<sup>8</sup>
m/s B) 3×10<sup>12</sup> m/s C) 3×10<sup>4</sup> m/s D) None
of these </div>
<div id="yui_3_13_0_ym1_1_1392649169696_2720" style="margin-bottom: 0in;">
b. Describe Davisson and
Germer experiment for confirmation of de-Broglie hypothesis.
(06marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2721" style="margin-bottom: 0in;">
c. What is Planck’s radiation law?
Show how Wien’s law and Rayleigh-Jean’s law can be
derived from it. (06 Marks)
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2722" style="margin-bottom: 0in;">
d<b>.</b> Find the de-Broglie
wavelength of particle of mass 0.65 MeV/C<sup>2 </sup>has a kinetic
energy 80 eV. (04 marks)</div>
<div style="margin-bottom: 0in;">
<b>2</b> a. i) The probability of
finding the particle within an element of volume d<span lang="el-GR">τ</span>
is</div>
<ol id="yui_3_13_0_ym1_1_1392649169696_2725" type="A">
<li id="yui_3_13_0_ym1_1_1392649169696_2724"><div id="yui_3_13_0_ym1_1_1392649169696_2723" style="margin-bottom: 0in;">
0 B) ∫│<span lang="el-GR">ψ</span><sup>2</sup>│d<span lang="el-GR">τ</span>
C) <span lang="el-GR">∫│ψ│</span>d<span lang="el-GR">τ</span>
D) <span lang="el-GR">∫│ψ</span><sup>*</sup><span lang="el-GR">│</span>d<span lang="el-GR">τ</span>
</div>
</li>
</ol>
<div style="margin-bottom: 0in;">
ii) The product of
uncertainty between angular momentum and angular displacement is
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2726" style="margin-bottom: 0in;">
A) ≥ ħ/2p B) ≥ ħ
/4p C) ≤ ħ /4p D) ≥ ħ /2</div>
<div style="margin-bottom: 0in;">
iii) For a particle which is not
bound to any system and is free, the energy eigen value is,</div>
<div style="margin-bottom: 0in;">
A) zero B) finite but not
quantized C) infinity D) finite but quantized</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2727" style="margin-bottom: 0in;">
iv) The wavefunction is
acceptable if it is</div>
<div style="margin-bottom: 0in;">
A) Finite
everywhere B) Continuous
everywhere </div>
<div style="margin-bottom: 0in;">
C) Single valued
everywhere D) All of these
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2728" style="margin-bottom: 0in;">
(04 Marks)</div>
<div style="margin-bottom: 0in;">
b. Solve the
Schrödinger’s wave equation for allowed energy values in case of a
particle in a potential box. (06 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2729" style="margin-bottom: 0in;">
c. State and explain
Heisenberg’s uncertainty principle and prove that nuclei do not
contain electron. (05 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2732" style="margin-bottom: 0in;">
<span id="yui_3_13_0_ym1_1_1392649169696_2731" style="font-family: Times New Roman, serif;"><span id="yui_3_13_0_ym1_1_1392649169696_2730" style="font-size: small;">d.
A quantum particle confined to one dimensional box of width ‘a’
is in its first excited state. What is the probability of finding the
particle over an interval of ( marked symmetrically at the centre of
box.
(05 Marks)</span></span></div>
<div id="yui_3_13_0_ym1_1_1392649169696_2733" style="margin-bottom: 0in;">
<b>3</b> a. i) The fermi
factor for E = E<sub>F</sub> at T > 0K is</div>
<div style="margin-bottom: 0in;">
A) 1 B) ½ C)
0 D) 2</div>
<div style="margin-bottom: 0in;">
ii) Mobility of
electron is
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2735" style="margin-bottom: 0in;">
A) Reciprocal of
conductivity B) Flow of electrons per unit</div>
<div style="margin-bottom: 0in;">
C) Reciprocal of
resistivity D) Average electron drift velocity per unit electric
field</div>
<div style="margin-bottom: 0in;">
iii) According to
quantum free electron theory, the energy level in a metal are</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2736" style="margin-bottom: 0in;">
A) Continuous
B) Discrete C) Overlapping D) None</div>
<div style="margin-bottom: 0in;">
iv) For ordinary
metals, resistivity versus temperature curve at T = 0K</div>
<div style="margin-bottom: 0in;">
A) has a positive
intercept B) has a negative intercept
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2737" style="margin-bottom: 0in;">
C) goes through the
origin D) none of these (04 Marks)</div>
<div style="margin-bottom: 0in;">
<b>b. </b>Using the free
electron theory, derive an expression for electrical conductivity in
metals.
<b> </b>(06 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2738" style="margin-bottom: 0in;">
c. Discuss the various
drawbacks of classical free electron theory of metals. What are the
assuptions made in Quantum theory to overcome the same? (06 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2740" style="margin-bottom: 0in;">
d. Calculate the
probability of an electron occupying an energy level 0.02 eV above
the Fermi level and 0.02 eV below the Fermi level at 200 K. (04
marks)
</div>
<div style="margin-bottom: 0in;">
<b>4</b> a. i) Electronic
polarisation</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2741" style="margin-bottom: 0in;">
A) Independent of
temperature B) Increases with temperature</div>
<div style="margin-bottom: 0in;">
C) Decreases with
temperature D) None of these</div>
<div style="margin-bottom: 0in;">
ii) Which of the
following is a piezoelectric material?</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2742" style="margin-bottom: 0in;">
A) lead B) mica C)
iron D) quartz</div>
<div style="margin-bottom: 0in;">
iii) Above Curie
temperature, ferromagnetic substance becomes</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2743" style="margin-bottom: 0in;">
A) antiferromagnetic B)
strongly ferromagnetic C) paramagnetic D) diamagnetic</div>
<div style="margin-bottom: 0in;">
iv) If two charges q
are separated by a distance L, dipole moment of the system is</div>
<div style="margin-bottom: 0in;">
A) q/L B) L/q C) qL D)
q/L<sup>2</sup> (04 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2744" style="margin-bottom: 0in;">
b. Derive the expression
for internal field in solids. (06 Marks)</div>
<div style="margin-bottom: 0in;">
c. Derive
Claussius-Mossoti equation. (06 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2745" style="margin-bottom: 0in;">
d. Sulphur is elemental
solid dielectric whose dielectric constant is 3.4. Calculate
electronic polarizability if its density is 2.07× 10<sup>3</sup>
kg/m<sup>3</sup> and atomic weight is 32.07. (04 Marks)</div>
<div style="margin-bottom: 0in;">
<br />
</div>
<div align="CENTER" style="margin-bottom: 0in;">
<b>PART-B</b></div>
<div id="yui_3_13_0_ym1_1_1392649169696_2746" style="margin-bottom: 0in;">
<b>5</b> a. The pumping
action in diode laser is by,</div>
<ol type="A">
<li><div style="margin-bottom: 0in;">
Optical pumping B)
Electric discharge C) Reverse bias D) Forward bias
</div>
</li>
</ol>
<div style="margin-bottom: 0in;">
ii) The life time of
an atom in a metastable state is of the order of
</div>
<ol id="yui_3_13_0_ym1_1_1392649169696_2749" type="A">
<li id="yui_3_13_0_ym1_1_1392649169696_2748"><div id="yui_3_13_0_ym1_1_1392649169696_2747" style="margin-bottom: 0in;">
A few seconds B)
unlimited time C) a nanosecond D) few milliseconds</div>
</li>
</ol>
<div id="yui_3_13_0_ym1_1_1392649169696_2750" style="margin-bottom: 0in;">
iii) Emission of a photon by an
excited atom due to interaction of external energy is called</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2751" style="margin-bottom: 0in;">
A) Spontaneous
emission B) Stimulated emission C) Induced absorption
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2752" style="margin-bottom: 0in;">
D) Light
amplification</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2753" style="margin-bottom: 0in;">
iv) The required
condition to achieve laser action in a system is</div>
<div style="margin-bottom: 0in;">
A) state of
population inversion B) existence of metastable
state</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2754" style="margin-bottom: 0in;">
C) a resonant
cavity D) all the three</div>
<div style="margin-bottom: 0in;">
b. What is holography? Explain
principle of hologram recording using laser. (05Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2755" style="margin-bottom: 0in;">
c. Explain the
construction and working of He-Ne laser, with the help of suitable
diagrams.</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2760" style="margin-bottom: 0in;">
(07 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2756" style="margin-bottom: 0in;">
d. The average output
power of laser source emitting a laser beam of wavelength 633nm is 5
mW. Find the number of photons emitted per second by the laser
source. (04 Marks) </div>
<div id="yui_3_13_0_ym1_1_1392649169696_2757" style="margin-bottom: 0in;">
<b>6</b> a. i) According to Meissner
effect, material in superconducting state is,</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2761" style="margin-bottom: 0in;">
A) Paramagnetic B)diamagnetic C)
ferromagnetic D) anti-ferromagnetic </div>
<div id="yui_3_13_0_ym1_1_1392649169696_2758" style="margin-bottom: 0in;">
ii) Attenuation in optic fiber is
due to
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2762" style="margin-bottom: 0in;">
A) absorption B) scattering
C) radiation loss D) all the above</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2763" style="margin-bottom: 0in;">
iii) The conductivity of a
superconductor is</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2764" style="margin-bottom: 0in;">
A) infinite B) Zero C) finite
D) none of these</div>
<div style="margin-bottom: 0in;">
iv)<b> </b>In a single
mode fiber, the diameter of the core is nearly equal to
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2765" style="margin-bottom: 0in;">
A) 125 m
B) 100 m C) 50 m D) 10 m
<b>(</b>04 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2766" style="margin-bottom: 0in;">
b. Discuss BCS theory of
superconductor. Explain SQUID. (07 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2767" style="margin-bottom: 0in;">
c. Describe the point to
point communication system, with the help of block diagram (05 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2768" style="margin-bottom: 0in;">
d.<b> </b>The refractive
indices of core and cladding are 1.50 and 1.48 respectively in an
optical fiber. Find the numerical aperture and angle of acceptance.
<b> </b>(04 Marks)</div>
<div style="margin-bottom: 0in;">
<b>7</b> a. i) Packing
factor of diamond crystal is
</div>
<ol type="A">
<li><div style="margin-bottom: 0in;">
34% B) 52% C) 68% D)
74%</div>
</li>
</ol>
<div id="yui_3_13_0_ym1_1_1392649169696_2769" style="margin-bottom: 0in;">
ii) In Bragg’s
spectrometer, for every rotation <span lang="el-GR">θ</span> of the
turn table, the detector turns by an angle,
</div>
<div style="margin-bottom: 0in;">
A)<span lang="el-GR">θ
</span> B) 4<span lang="el-GR">θ</span> C) 2<span lang="el-GR">θ</span> D)
<span lang="el-GR">θ</span>/2
</div>
<div style="margin-bottom: 0in;">
iii) The miller
indices of the plane parallel to the x and y axes are
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2770" style="margin-bottom: 0in;">
A) (100) B) (010) C)
(001) D) (111)</div>
<div style="margin-bottom: 0in;">
iv<b>) </b>Which one
of the following Bravais lattices is not found in cubic crystal?</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2771" style="margin-bottom: 0in;">
A) Simple cubic B) Face
centered C) Body centered D) Base centered (04 Marks)</div>
<div style="margin-bottom: 0in;">
b. Derive expression for
interplanar spacing in terms of Miller indices (06 Marks)
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2772" style="margin-bottom: 0in;">
c. Explain how Bragg’s
spectrometer is used for determination of interplanar spacing in a
crystal. (04Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2773" style="margin-bottom: 0in;">
d. Calculate the glancing
angle of the (110) plane of a simple cubic crystal (a=2.814Å)
corresponding to second order diffraction maximum for the x-rays of
wavelength 0.710 Å. (04 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2774" style="margin-bottom: 0in;">
8 a. i) The minimum size
of the matter below which the properties become size dependent is
called</div>
<div style="margin-bottom: 0in;">
A) Pico size B) Nano
size C) Micro size D) Macro size</div>
<div style="margin-bottom: 0in;">
ii) A constant testing
of product without causing any damage is called</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2775" style="margin-bottom: 0in;">
A) minute testing B)
destructive testing C) non-destructive testing D) random
testing</div>
<div style="margin-bottom: 0in;">
iii) The elastic
behavior of a liquid is characterized by its
</div>
<div style="margin-bottom: 0in;">
A) Youngs modulus B)
Modulus of rigidity C) Bulk modulus D) Poisson’s ratio</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2776" style="margin-bottom: 0in;">
iv) The state of
matter around the nanosize is known as
</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2789" style="margin-bottom: 0in;">
A) Liquid state B) Plasma
state</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2777" style="margin-bottom: 0in;">
C) Mesoscopic state D)
Solid state (04 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2788" style="margin-bottom: 0in;">
b. Explain density of
states for various quantum structures. (06 Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2778" style="margin-bottom: 0in;">
c. What is NDT? Describe
the NDT method of detection of flaws in solid using ultrasound.
(06Marks)</div>
<div id="yui_3_13_0_ym1_1_1392649169696_2779" style="margin-bottom: 0in;">
d. Explain two methods of
preparation of Nanomaterials in brief. (04 Marks)</div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com5tag:blogger.com,1999:blog-4803935933670175751.post-71060550512312620582013-12-25T20:43:00.003-08:002013-12-25T20:43:40.909-08:00Answer key for First/Second Semester B.E.Degree examination Dec2013/Jan2014 Enginnering Physics VTU exam<div dir="ltr" style="text-align: left;" trbidi="on">
<link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><style>
<!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:0 0 0 0 0 0 0 0 0 0;
mso-font-charset:1;
mso-generic-font-family:roman;
mso-font-format:other;
mso-font-pitch:variable;
mso-font-signature:0 0 0 0 0 0;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;
mso-font-charset:0;
mso-generic-font-family:swiss;
mso-font-pitch:variable;
mso-font-signature:-1610611985 1073750139 0 0 159 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
margin-top:0in;
margin-right:0in;
margin-bottom:10.0pt;
margin-left:0in;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:ML;}
.MsoChpDefault
{mso-style-type:export-only;
mso-default-props:yes;
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;}
.MsoPapDefault
{mso-style-type:export-only;
margin-bottom:10.0pt;
line-height:115%;}
@page Section1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.Section1
{page:Section1;}
-->
</style><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin-top:0in;
mso-para-margin-right:0in;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0in;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;}
</style>
<![endif]-->
<br />
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>1 a i) B<span> </span>ii)
B<span> </span>iii) A<span> </span>iv) D</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>d. 2.42Å</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>2 a i) A<span> </span>ii)
C<span> </span>iii) D<span> </span>iv) D</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>d. 104.67eV 1.2 Å<o:p></o:p></b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>3 a i) B<span> </span>ii)
B<span> </span>iii) C<span> </span>iv) D</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>d. 1261 K</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>4 a i) B<span> </span>ii)
B<span> </span>iii) B<span> </span>iv) A</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>d. 5.855</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>5a i) B<span> </span>ii)
A<span> </span>iii) A<span> </span>iv) C</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>d. 694 nm</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>6 a i) A<span> </span>ii)
B<span> </span>iii) B<span> </span>iv) C</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>d. 22<sup>0<o:p></o:p></sup></b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>7 a i) B<span> </span>ii)
D<span> </span>iii) C<span> </span>iv) B</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>d. 0.825Å</b></div>
<div class="MsoNormal" style="font-family: Times,"Times New Roman",serif;">
<b>8 a i) D<span> </span>ii)
C<span> </span>iii) C<span> </span>iv) C</b></div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com1tag:blogger.com,1999:blog-4803935933670175751.post-17223086466109825852013-08-17T05:43:00.000-07:002013-08-17T05:50:56.508-07:00First/Second Semester B.E. Degree Examination, December 2013 Engineering Physics-Model question paper<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<table align="left" border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none; margin-left: 6.75pt; margin-right: 6.75pt;">
<tbody>
<tr>
<td style="border: 1pt solid black; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 115%;">USN 10PHY12/22
<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 115%;">First/Second Semester B.E. Degree Examination, December 2013<o:p></o:p></span></div>
<div>
</div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 16pt; line-height: 115%;">Engineering Physics<o:p></o:p></span></div>
<div style="text-align: center;">
</div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-family: "Times New Roman","serif";">Time: 3 hrs. Max.
Marks:100<o:p></o:p></span></div>
<div style="text-align: center;">
</div>
<div class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">Note: 1. Answer any FIVE full questions,
choosing atleast two from each part.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">
2. Answer all objective type questions only in OMR sheet page 5 of the
answer booklet.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">
3. Answer to objective type questions on sheets other than OMR will not
be valued.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">
4. Physical constants: h = 6.626×10<sup>-34</sup> Js, c = 3×10<sup>8</sup>
m/s, m<sub>e</sub> = 9.1×10<sup>-31</sup> kg, <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> k
= 1.38×10<sup>-23</sup> J/K, ε<sub>0</sub> = 8.854×10<sup>-12</sup> F/m<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: center;">
<b><span style="font-family: "Times New Roman","serif";">PART-A</span></b><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">1 a. i)
</span>The law which failed to account
for shorter wavelength region of blackbody radiation spectrum is <o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
A) Wien’s law B) Rayleigh-Jean’s
law C) Planck’s law D) Maxwell’s law<span style="font-family: "Times New Roman","serif";"> <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> ii) </span>The group velocity of the particle is 3×10<sup>6</sup>
m/s, whose phase velocity is <o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
A) 6.06×10<sup>6</sup> m/s B)
3×10<sup>10</sup> m/s C) 3×10<sup>6</sup>
m/s D) 1.5×10<sup>10</sup> m/s <span style="font-family: "Times New Roman","serif";"><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">
ii) </span>Photoelectric effect
establishes <o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
A) wave nature of light B)
particle nature of light C) dual nature
of light D) None of these<sub> </sub><o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">
iv) </span>The Compton wavelength is given by</div>
<div class="MsoNormal" style="text-align: justify;">
A) h/m<sub>0</sub>C<sup>2</sup> B) h<sup>2</sup>/m<sub>0</sub>C<sup>2</sup>
C) h/m<sub>0</sub>C D) h<sup>2</sup>/2m<sub>0</sub>C</div>
<div class="MsoNormal" style="margin: 0in -0.1in 10pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> (04
marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> b. </span>Derive de-Broglie wavelength using group
velocity.<span style="font-family: "Times New Roman","serif";"> (05marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> c. </span>Describe Davisson and Germer experiment for
confirmation of de-Broglie hypothesis<span style="font-family: "Times New Roman","serif";"> (07 Marks)
<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> d. </span>Find the de-Broglie wavelength of particle of
mass 0.65 MeV/C<sup>2 </sup>has a kinetic energy 80 eV. <span style="font-family: "Times New Roman","serif";">(04 marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">2
a. i) </span>According to Max Born approximation, <span style="font-family: Symbol;">|</span><span style="font-family: Symbol;">y</span><span style="font-family: Symbol;">|</span><sup>2</sup> represents </div>
<div class="MsoNormal" style="text-align: justify;">
A) Energy density
B) Particle density C)
Probability density D) Charge density</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> ii)
The product of uncertainty between angular momentum and angular displacement is
<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">A) ≥ ħ/2</span><span style="font-family: Symbol;">p</span><span style="font-family: "Times New Roman","serif";"> B) ≥ ħ /4</span><span style="font-family: Symbol;">p</span><span style="font-family: "Times New Roman","serif";"> C) ≤ ħ /4</span><span style="font-family: Symbol;">p</span><span style="font-family: "Times New Roman","serif";">
D) ≥ ħ /2<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">
iii) </span>The ground state energy of an electron in an one dimensional
infinite potential well of width 2Å is 16 eV. Its energy in third excited state
is</div>
<div class="MsoNormal" style="text-align: justify;">
A) 32 eV B) 64 eV C) 144 eV D) 256 eV <span style="font-family: "Times New Roman","serif";"> <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iv)
The wavefunction is acceptable if it is<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> A) Finite everywhere B)
Continuous everywhere <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">
C) Single valued everywhere D) All of
these <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> (04
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> b. </span>State
and explain Heisenberg’s uncertainty principle and prove that nuclei do not
contain electron. <span style="font-family: "Times New Roman","serif";"> (06
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">c. What is a wave function? Explain the
properties of a wave function. (04
Marks)<o:p></o:p></span></div>
<div class="MsoNoSpacing">
d. A
quantum particle confined to one dimensional box of width ‘a’ is in its first
excited state. What is the probability of finding the particle over an interval
of (<!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
style='font-family:"Cambria Math","serif"'><m:r> </m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>a</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>2</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>
)</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 7pt;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock><v:shape id="_x0000_i1025" style="height: 18.75pt; width: 15.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:%5CDOCUME%7E1%5CADMINI%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image001.png">
</v:imagedata></v:shape></v:path></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas></v:stroke></v:shapetype></span><!--[endif]--> marked
symmetrically at the centre of box. (06
Marks)<o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">3 a. i) The classical value of molar specific
heat of a conductor is<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">A) <sup>3</sup>/<sub>2</sub> R B) ½ R C) 3R D)
<sup>5</sup>/<sub>2</sub> R<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="SV" style="font-family: "Times New Roman","serif";"> </span><span style="font-family: "Times New Roman","serif";">ii) </span>For
ordinary metals, the resistivity versus temperature curve at T = 0, </div>
<div class="MsoNormal" style="text-align: justify;">
A) has a positive intercept B)
has a negative intercept </div>
<div class="MsoNormal" style="text-align: justify;">
C) goes through the origin D)
none of these</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">
iii) According to quantum free electron theory, the energy level in a
metal are<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">
A) Continuous B) Discrete C)
Overlapping D) None<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="IT" style="font-family: "Times New Roman","serif";"> </span><span style="font-family: "Times New Roman","serif";">iv) </span>The fermi
factor for E = E<sub>F</sub> at T > 0K is</div>
<div class="MsoNormal" style="text-align: justify;">
A) 1 B) ½ C) 0 D)
2</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> (04
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">b. </span>Obtain the expression for electrical
conductivity on the basis of free electron theory of metals. <span style="font-family: "Times New Roman","serif";"> (06
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">c. </span>Explain how quantum free electron
theory succeeds in overcoming the drawbacks of classical free electron theory.<span style="font-family: "Times New Roman","serif";"> (06 marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">d. </span>Calculate the probability of an
electron occupying an energy level 0.02 eV above the Fermi level and 0.02 eV
below the Fermi level at 200 K.<span style="font-family: "Times New Roman","serif";"> (04
marks) <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">4 a. i) In the inverse piezo electric effect,<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">A) Ultrasonic waves are produced B) electromagnetic
waves are produced<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">C) microwaves are produced D) none of the above<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> ii) If
two electric charges are q, separated by a distance L, the dipole moment of the
system is<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> A)
q/L B) L/q C) qL D)
q/L<sup>2</sup><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iii) The
relation between B, M and H is <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> A)
H = </span><span style="font-family: Symbol;">m</span><sub><span style="font-family: "Times New Roman","serif";">0</span></sub><span style="font-family: "Times New Roman","serif";">(M+B) B) M = </span><span style="font-family: Symbol;">m</span><sub><span style="font-family: "Times New Roman","serif";">0</span></sub><span style="font-family: "Times New Roman","serif";">(H+B) C) B = </span><span style="font-family: Symbol;">m</span><sub><span style="font-family: "Times New Roman","serif";">0</span></sub><span style="font-family: "Times New Roman","serif";">(H+M) D) None of these<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iv) The
relative permeability for diamagnetic materials is <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> A) Slightly
greater than one B) Zero C) less than one D) very much greater than one (04
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">b. Derive the expression for internal field in
solids. (08
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">c. Distinguish between hard and soft magnetic
materials. (04
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">d. The atomic weight and density of sulphur
are 32 and 2.08 g/cc respectively. The electronic polarizability of the atom is
3.28×10<sup>-40</sup> F.m<sup>2</sup>. If sulphur solid has cubic symmetry,
what will be its relative permittivity? (04
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: "Times New Roman","serif";"><b>PART-B</b><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">5 a. i) </span>The emission of photon without
aided by any external agency is called </div>
<div class="MsoNormal" style="text-align: justify;">
A) Light amplification B) Induced absorption C) Stimulated emission D) Spontaneous emission<span style="font-family: "Times New Roman","serif";"> <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">ii) </span>The life time of an atom at the
ordinary excited state is of the order of</div>
<div class="MsoNormal" style="text-align: justify;">
A) few milli second B) few nano second C) few micro second D) Unlimited</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iii) </span>Pumping
technique used in He-Ne gas laser is </div>
<div class="MsoNormal" style="text-align: justify;">
A) Forward bias B)
Optical pumping C) Electrical discharge D) High injection current
</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iv) </span>From
a broken hologram which is 10% of the original, if reconstruction of image is
being done, then</div>
<div class="MsoNormal" style="text-align: justify;">
A)
Only 10% of information of the object can be obtained</div>
<div class="MsoNormal" style="text-align: justify;">
B) Complete information of the
object is obtained</div>
<div class="MsoNormal" style="text-align: justify;">
C) No information of the object can be
obtained D) None of these<span style="font-family: "Times New Roman","serif";"> (04 Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">b. </span>Obtain an expression for energy
density of radiation under equilibrium condition in terms of Einstein
coefficient.<span style="font-family: "Times New Roman","serif";"> (06Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">c. </span>Describe the recording and
reconstruction processes in holography, with the help of suitable diagrams.<span style="font-family: "Times New Roman","serif";"> (06
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">d. </span>Calculate on the basis of Einstein’s
theory the number of photons emitted per second by He-Ne laser source emitting
light of wavelength 6328Å with an optical power 10 mW.<span style="font-family: "Times New Roman","serif";"> (04 Marks) <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">6 a. i) </span>The critical temperature of
mercury is </div>
<div class="MsoNormal" style="text-align: justify;">
A) 4.2 K B)
6.2 K C) 7.8 K D) 20 K</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> ii) </span>Attenuation
in the optical fiber causes due to</div>
<div class="MsoNormal" style="text-align: justify;">
A) Absorption B) Scattering C) Dispersion D) All the three</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iii) </span>Numerical
aperture of an optical fiber depends on </div>
<div class="MsoNormal" style="text-align: justify;">
A) Diameter of the fiber B) Acceptance angle C) Critical angle D) <span style="font-family: Symbol;">h</span><sub>core</sub>
material</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iv)
Superconductors are <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">Diamagnetic B) paramagnetic C) ferromagnetic
D) antiferromagnetic (04
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">b. Discuss BCS theory of superconductor.
Explain SQUID. (07
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">c. </span>Describe the point to point
communication system, with the help of block diagram. (<span style="font-family: "Times New Roman","serif";">05 Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">d. </span>A fiber 500m long has an input power
of 8.6 mw and output power 7.5 mw. What is the loss specification in cable? <span style="font-family: "Times New Roman","serif";"> (04 Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif";">7 a. i) </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">For every rotation by angle </span><span style="font-family: Symbol; font-size: 12pt;">q</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> in Bragg’s spectrometer, detector
turns by an angle<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">A) </span><span style="font-family: Symbol; font-size: 12pt;">q</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> B)3</span><span style="font-family: Symbol; font-size: 12pt;">q</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> C) 4</span><span style="font-family: Symbol; font-size: 12pt;">q</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> D) 2</span><span style="font-family: Symbol; font-size: 12pt;">q</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> ii) </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">APf of diamond crystal structure is <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">A) 0.68 B) 0.74 C) 0.52 D) 0.34<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iii)
</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">In a simple cubic
lattice the ratio d<sub>100</sub>:d<sub>110</sub>:d<sub>111</sub> is<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">A) 6:3:1 B) √3:√6:1 C) 6:3:√2 D) √6:√3:√2<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iv) </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">The miller indices of the plane
parallel to the x and y axes are <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">A) (100) B) (010) C) (001) D) (111)</span><span style="font-family: "Times New Roman","serif";"> (04 Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">b. </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Discuss the Bravais lattice and any
five crystal systems with the help of illustrations.</span><span style="font-family: "Times New Roman","serif";"> (07Marks) <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">c. </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">How do you find Miller indices of a
given plane</span><span style="font-family: "Times New Roman","serif";">. (05Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">d. </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The minimum order of Bragg’s reflection
occurs at an angle 20</span><sup><span style="font-family: "Times New Roman","serif"; font-size: 10pt; line-height: 115%;">0</span></sup><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> in the plane [212]. Find the
wavelength of X-ray if lattice constant is 3.615 Å. </span><span style="font-family: "Times New Roman","serif";"> (04 Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">8 a. i) Testing of a product without causing
any damage is called<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">A) minute testing B) destructive testing
C) non-destructive testing D) random testing<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> ii) The
state of matter around the nanosize is known as <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">A) Liquid state B) Plasma state C) Mesoscopic state D)
Solid state <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iii) In
a carbon nanotubes, the bond between the carbon atoms is <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">A) metallic B)
ionic C) hydrogen D) covalent<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> iv) A
bulk material (three dimensions) reduced in two directions is known as<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">A) Quantum dot B)
Quantum particle C) Film D) Quantum wire (04 Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">b. What are Nanomaterials? Explain carbon
nanotubes and their physical properties. Mention few applications of carbon
nanotubes. (08
Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">c. Explain the principle and method of
nondestructive method of testing of material using ultrasonics. (08 Marks)<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h2>
</h2>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-89773448118986124332013-06-20T06:15:00.004-07:002013-06-20T06:18:30.773-07:00VTU June 18 2013 Engineering physics (10 PHY22) Examination Answer key<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="text-align: justify;"><span style="font-family: 'Times New Roman', serif; line-height: 115%;">1(a) i) A</span><span style="font-family: 'Times New Roman', serif; line-height: 115%;"> </span><span style="font-family: 'Times New Roman', serif; line-height: 115%;">ii) B</span><span style="font-family: 'Times New Roman', serif; line-height: 115%;"> </span><span style="font-family: 'Times New Roman', serif; line-height: 115%;">iii) C</span><span style="font-family: 'Times New Roman', serif; line-height: 115%;"> </span><span style="font-family: 'Times New Roman', serif; line-height: 115%;">iv) C</span></b><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>2(a) i) A ii) B iii) C iv) D<o:p></o:p></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>3(a) i) A ii) B iii) C iv) C<o:p></o:p></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>4(a) i) A ii) B iii) C iv) A<o:p></o:p></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>5(a) i) D ii) C iii) B iv) A<o:p></o:p></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>6(a) i) D ii) C iii) B iv) A<o:p></o:p></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>7(a) i) D ii) C iii) B iv) A<o:p></o:p></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>8(a) i) D ii) C iii) B/C iv) A<o:p></o:p></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: 'Times New Roman', serif; line-height: 115%;">Problems<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>1(d) 10<sup>-9</sup> m<o:p></o:p></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>2(d) 8×10<sup>-9</sup>
s<o:p></o:p></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>6(d) 22<sup>0</sup></b><span style="font-size: small;"><o:p></o:p></span></span></div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-87300298397290244592013-06-20T06:14:00.002-07:002013-06-20T06:14:41.136-07:00Part B Unit 6 Superconductivity some extra points<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Supercurrent in
Josephson junction<o:p></o:p></span></b></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">If
α<sub>1 </sub>and α<sub>2</sub> are the phases of two superconductors in a
Josephson effect experimental setup, supercurrent in the junction is given by,<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">I<sub>s</sub>
= I<sub>c</sub> sin (α<sub>2 - </sub>α<sub>1</sub>)<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Here
I<sub>c </sub>represent the critical current which is the maximum current
across the junction under zero voltage conditions. <o:p></o:p></span></div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-1812751735864596822013-05-07T05:49:00.001-07:002013-05-07T05:49:07.419-07:00Unit 1 Modern Physics-Some more important points<div dir="ltr" style="text-align: left;" trbidi="on">
<!--[if !mso]>
<style>
v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style>
<![endif]--><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin-top:0in;
mso-para-margin-right:0in;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0in;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;}
</style>
<![endif]--><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1027"/>
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1"/>
<o:rules v:ext="edit">
<o:r id="V:Rule1" type="connector" idref="#_x0000_s1026"/>
</o:rules>
</o:shapelayout></xml><![endif]-->
<br />
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Einstein’s theory of
photoelectric effect was verified in the year 1916 by <b>Millikan</b>. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="height: 2px; left: 0px; margin-left: 45px; margin-top: 32px; mso-ignore: vglayout; position: absolute; width: 45px; z-index: 251658240;"></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">de-Broglie wavelength
of a particle at a temperature T is given by</span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> λ = h/(3mkT)<sup>1/2</sup></span></b></div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-36704276690417656082013-03-06T04:50:00.001-08:002013-03-06T04:51:48.138-08:00First/Second Semester B.E. Degree Examination, June 2013 Engineering Physics-Model question paper<div dir="ltr" style="text-align: left;" trbidi="on">
<!--[if gte mso 9]><xml>
<o:OfficeDocumentSettings>
<o:RelyOnVML/>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:10.0pt;
font-family:"Calibri","sans-serif";}
</style>
<![endif]-->
<br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: 14.0pt;">USN<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 5;"> </span><span style="mso-tab-count: 1;"> </span>10PHY12/22<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 14.0pt;">First/Second Semester B.E. Degree Examination, June
2013</span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 16.0pt;">Engineering Physics</span></b></div>
<div align="center" class="MsoNormal" style="text-align: center;">
Time: 3 hrs.<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 9;"> </span>Max.
Marks:100</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Note: 1. Answer any FIVE full
questions, choosing atleast two from each part.</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>2. Answer all objective type
questions only in OMR sheet page 5 of the answer booklet.</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>3. Answer to objective type questions
on sheets other than OMR will not be valued.</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>4. Physical constants: h = 6.626×10<sup>-34</sup>
Js, c = 3×10<sup>8</sup> m/s, m<sub>e</sub> = 9.1×10<sup>-31</sup> kg, </div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>k
= 1.38×10<sup>-23</sup> J/K, ε<sub>0</sub> = 8.854×10<sup>-12</sup> F/m</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b style="mso-bidi-font-weight: normal;">PART-A</b><span style="font-size: 14.0pt;"></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">1 </b>a. <span style="mso-spacerun: yes;"> </span>i) <span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;">K<sub>e</sub>,K<sub>p</sub>
and K</span><sub><span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-char-type: symbol; mso-fareast-font-family: Calibri; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">a</span></span></sub><sub><span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;"> </span></sub><span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;">are
respective energy of an e<sup>-</sup>, a proton and </span><span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-char-type: symbol; mso-fareast-font-family: Calibri; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">a</span></span><span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;">particle of
same de-Broglie wavelength. Then,</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-fareast-font-family: Calibri;">A) <span style="mso-bidi-font-weight: bold;">K<sub>e</sub>>K<sub>p</sub>>K</span></span><sub><span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-fareast-font-family: Calibri; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">a</span></span></sub><sub><span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></sub><span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;">B) K<sub>e</sub>>K<sub>p</sub><k span=""><sub><span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-fareast-font-family: Calibri; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">a</span></span></sub><sub><span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></sub><span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>C) K<sub>e</sub><k sub="">p</k></span></k></span></div>
<k span=""><sub><span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-fareast-font-family: Calibri; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">a</span></span></sub><sub><span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;"> </span></sub><span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>D) K<sub>e</sub>=K<sub>p</sub>=
K</span><sub><span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-fareast-font-family: Calibri; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">a</span></span></sub><sub><span style="mso-bidi-font-weight: bold; mso-fareast-font-family: Calibri;"> </span></sub><span style="mso-fareast-font-family: Calibri;"></span></k>
<br />
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>ii) <span style="mso-fareast-font-family: Calibri;">Recoil electron in Compton scattering carry maximum kinetic energy
when x-ray scattering angle θ =</span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
<span style="mso-fareast-font-family: Calibri;"><span style="mso-spacerun: yes;">
</span>A) 180<sup>0<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span></sup>B) 0<sup>0<span style="mso-tab-count: 2;"> </span></sup> C) 90<sup>0<span style="mso-tab-count: 1;"> </span> <span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span></sup>D) 65<sup>0</sup><span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
<span style="mso-spacerun: yes;"> </span>ii) Experimental evidence for the
existence of matter waves was first provided by</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) de-Broglie<span style="mso-spacerun: yes;"> </span>B) Davisson and Germer<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;">
</span>C) G.P.Thomson<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>D)
Max Planck</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>iv) Green light incident on a surface
releases photoelectrons from the surface. If now blue light is incident on the
same surface, the velocity of electrons</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) increases <span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>B) decreases<span style="mso-tab-count: 1;"> </span>C) remains same<span style="mso-tab-count: 1;"> </span>D) becomes zero<span style="mso-tab-count: 1;"> </span>(04 marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;">
</span>b. Show that group velocity is equal to particle velocity.<span style="mso-tab-count: 1;"> </span>(05marks)</div>
<div class="MsoNormal">
<span style="mso-spacerun: yes;"> </span>c. What is Planck’s
radiation law?<span style="mso-spacerun: yes;"> </span>Show how Wien’s law and
Rayleigh-Jean’s law can be<span style="mso-spacerun: yes;">
</span>derived from it. (07 Marks) <b style="mso-bidi-font-weight: normal;"><span style="mso-spacerun: yes;"> </span></b></div>
<div class="MsoNormal">
<span style="mso-bidi-font-weight: bold;"><span style="mso-spacerun: yes;"> </span>d</span><b style="mso-bidi-font-weight: normal;">.</b>
An electron beam has a de-Broglie wavelength of 2 ×10<sup>-12</sup> m. Find the
kinetic energy, phase and group velocities of de-Broglie waves.<span style="mso-tab-count: 1;"> </span>(04 marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">2</b> a. i) If free electron exists in a nucleus, its energy value must
have a minimum energy of about</div>
<div class="MsoNormal" style="text-align: justify;">
A) 4 MeV<span style="mso-tab-count: 1;"> </span>B) 9.9 MeV<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>C) 9.9 KeV<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>D) 4 KeV</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>ii) The product of uncertainty between
angular momentum and angular displacement is </div>
<div class="MsoNormal" style="text-align: justify;">
A) ≥ ħ/2<span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">p</span></span><span style="mso-tab-count: 1;"> </span>B) ≥ ħ /4<span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">p</span></span><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>C) ≤ ħ /4<span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">p</span></span><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;">
</span>D) ≥ ħ /2</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>iii) If E<sub>1</sub> is the energy of the
lowest state of a one dimensional potential box of length ‘a’ and E<sub>2</sub>
is the energy of the lowest state when the length of the box is halved, then</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) E<sub>2</sub> = E<sub>1</sub> <span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>B) E<sub>2</sub> = 2E<sub>2</sub><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;">
</span>C) E<sub>2</sub> = E<sub>1</sub>/2<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>D) E<sub>2</sub> = 4E<sub>1</sub></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>iv) The wavefunction is acceptable if it is</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) Finite everywhere<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>B) Continuous everywhere<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>C) Single valued everywhere<span style="mso-spacerun: yes;"> </span>D) All of
these<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-tab-count: 2;"> </span><span style="mso-tab-count: 10;"> </span>(04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>b. Solve the Schrödinger’s wave equation for
allowed energy values in case of a particle in a potential box.<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 9;"> </span>(06
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. What is a wave function?
Explain the properties of a wave function.<span style="mso-tab-count: 2;"> </span><span style="mso-tab-count: 1;"> </span>(04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. An electron is bound in one
dimensional potential well of width 0.18 nm. Find the energy value in eV of the
second excited state.<span style="mso-tab-count: 2;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>(04
Marks)</div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">3</b> a. i) The
classical value of molar specific heat of a conductor is</div>
<div class="MsoNormal" style="text-align: justify;">
A) <sup>3</sup>/<sub>2</sub> R<span style="mso-tab-count: 1;"> </span>B) ½ R<span style="mso-tab-count: 2;"> </span>C) 3R<span style="mso-tab-count: 2;"> </span>D)
<sup>5</sup>/<sub>2</sub> R</div>
<div class="MsoNormal">
<span lang="SV" style="mso-ansi-language: SV;"><span style="mso-spacerun: yes;"> </span></span>ii) The Fermi energy of a metal at
absolute zero temperature is proportional to</div>
<div class="MsoNormal" style="text-align: justify;">
A) n<sup>1/3</sup><span style="mso-tab-count: 2;"> </span>B) n<sup>3/2</sup><span style="mso-tab-count: 2;"> </span>C) n<sup>2/3</sup><span style="mso-tab-count: 2;"> </span>D) n<sup>2<span style="mso-tab-count: 2;"> </span></sup></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>iii) According to quantum free electron
theory, the energy level in a metal are</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) Continuous<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>B)
Discrete<span style="mso-tab-count: 1;"> </span>C) Overlapping<span style="mso-tab-count: 1;"> </span>D) None</div>
<div class="MsoNormal">
<span lang="IT" style="mso-ansi-language: IT;"><span style="mso-spacerun: yes;"> </span></span>iv) Which one of the following is
correct for current density?</div>
<div class="MsoNormal" style="text-align: justify;">
A) J = neAv<sub>d</sub><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>B) J = neA/v<sub>d</sub><span style="mso-tab-count: 1;"> </span> C) J = nev<sub>d</sub><span style="mso-tab-count: 1;"> </span>D) J = 1/nev<sub>d<b> </b></sub></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-tab-count: 2;"> </span>(04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Define relaxation time and
discuss the dependence of electrical resistivity of metals with temperature and
impurity. <span style="mso-tab-count: 2;"> </span><span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 6;"> </span>(06
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. What is Fermi energy? Discuss
variation of Fermi factor with energy and temperature.<span style="mso-tab-count: 1;"> </span>(06 marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. A uniform silver wire has
resistivity 1.54×10<sup>-8</sup> ohm-m at room temperature for an electric
field 2 v/m.<span style="mso-spacerun: yes;"> </span>Calculate relaxation time
and drift velocity of the electrons, assuming that there are 5.8×10<sup>22</sup>
conduction electrons per cm<sup>3 </sup>of the material.<span style="mso-tab-count: 3;"> </span><span style="mso-tab-count: 4;"> </span>(04
marks) </div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">4</b> a. i) Orientation polarization occurs</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) In all dielectrics<span style="mso-spacerun: yes;"> </span>B) in polar dielectrics<span style="mso-tab-count: 1;"> </span>C) in non-polar dielectrics<span style="mso-tab-count: 1;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>D) in ionic dielectrics</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>ii) Ultrasonic waves can be produced by</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) Photoelectric effect method<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;">
</span>B) Inverse piezoelectric effect method </div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>C) Dielectric heating method<span style="mso-tab-count: 2;"> </span>D) High energy ball milling
method</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;">
</span>iii) The susceptibility of a diamagnetic material is</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) Infinity<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"> </span>B) positive<span style="mso-tab-count: 1;"> </span>C) zero<span style="mso-tab-count: 2;"> </span>D)
negative</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;">
</span>iv) In a magnetic material, the major contributor to magnetism is </div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) orbital motion of electrons<span style="mso-tab-count: 2;"> </span>B) nuclear spin</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>C) spin motion of electrons<span style="mso-tab-count: 2;"> </span>D) none of these<span style="mso-tab-count: 4;"> </span>(04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Derive the expression for
internal field in solids.<span style="mso-tab-count: 2;"> </span><span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"> </span>(08
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. What are soft magnetic
materials? Discuss their properties.<span style="mso-tab-count: 3;"> </span><span style="mso-tab-count: 1;"> </span>(04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. If NaCl crystal is subjected
to an electric field of 1000 V/m and the resulting polarization is 4.3×10<sup>-8</sup>
c/m<sup>2</sup>, calculate the static dielectric constant of NaCl.<span style="mso-tab-count: 2;"> </span><span style="mso-tab-count: 1;"> </span>(04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b style="mso-bidi-font-weight: normal;">PART-B</b></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">5</b> a. i) In
semiconductor laser, the material used is</div>
<div class="MsoNormal" style="text-align: justify;">
A) any semiconductor<span style="mso-tab-count: 3;"> </span>B) direct band gap
semiconductor</div>
<div class="MsoNormal" style="text-align: justify;">
C) indirect band gap
semiconductor<span style="mso-tab-count: 1;"> </span>D) not a semiconductor</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>ii) The number of modes of standing waves
in the resonant cavity of length 1m, if He-Ne laser operating at wavelength
6328 Å is</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
A) 3.16 × 10<sup>6<span style="mso-spacerun: yes;"> </span></sup><span style="mso-spacerun: yes;"> </span>B) 3.16 × 10<sup>10</sup><span style="mso-spacerun: yes;"> </span>C) 3.16 × 10<sup>8<span style="mso-spacerun: yes;"> </span></sup><span style="mso-spacerun: yes;"> </span>D) None of these</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;">
</span>iii) Emission of a photon by an excited atom due to interaction of
external energy is called</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) Spontaneous emission<span style="mso-spacerun: yes;"> </span>B) Stimulated emission <span style="mso-spacerun: yes;"> </span>C) Induced absorption<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>D) Light amplification</div>
<div class="MsoNormal">
<span style="mso-spacerun: yes;"> </span>iv) 3D image of an
object constructed by hologram is the process of</div>
<div class="MsoNormal" style="text-align: justify;">
A) Intensity recording <span style="mso-tab-count: 3;"> </span>B) Phase
information recording </div>
<div class="MsoNormal" style="text-align: justify;">
C) Both phase and intensity
information recording <span style="mso-tab-count: 1;"> </span>(04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Write a note on measurement of
pollutants in atmosphere using laser.<span style="mso-tab-count: 2;"> </span><span style="mso-tab-count: 1;"> </span>(06Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Explain the construction and
working of He-Ne laser, with the help of suitable diagrams.</div>
<div class="MsoNormal" style="text-align: justify;">
(05 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. The ratio of population of two
energy levels is 1.059×10<sup>-30</sup>. Find the wavelength of light emitted
at 300K.<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>(04 Marks)<span style="mso-tab-count: 1;"> </span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">6</b> a. i) Graded
index fiber can be</div>
<div class="MsoNormal" style="text-align: justify;">
A) single mode fiber only<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;">
</span>B) multimode fiber only</div>
<div class="MsoNormal" style="text-align: justify;">
C) both single mode and multimode
D) depends on the surrounding medium</div>
<div class="MsoNormal">
<span style="mso-spacerun: yes;"> </span>ii) The loss of
power by the optical signal through the optical fiber is mainly due to</div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="mso-list: Ignore;">A)<span style="font: 7.0pt "Times New Roman";">
</span></span>Rayleigh scattering<span style="mso-spacerun: yes;">
</span>B) Raman scattering<span style="mso-spacerun: yes;"> </span>C) Wien’s
scattering<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
D) All of these</div>
<div class="MsoNormal">
<span style="mso-spacerun: yes;"> </span>iii) When the
type-I superconducting material is placed in an external magnetic field, it</div>
<div class="MsoNormal" style="text-align: justify;">
A) attracts the magnetic
lines<span style="mso-spacerun: yes;"> </span>B) enhances the magnetic flux
lines </div>
<div class="MsoNormal" style="text-align: justify;">
C) repels the magnetic flux lines
</div>
<div class="MsoNormal" style="text-align: justify;">
D) does not influence magnetic
field of lines </div>
<div class="MsoNormal">
<span style="mso-spacerun: yes;"> </span>iv) Superconductors
are </div>
<div class="MsoNormal" style="margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="mso-list: Ignore;">A)<span style="font: 7.0pt "Times New Roman";">
</span></span>Diamagnetic B) paramagnetic C) ferromagnetic D)
antiferromagnetic<b> </b><span style="mso-tab-count: 1;"> </span>(04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Discuss BCS theory of
superconductor. Explain SQUID.<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 3;"> </span><span style="mso-tab-count: 1;"> </span>(07 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Derive the expression for
numerical aperture of an optical fiber.<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"> </span>(05 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. The angle of acceptance of an
optical fiber is 30<sup>0</sup> when kept in air. Find the angle of acceptance
when it is in a medium of refractive index 1.33.<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"> </span>(04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">7</b> a. i) Four types of Bravais lattices are observed in </div>
<div class="MsoNormal" style="text-align: justify;">
A) Rhomohedral system <span style="mso-tab-count: 2;"> </span><span style="mso-spacerun: yes;"> </span>B) Orthorhombic system</div>
<div class="MsoNormal" style="text-align: justify;">
C) Triclinic system<span style="mso-tab-count: 2;"> </span> D) Monoclinic system<b> </b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>ii) A plane intercepts at a, b/2, 2c in a
simple cubic unit cell. The miller indices of the plane are</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) (214)<span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>B) (241)<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>C)
(421)<span style="mso-tab-count: 1;"> </span>D) (124)</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>iii) The coordination number for a face
centered cubic lattice is</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>A) 12<span style="mso-tab-count: 2;"> </span>B)
8<span style="mso-tab-count: 2;"> </span>C) 6<span style="mso-tab-count: 2;"> </span>D) 26</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>iv) For every rotation by angle <span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">q</span></span> in
Bragg’s spectrometer, detector turns by an angle</div>
<div class="MsoNormal" style="text-align: justify;">
A) <span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">q</span></span> <span style="mso-tab-count: 2;"> </span>B)3<span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">q</span></span> <span style="mso-tab-count: 2;"> </span>C)
4<span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">q</span></span>
<span style="mso-tab-count: 2;"> </span>D) 2<span style="font-family: Symbol; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">q</span></span> <span style="mso-tab-count: 3;"> </span>(04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Define unit cell and primitive
cell. Describe crystal structure of diamond. <span style="mso-tab-count: 1;"> </span>(08
Marks) </div>
<div class="MsoNormal" style="text-align: justify;">
c. Derive Bragg’s law for X-ray
diffraction.<span style="mso-tab-count: 5;"> </span><span style="mso-tab-count: 2;"> </span>(04Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. Calculate the glancing angle
for incidence of X-rays of wavelength 0.58Å on the plane (132) of NaCl which
results in second order diffraction maxima taking the lattice as 3.81Å.<span style="mso-tab-count: 1;"> </span><span style="mso-tab-count: 1;"> </span>(04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">8</b> a. i) In a carbon nanotube, the bond between the carbon atoms is</div>
<div class="MsoNormal" style="text-align: justify;">
A) Metallic<span style="mso-tab-count: 1;"> </span>B) ionic<span style="mso-tab-count: 1;"> </span>C)
covalent<span style="mso-tab-count: 1;"> </span>D) hydrogen</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;">
</span>ii) A constant testing of product without causing any damage is called</div>
<div class="MsoNormal" style="text-align: justify;">
A) minute testing<span style="mso-spacerun: yes;"> </span>B) destructive testing<span style="mso-spacerun: yes;"> </span>C) non-destructive testing<span style="mso-spacerun: yes;"> </span>D) random testing</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;">
</span>iii) Ultrasonic waves can exist only as longitudinal waves in </div>
<div class="MsoNormal" style="text-align: justify;">
A) Solid<span style="mso-tab-count: 1;"> </span>B) Liquid<span style="mso-tab-count: 1;"> </span>C) Gases<span style="mso-tab-count: 1;"> </span>D) All the above</div>
<div class="MsoNormal" style="text-align: justify;">
<span style="mso-spacerun: yes;"> </span>iv) The state of matter around the nanosize
is known as </div>
<div class="MsoNormal" style="text-align: justify;">
A) Liquid state<span style="mso-tab-count: 1;"> </span>B) Plasma state</div>
<div class="MsoNormal" style="text-align: justify;">
C) Mesoscopic state<span style="mso-tab-count: 1;"> </span>D) Solid state<span style="mso-tab-count: 7;"> </span><span style="mso-tab-count: 1;"> </span>(04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Explain density of states for
various quantum structures.<span style="mso-tab-count: 4;"> </span><span style="mso-tab-count: 1;"> </span>(08 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Describe a method of measuring
velocity of ultrasonic waves in liquid. (08 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 6.0in; text-indent: .5in;">
<br /></div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-8028683648524635732013-01-12T05:35:00.001-08:002013-01-12T05:35:09.590-08:00January 2013 VTU Exam Engineering physics Answer key<div dir="ltr" style="text-align: left;" trbidi="on">
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;}
</style>
<![endif]-->
<br />
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><span style="color: blue; font-size: large;"><b>Our model question paper which published 4 months back carries more than 100 marks question from actual question paper!</b></span></span></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Objective questions</span></b></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">1(a) i) B<span style="mso-spacerun: yes;">
</span>ii) B<span style="mso-spacerun: yes;"> </span>iii) D<span style="mso-spacerun: yes;"> </span>iv) A</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">2(a) i) C<span style="mso-spacerun: yes;">
</span>ii) B<span style="mso-spacerun: yes;"> </span>iii) A<span style="mso-spacerun: yes;"> </span>iv) D</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">3(a) i) C<span style="mso-spacerun: yes;">
</span>ii) A<span style="mso-spacerun: yes;"> </span>iii) B<span style="mso-spacerun: yes;"> </span>iv) D</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">4(a) i) C<span style="mso-spacerun: yes;">
</span>ii) D<span style="mso-spacerun: yes;"> </span>iii) B<span style="mso-spacerun: yes;"> </span>iv) C</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">5(a) i) B<span style="mso-spacerun: yes;">
</span>ii) C<span style="mso-spacerun: yes;"> </span>iii) C<span style="mso-spacerun: yes;"> </span>iv) A</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">6(a) i) B<span style="mso-spacerun: yes;">
</span>ii) D<span style="mso-spacerun: yes;"> </span>iii) C<span style="mso-spacerun: yes;"> </span>iv) B</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">7(a) i) B<span style="mso-spacerun: yes;">
</span>ii) A<span style="mso-spacerun: yes;"> </span>ii) D<span style="mso-spacerun: yes;"> </span>iv) C</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">8(a) i) B<span style="mso-spacerun: yes;">
</span>ii) A<span style="mso-spacerun: yes;"> </span>iii) C<span style="mso-spacerun: yes;"> </span>iv) D</span></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Problems</span></b></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">1(d) m=0.65 MeV/c<sup>2</sup> = (0.65×10<sup>6</sup>×1.6×10<sup>-19</sup>)/(3×10<sup>8</sup>)<sup>2</sup>
= 1.156×10<sup>-30</sup></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><span style="mso-spacerun: yes;"> </span>λ = h/√2mE =
6.625×10<sup>-34</sup>/√(2×1.156×10<sup>-30</sup>×80×1.6×10<sup>-19</sup>) =
1.218×10<sup>-10</sup> m</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">2(d) Δt = λ<sup>2</sup>/4πcΔλ = (4000×10<sup>-10</sup>)<sup>2</sup>/(4×3.14×3×10<sup>8</sup>×8×10<sup>-5</sup>×10<sup>-10</sup>)=5.31×10<sup>-9</sup>s</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">3(d) V<sub>F</sub> = (2E<sub>F</sub>/m)<sup>1/2</sup>
= [(2×5.5×1.6×10<sup>-19</sup>)/(9.1×10<sup>-31</sup>)]<sup>1/ 2</sup> =
1.39×10<sup>6</sup> m/s</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">4(d) p = [(k-1)ε<sub>0</sub>E]/n =<span style="mso-spacerun: yes;"> </span>[(1.00014-1) × 8.85×10<sup>-12</sup>×10<sup>5</sup>]/(6.02×10<sup>26</sup>/22.4)
=4.61×10<sup>-36</sup> Coul-m</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Α = p/E = 4.61×10<sup>-36</sup>/10<sup>5</sup> =
4.61×10<sup>-41</sup> Coul-m<sup>2</sup>/volt</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">5(d) λ= nhc/p = (5×10<sup>7</sup>×6.625×10<sup>-34</sup>×3×10<sup>8</sup>)/(10<sup>-3</sup>×10×10<sup>-9</sup>)
=993.75 nm</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">6(d) α = 10/L × log (p<sub>i</sub>/p<sub>o</sub>) =
10/0.6 × log(120mw/90mw) = 2.06 dB/km</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">7(d) intercepts=3a:4b:∞</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Reciprocal = 1/3:1/4:0</span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Miller indices = 12×(1/3:1/4:0) = (4 3 0)</span></div>
<div class="MsoNormal">
<br /></div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-409666839661840942012-12-18T05:25:00.001-08:002012-12-18T05:25:10.806-08:00Quantum mechanics eigenfunction and probability density graphs for ground state, first excited state and second excited state<div dir="ltr" style="text-align: left;" trbidi="on">
<link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if !mso]>
<style>
v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style>
<![endif]--><link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><style>
<!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;
mso-font-charset:0;
mso-generic-font-family:roman;
mso-font-pitch:variable;
mso-font-signature:-1610611985 1107304683 0 0 159 0;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;
mso-font-charset:0;
mso-generic-font-family:swiss;
mso-font-pitch:variable;
mso-font-signature:-1610611985 1073750139 0 0 159 0;}
@font-face
{font-family:Kartika;
panose-1:0 0 0 0 0 0 0 0 0 0;
mso-font-alt:"Times New Roman";
mso-font-charset:0;
mso-generic-font-family:roman;
mso-font-format:other;
mso-font-pitch:auto;
mso-font-signature:0 0 0 0 0 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
margin-top:0in;
margin-right:0in;
margin-bottom:10.0pt;
margin-left:0in;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:Kartika;
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:ML;}
.MsoChpDefault
{mso-style-type:export-only;
mso-default-props:yes;
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:Kartika;
mso-bidi-theme-font:minor-bidi;}
.MsoPapDefault
{mso-style-type:export-only;
margin-bottom:10.0pt;
line-height:115%;}
@page Section1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.Section1
{page:Section1;}
-->
</style><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin-top:0in;
mso-para-margin-right:0in;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0in;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;}
</style>
<![endif]-->
<br />
<link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_editdata.mso" rel="Edit-Time-Data"></link><!--[if !mso]>
<style>
v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style>
<![endif]--><link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves>false</w:TrackMoves>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><style>
<!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;
mso-font-charset:0;
mso-generic-font-family:roman;
mso-font-pitch:variable;
mso-font-signature:-1610611985 1107304683 0 0 159 0;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;
mso-font-charset:0;
mso-generic-font-family:swiss;
mso-font-pitch:variable;
mso-font-signature:-1610611985 1073750139 0 0 159 0;}
@font-face
{font-family:Kartika;
panose-1:0 0 0 0 0 0 0 0 0 0;
mso-font-alt:"Times New Roman";
mso-font-charset:0;
mso-generic-font-family:roman;
mso-font-format:other;
mso-font-pitch:auto;
mso-font-signature:0 0 0 0 0 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
margin-top:0in;
margin-right:0in;
margin-bottom:10.0pt;
margin-left:0in;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:Kartika;
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:ML;}
.MsoChpDefault
{mso-style-type:export-only;
mso-default-props:yes;
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:Kartika;
mso-bidi-theme-font:minor-bidi;}
.MsoPapDefault
{mso-style-type:export-only;
margin-bottom:10.0pt;
line-height:115%;}
@page Section1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.Section1
{page:Section1;}
-->
</style><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin-top:0in;
mso-para-margin-right:0in;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0in;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;}
</style>
<![endif]--><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1027"/>
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1"/>
</o:shapelayout></xml><![endif]-->
<div class="MsoNormal" style="text-align: justify;">
<link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if !mso]>
<style>
v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style>
<![endif]--><link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CDOCUME%7E1%5Ccomputer%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><style>
<!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;
mso-font-charset:0;
mso-generic-font-family:roman;
mso-font-pitch:variable;
mso-font-signature:-1610611985 1107304683 0 0 159 0;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;
mso-font-charset:0;
mso-generic-font-family:swiss;
mso-font-pitch:variable;
mso-font-signature:-1610611985 1073750139 0 0 159 0;}
@font-face
{font-family:Kartika;
panose-1:0 0 0 0 0 0 0 0 0 0;
mso-font-alt:"Times New Roman";
mso-font-charset:0;
mso-generic-font-family:roman;
mso-font-format:other;
mso-font-pitch:auto;
mso-font-signature:0 0 0 0 0 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
margin-top:0in;
margin-right:0in;
margin-bottom:10.0pt;
margin-left:0in;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:Kartika;
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:ML;}
.MsoChpDefault
{mso-style-type:export-only;
mso-default-props:yes;
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:Kartika;
mso-bidi-theme-font:minor-bidi;}
.MsoPapDefault
{mso-style-type:export-only;
margin-bottom:10.0pt;
line-height:115%;}
@page Section1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.Section1
{page:Section1;}
-->
</style><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin-top:0in;
mso-para-margin-right:0in;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0in;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;}
</style>
<![endif]-->
</div>
<div class="MsoNormal" style="text-align: justify;">
<b>Case 1: <o:p></o:p></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b>When n = 1 (Ground state):<o:p></o:p></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span> </span>The Eigen function is<!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math"'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr> ψ</m:r></span></m:e><m:sub><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>1</m:r></span></m:sub></m:sSub></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 5.5pt;"><!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:15pt;
height:15pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="20" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_i1025" width="20" /><!--[endif]--></span><!--[endif]--><span> </span>= <!--[if gte msEquation 12]><m:oMath><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/><m:nor/></m:rPr>2</m:r></span></m:num><m:den><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/><m:nor/></m:rPr>L</m:r></span></m:den></m:f></m:e></m:rad></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 11.5pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:12.75pt;
height:28.5pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="38" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif" v:shapes="_x0000_i1025" width="17" /><!--[endif]--></span><!--[endif]--><span> </span>sin(<!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math"'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>πx</m:r></span></m:num><m:den><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>L</m:r></span></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 8.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:9.75pt;height:19.5pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image005.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="26" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image006.gif" v:shapes="_x0000_i1025" width="13" /><!--[endif]--></span><!--[endif]-->)</div>
<div class="MsoNormal" style="text-align: justify;">
<span> </span>Plot of ψ<sub>1</sub>
versus x and <!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><m:begChr m:val="|"/><m:endChr
m:val="|"/><span style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSub><m:sSubPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math"'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>ψ</m:r></span></m:e><m:sub><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>1</m:r></span></m:sub></m:sSub></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>
</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 5.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:22.5pt;height:15pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image007.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="20" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image008.gif" v:shapes="_x0000_i1025" width="30" /><!--[endif]--></span><!--[endif]--><sup>2</sup> versus x are as
shown in the figure<b><o:p></o:p></b></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgp1FH1TObSS-iPkdUx6JxfQaus7GbY-WR8RVM3TvM-wL7czB4S0VggRfFk3J1E45gXNgMglT0p6Et7njzug8OPC48quZr_3rbdjwDEMr0kaHL_0xlIHqD9y5odh1wI7BbLViFhIJ4914A/s1600/test.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="145" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgp1FH1TObSS-iPkdUx6JxfQaus7GbY-WR8RVM3TvM-wL7czB4S0VggRfFk3J1E45gXNgMglT0p6Et7njzug8OPC48quZr_3rbdjwDEMr0kaHL_0xlIHqD9y5odh1wI7BbLViFhIJ4914A/s400/test.bmp" width="400" /></a></div>
<div class="MsoNormal" style="text-align: justify;">
<b> Case 2: When n = 2 (First excited state):<o:p></o:p></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span> </span>The Eigen function is<!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math"'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr> ψ</m:r></span></m:e><m:sub><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:sub></m:sSub></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 5.5pt;"><!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:15.75pt;
height:15pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="20" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_i1025" width="21" /><!--[endif]--></span><!--[endif]--><span> </span>= <!--[if gte msEquation 12]><m:oMath><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/><m:nor/></m:rPr>2</m:r></span></m:num><m:den><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/><m:nor/></m:rPr>L</m:r></span></m:den></m:f></m:e></m:rad></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 11.5pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:12.75pt;
height:28.5pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="38" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif" v:shapes="_x0000_i1025" width="17" /><!--[endif]--></span><!--[endif]--><span> </span>sin(<!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math"'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>2πx</m:r></span></m:num><m:den><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>L</m:r></span></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 8.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:14.25pt;height:20.25pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image005.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="27" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image006.gif" v:shapes="_x0000_i1025" width="19" /><!--[endif]--></span><!--[endif]-->)</div>
<div class="MsoNormal" style="text-align: justify;">
<span> </span>Plot of ψ<sub>2</sub>
versus x and <!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><m:begChr m:val="|"/><m:endChr
m:val="|"/><span style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSub><m:sSubPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math"'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>ψ</m:r></span></m:e><m:sub><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>2</m:r></span></m:sub></m:sSub></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>
</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 5.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:22.5pt;height:15pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image007.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="20" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image008.gif" v:shapes="_x0000_i1025" width="30" /><!--[endif]--></span><!--[endif]--><sup>2</sup> versus x are as
shown in the figure<b><o:p></o:p></b></div>
<div class="MsoNormal" style="text-align: justify;">
<!--[if gte vml 1]><v:shape id="Picture_x0020_4"
o:spid="_x0000_s1026" type="#_x0000_t75" style='position:absolute;left:0;
text-align:left;margin-left:84.75pt;margin-top:549pt;width:296.25pt;height:128.25pt;
z-index:1;visibility:visible;mso-wrap-style:square;mso-wrap-distance-left:9pt;
mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
mso-wrap-distance-bottom:0;mso-position-horizontal:absolute;
mso-position-horizontal-relative:margin;mso-position-vertical:absolute;
mso-position-vertical-relative:margin'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image009.png"
o:title=""/>
<w:wrap type="square" anchorx="margin" anchory="margin"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><b><o:p></o:p></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGlvB256L4cE3JuSd7qc3csFTwxKHMZVI2DnigVFkg8R88CB9tKZJYzoaytfTjObwybBQJRWTmITt02zBFJJpOqe0RY43_71v6nGzrKzPxpcNvKGbBvSD9sqLEvFLf2EBiZR5HfUSrJUA/s1600/test.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGlvB256L4cE3JuSd7qc3csFTwxKHMZVI2DnigVFkg8R88CB9tKZJYzoaytfTjObwybBQJRWTmITt02zBFJJpOqe0RY43_71v6nGzrKzPxpcNvKGbBvSD9sqLEvFLf2EBiZR5HfUSrJUA/s400/test.bmp" width="400" /></a></div>
<div class="MsoNormal" style="text-align: justify;">
<b> Case 3: When n = 3 (Second excited state):<o:p></o:p></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span> </span>The Eigen function is<!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math"'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr> ψ</m:r></span></m:e><m:sub><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>3</m:r></span></m:sub></m:sSub></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 5.5pt;"><!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:15.75pt;
height:15pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="20" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_i1025" width="21" /><!--[endif]--></span><!--[endif]--><span> </span>= <!--[if gte msEquation 12]><m:oMath><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/><m:nor/></m:rPr>2</m:r></span></m:num><m:den><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/><m:nor/></m:rPr>L</m:r></span></m:den></m:f></m:e></m:rad></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 11.5pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:12.75pt;
height:28.5pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="38" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif" v:shapes="_x0000_i1025" width="17" /><!--[endif]--></span><!--[endif]--><span> </span>sin(<!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math"'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>3πx</m:r></span></m:num><m:den><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>L</m:r></span></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 8.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:14.25pt;height:20.25pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image005.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="27" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image006.gif" v:shapes="_x0000_i1025" width="19" /><!--[endif]--></span><!--[endif]-->)</div>
<div class="MsoNormal" style="text-align: justify;">
<span> </span>Plot of ψ<sub>3</sub>
versus x and <!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><m:begChr m:val="|"/><m:endChr
m:val="|"/><span style='font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSub><m:sSubPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math"'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><span
style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
m:val="p"/></m:rPr>ψ</m:r></span></m:e><m:sub><span style='font-family:
"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="roman"/><m:sty m:val="p"/></m:rPr>3</m:r></span></m:sub></m:sSub></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>
</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11pt; line-height: 115%; position: relative; top: 5.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:22.5pt;height:15pt'>
<v:imagedata src="file:///C:\DOCUME~1\computer\LOCALS~1\Temp\msohtmlclip1\01\clip_image007.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="20" src="file:///C:/DOCUME%7E1/computer/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image008.gif" v:shapes="_x0000_i1025" width="30" /><!--[endif]--></span><!--[endif]--><sup>2</sup> versus x are as
shown in the figure</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR8DgTKdUpV5Ek5HEAsbBKYvIxa8UwGEDc_AJM9s2MieN4tpVJfGHphtekqc8zsZ0u4MJOr8UntkxDGh9V0y_zd9GMaNlz_fcgJhYUNByaPQN6V50N9SZLa03WrBgzKyVkbTUE9dJPK0Y/s1600/test.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="172" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR8DgTKdUpV5Ek5HEAsbBKYvIxa8UwGEDc_AJM9s2MieN4tpVJfGHphtekqc8zsZ0u4MJOr8UntkxDGh9V0y_zd9GMaNlz_fcgJhYUNByaPQN6V50N9SZLa03WrBgzKyVkbTUE9dJPK0Y/s400/test.bmp" width="400" /></a></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-26894247220566266362012-11-29T05:01:00.003-08:002012-11-29T05:01:40.686-08:00Fermi temperature (TF)-Unit3<div dir="ltr" style="text-align: left;" trbidi="on">
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;}
</style>
<![endif]-->
<br />
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Fermi temperature is
the temperature at which average thermal energy of the free electron in a solid
becomes equal to the Fermi energy at absolute zero temperature. The thermal
energy possessed by the electrons is kT<sub>F</sub> where k is Boltzmann constant. By definition kT<sub>F</sub>
= E<sub>F </sub></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;"> Therefore, </span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">T<sub>F
</sub>= E<sub>F</sub>/k</span></div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-18667020198389491272012-11-15T06:02:00.000-08:002012-11-29T04:54:13.213-08:00Unit 3 Addition:Mean energy of an electron at absolute zero temperature <div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.blogger.com/blogger.g?blogID=4803935933670175751" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiergRAM10pbuE9PNi1SVDb25f1EOdrIuOwvnbtDpUd4hOePiaL0X8NS1nxHi2Ay1VFdkZi8ygWpcHjjyeATttUY-0fl7oaZgA-z0yQ6NRYcCOzuzX5COssWbOS9UPh3n0rGPn-oH_jPFw/s1600/tru.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="336" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiergRAM10pbuE9PNi1SVDb25f1EOdrIuOwvnbtDpUd4hOePiaL0X8NS1nxHi2Ay1VFdkZi8ygWpcHjjyeATttUY-0fl7oaZgA-z0yQ6NRYcCOzuzX5COssWbOS9UPh3n0rGPn-oH_jPFw/s400/tru.bmp" width="400" /></a></div>
<link href="file:///C:%5CDOCUME%7E1%5Cadmin%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><link href="file:///C:%5CDOCUME%7E1%5Cadmin%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_editdata.mso" rel="Edit-Time-Data"></link><!--[if !mso]>
<style>
v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style>
<![endif]--><link href="file:///C:%5CDOCUME%7E1%5Cadmin%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CDOCUME%7E1%5Cadmin%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><style>
<!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;
mso-font-charset:0;
mso-generic-font-family:roman;
mso-font-pitch:variable;
mso-font-signature:-1610611985 1107304683 0 0 159 0;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;
mso-font-charset:0;
mso-generic-font-family:swiss;
mso-font-pitch:variable;
mso-font-signature:-1610611985 1073750139 0 0 159 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
margin-top:0in;
margin-right:0in;
margin-bottom:10.0pt;
margin-left:0in;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-fareast-font-family:Calibri;
mso-bidi-font-family:"Times New Roman";}
.MsoChpDefault
{mso-style-type:export-only;
mso-default-props:yes;
font-size:10.0pt;
mso-ansi-font-size:10.0pt;
mso-bidi-font-size:10.0pt;
mso-ascii-font-family:Calibri;
mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;}
@page Section1
{size:595.45pt 841.7pt;
margin:1.0in 1.0in 1.0in 1.0in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.Section1
{page:Section1;}
</style>
Mean energy of an electron at absolute zero temperature in terms of Fermi energy-One objective type question came in VTU June 2012 question paper.</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-80395366143257549972012-10-16T06:42:00.000-07:002012-10-16T06:47:19.125-07:00First/Second Semester B.E. Degree Examination, January 2013-Model Question Paper<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<table align="left" border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: medium none; margin-left: 6.75pt; margin-right: 6.75pt;">
<tbody>
<tr>
<td style="border: 1pt solid black; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
<td style="border-color: black black black -moz-use-text-color; border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; padding: 0in 5.4pt; width: 0.2in;" valign="top" width="19"><div class="MsoNormal" style="text-align: justify;">
<br /></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: 14pt;">USN 10PHY12/22 <o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 14pt;">First/Second Semester B.E. Degree Examination, January
2013<o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b><span style="font-size: 16pt;">Engineering Physics<o:p></o:p></span></b></div>
<div align="center" class="MsoNormal" style="text-align: center;">
Time: 3 hrs. Max.
Marks:100</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Note: 1. Answer any FIVE full
questions, choosing atleast two from each part.</div>
<div class="MsoNormal" style="text-align: justify;">
2. Answer all objective type
questions only in OMR sheet page 5 of the answer booklet.</div>
<div class="MsoNormal" style="text-align: justify;">
3. Answer to objective type questions
on sheets other than OMR will not be valued.</div>
<div class="MsoNormal" style="text-align: justify;">
4. Physical constants: h = 6.626×10<sup>-34</sup>
Js, c = 3×10<sup>8</sup> m/s, m<sub>e</sub> = 9.1×10<sup>-31</sup> kg, </div>
<div class="MsoNormal" style="text-align: justify;">
k
= 1.38×10<sup>-23</sup> J/K, ε<sub>0</sub> = 8.854×10<sup>-12</sup> F/m</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b>PART-A</b><span style="font-size: 14pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b>1 </b>a. i) Electrons behaves as
a wave because they can be </div>
<div class="MsoNormal" style="text-align: justify;">
A) Diffracted by a crystal B) Deflected by magnetic
field </div>
<div class="MsoNormal" style="text-align: justify;">
C) Deflected by electric field D) Ionise a gas</div>
<div class="MsoNormal" style="text-align: justify;">
ii) In a blackbody radiation
spectrum, the Wien’s distribution law is applicable only for </div>
<div class="MsoNormal" style="text-align: justify;">
A) Longer wavelength B) Shorter wavelength C) Entire wavelength D) None of these</div>
<div class="MsoNormal" style="text-align: justify;">
ii) If the momentum of a particle is
increased to four times, the de-Broglie wavelength is </div>
<div class="MsoNormal" style="text-align: justify;">
A) become twice B) become for times C) become one-fourth D) become half</div>
<div class="MsoNormal" style="text-align: justify;">
iv) If the group velocity of a particle
is 3×10<sup>6</sup> m/s, its phase velocity is </div>
<div class="MsoNormal" style="text-align: justify;">
A) 100 m/s B) 3×10<sup>6</sup>
m/s C) 3×10<sup>8</sup> m/s
D) 3×10<sup>10 </sup>m/s<b> </b>(04
marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Describe Davisson-Germer experiment to prove the dual nature of
matter waves. (06marks)</div>
<div class="MsoNormal">
c. Derive
de-Broglie wavelength using Group velocity.
(06 marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. Compare the energy of a photon
with that of a neutron when both are associated with wavelength of 1 Å. Given
that mass of neutron is 1.678 × 10 <sup>-27</sup> kg. (04 marks)</div>
<div class="MsoNormal" style="margin-left: 6in; text-indent: 0.5in;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b>2</b> a. i) According to Max Born
approximation, <span style="font-family: Symbol;">|</span><span style="font-family: Symbol;">y</span><span style="font-family: Symbol;">|</span><sup>2</sup>
represents </div>
<div class="MsoNormal" style="text-align: justify;">
A) Energy density B) Particle density C) Probability density
D) Charge density</div>
<div class="MsoNormal" style="text-align: justify;">
ii) The wavefunction is acceptable if it
is</div>
<div class="MsoNormal" style="text-align: justify;">
A) Finite everywhere B)
Continuous everywhere </div>
<div class="MsoNormal" style="text-align: justify;">
C) Single valued everywhere D)
All of these </div>
<div class="MsoNormal" style="text-align: justify;">
iii) The first permitted energy level is
called</div>
<div class="MsoNormal" style="text-align: justify;">
A) Excited energy level B) Zero
point energy C) Ground level
D) None of these</div>
<div class="MsoNormal" style="text-align: justify;">
iv) The wavefunction for the motion of
particles in one dimensional potential box of length ‘a’ is given by <span style="font-family: Symbol;">y</span><sub>n</sub>
= D sin n<span style="font-family: Symbol;">p</span>x/a
where ‘D’ is normalization constant. The value of ‘D’ is </div>
<div class="MsoNormal" style="text-align: justify;">
A) <!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>QUOTE <span style='position:relative;
top:7.0pt;mso-text-raise:-7.0pt'><v:shapetype id="_x0000_t75" coordsize="21600,21600"
o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f"
stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:4.5pt;
height:20.25pt' equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?> <?mso-application progid="Word.Document"?> <w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="00654A4A"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="00654A4A"><m:oMathPara><m:oMath><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>1</m:t></m:r></m:num><m:den><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>a</m:t></m:r></m:den></m:f></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>">
<v:imagedata src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.png"
o:title="" chromakey="white"/>
</v:shape></span><span style='mso-spacerun:yes'> </span><span style='mso-element:
field-separator'></span><![endif]--><span style="position: relative; top: 7pt;"><v:shape equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<?mso-application progid="Word.Document"?>
<w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="00654A4A"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="00654A4A"><m:oMathPara><m:oMath><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>1</m:t></m:r></m:num><m:den><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>a</m:t></m:r></m:den></m:f></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>" id="_x0000_i1026" style="height: 20.25pt; width: 4.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:%5CDOCUME%7E1%5CADMINI%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image001.png">
</v:imagedata></v:shape></span><!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--> B) <!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>QUOTE <span style='position:relative;
top:10.0pt;mso-text-raise:-10.0pt'><v:shape id="_x0000_i1027" type="#_x0000_t75"
style='width:14.25pt;height:29.25pt' equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?> <?mso-application progid="Word.Document"?> <w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00722822"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="00722822"><m:oMathPara><m:oMath><m:rad><m:radPr><m:degHide m:val="on"/><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:radPr><m:deg/><m:e><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>2</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>a</m:t></m:r></m:den></m:f></m:e></m:rad></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>">
<v:imagedata src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image002.png"
o:title="" chromakey="white"/>
</v:shape></span><span style='mso-spacerun:yes'> </span><span style='mso-element:
field-separator'></span><![endif]--><span style="position: relative; top: 10pt;"><v:shape equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<?mso-application progid="Word.Document"?>
<w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00722822"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="00722822"><m:oMathPara><m:oMath><m:rad><m:radPr><m:degHide m:val="on"/><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:radPr><m:deg/><m:e><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>2</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>a</m:t></m:r></m:den></m:f></m:e></m:rad></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>" id="_x0000_i1028" style="height: 29.25pt; width: 14.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:%5CDOCUME%7E1%5CADMINI%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image002.png">
</v:imagedata></v:shape></span><!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--> C) a D) <!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>QUOTE <span style='position:relative;
top:10.5pt;mso-text-raise:-10.5pt'><v:shape id="_x0000_i1029" type="#_x0000_t75"
style='width:14.25pt;height:29.25pt' equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?> <?mso-application progid="Word.Document"?> <w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="000754A4"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="000754A4"><m:oMathPara><m:oMath><m:rad><m:radPr><m:degHide m:val="on"/><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:radPr><m:deg/><m:e><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>a</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:e></m:rad></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>">
<v:imagedata src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.png"
o:title="" chromakey="white"/>
</v:shape></span><span style='mso-spacerun:yes'> </span><span style='mso-element:
field-separator'></span><![endif]--><span style="position: relative; top: 10.5pt;"><v:shape equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<?mso-application progid="Word.Document"?>
<w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="000754A4"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="000754A4"><m:oMathPara><m:oMath><m:rad><m:radPr><m:degHide m:val="on"/><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:radPr><m:deg/><m:e><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>a</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>2</m:t></m:r></m:den></m:f></m:e></m:rad></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>" id="_x0000_i1030" style="height: 29.25pt; width: 14.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:%5CDOCUME%7E1%5CADMINI%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image003.png">
</v:imagedata></v:shape></span><!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--> (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Set up time independent one
dimensional Schrödinger wave equation. (06 Marks) </div>
<div class="MsoNoSpacing">
c. What is a wave function? Explain the properties of a
wave function. (04 Marks)</div>
<div class="MsoNoSpacing">
d. A quantum particle confined to one dimensional box of
width ‘a’ is in its first excited state. What is the probability of finding the
particle over an interval of (<!--[if supportFields]><span style='mso-element:
field-begin'></span> QUOTE <span style='position:relative;top:7.0pt;mso-text-raise:
-7.0pt'><v:shape id="_x0000_i1031" type="#_x0000_t75" style='width:15.75pt;
height:18.75pt' equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?> <?mso-application progid="Word.Document"?> <w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="009D3C64"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="009D3C64"><m:oMathPara><m:oMath><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t> </m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>a</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>2</m:t></m:r></m:den></m:f><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t> )</m:t></m:r></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>">
<v:imagedata src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image004.png"
o:title="" chromakey="white"/>
</v:shape></span><span style='mso-spacerun:yes'> </span><span style='mso-element:
field-separator'></span><![endif]--><span style="position: relative; top: 7pt;"><v:shape equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<?mso-application progid="Word.Document"?>
<w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="009D3C64"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="009D3C64"><m:oMathPara><m:oMath><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t> </m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>a</m:t></m:r></m:num><m:den><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t>2</m:t></m:r></m:den></m:f><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t> )</m:t></m:r></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>" id="_x0000_i1032" style="height: 18.75pt; width: 15.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:%5CDOCUME%7E1%5CADMINI%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image004.png">
</v:imagedata></v:shape></span><!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--> marked symmetrically at the centre of
box.
(06 marks)</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal">
<b>3</b> a. i) The
classical value of molar specific heat of a conductor is</div>
<div class="MsoNormal">
A) <sup>3</sup>/<sub>2</sub> R B) ½ R C)
3R D) <sup>5</sup>/<sub>2</sub>
R</div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="SV"> </span>ii) For ordinary metals,
the resistivity versus temperature curve at T = 0, </div>
<div class="MsoNormal" style="text-align: justify;">
A) has a positive intercept B)
has a negative intercept </div>
<div class="MsoNormal" style="text-align: justify;">
C) goes through the origin D)
none of these</div>
<div class="MsoNormal" style="text-align: justify;">
iii) Ohms law relates to the electric
field E, conductivity <span style="font-family: Symbol;">s</span> and current density J as</div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="IT">A) J = E/</span><span style="font-family: Symbol;">s</span><span lang="IT"> B)
J = </span><span style="font-family: Symbol;">s</span><span lang="IT">E<sup>2</sup> C) J = </span><span style="font-family: Symbol;">s</span><span lang="IT">/E D) J
= </span><span style="font-family: Symbol;">s</span><span lang="IT">E<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="IT"> </span>iv) If the Fermi energy of
silver is 5.5 eV, the Fermi velocity of conduction electron is </div>
<div class="MsoNormal" style="text-align: justify;">
A) 0.98 × 10<sup>6</sup> m/s B)
1.39 × 10<sup>6</sup> m/s C) 2.46 × 10<sup>5</sup> m/s D) None of these (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Obtain the expression for
electrical conductivity on the basis of free electron theory of metals. (06
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Explain how quantum free
electron theory succeeds in overcoming the drawbacks of classical free electron
theory. (06 marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. Calculate the probability of
an electron occupying an energy level 0.02 eV above the Fermi level and 0.02 eV
below the Fermi level at 200 K. (04
marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b>4</b> a. i) Hysteresis loss occurs when the magnetic material is
subjected to </div>
<div class="MsoNormal" style="text-align: justify;">
A) DC voltage B) AC voltage C) Both AC and DC voltage D) none of these</div>
<div class="MsoNormal" style="text-align: justify;">
ii) Which one of the following is a
piezoelectric material?</div>
<div class="MsoNormal" style="text-align: justify;">
A) Lead B) Mica C) Iron D)
Quartz</div>
<div class="MsoNormal" style="text-align: justify;">
iii) If two electric charges are q separated by a distance L, dipole
moment of the system is </div>
<div class="MsoNormal" style="text-align: justify;">
A) q/L B) L/q C) qL D)
q/L<sup>2</sup></div>
<div class="MsoNormal" style="text-align: justify;">
iv) The polarization that occurs in the frequency range 10<sup>13</sup>
to 10<sup>16</sup> Hz is </div>
<div class="MsoNormal" style="text-align: justify;">
A) Electronic B) Orientational C) Ionic D) Space charge (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Derive an expression for
internal field in the case of one dimensional array of atoms in dielectric
solids. (07
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. What are soft magnetic
materials? Discuss their properties. (05 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. A NaCl crystal is subjected to
an electric field of 1000 V/m and the resulting polarization is 4.3×10<sup>-8</sup>
c/m<sup>2</sup>. Calculate the
static dielectric constant of NaCl. (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b>PART-B</b></div>
<div class="MsoNormal" style="text-align: justify;">
<b>5</b> a. i) Emission of a photon by an excited atom due to interaction
of external energy is called</div>
<div class="MsoNormal" style="text-align: justify;">
A) Spontaneous emission B) Stimulated emission C) Induced absorption </div>
<div class="MsoNormal" style="text-align: justify;">
D) Light amplification</div>
<div class="MsoNormal">
ii) <b>) </b>Let<b> </b>n<sub>1</sub> be the number density of lower energy E<sub>1</sub>
and n<sub>2</sub> be the number density of higher energy E<sub>2</sub>, if n<sub>2</sub>>n<sub>1 </sub>is called</div>
<div class="MsoNormal" style="text-align: justify;">
A) Thick population B) Inverted population C) Normal population D) No population</div>
<div class="MsoNormal" style="text-align: justify;">
iii) The relation between Einstein’s coefficient’s A and B is</div>
<div class="MsoNormal">
A)<!--[if supportFields]><span
style='mso-element:field-begin'></span> QUOTE <span style='position:relative;
top:7.0pt;mso-text-raise:-7.0pt'><v:shape id="_x0000_i1033" type="#_x0000_t75"
style='width:30.75pt;height:22.5pt' equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?> <?mso-application progid="Word.Document"?> <w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="00213645"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00770500"/><wsp:rsid wsp:val="00770D3E"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009937B4"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A63572"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BB2A3A"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C5490A"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00D839A5"/><wsp:rsid wsp:val="00D938DB"/><wsp:rsid wsp:val="00D973EE"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E2046E"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F11D28"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FE48FF"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="00C5490A"><m:oMathPara><m:oMath><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t> </m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>8πh</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>λ</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>c</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>">
<v:imagedata src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image005.png"
o:title="" chromakey="white"/>
</v:shape></span><span style='mso-spacerun:yes'> </span><span style='mso-element:
field-separator'></span><![endif]--><span style="position: relative; top: 7pt;"><v:shape equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<?mso-application progid="Word.Document"?>
<w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="00213645"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00770500"/><wsp:rsid wsp:val="00770D3E"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009937B4"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A63572"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BB2A3A"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C5490A"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00D839A5"/><wsp:rsid wsp:val="00D938DB"/><wsp:rsid wsp:val="00D973EE"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E2046E"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F11D28"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FE48FF"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="00C5490A"><m:oMathPara><m:oMath><m:r><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr><m:t> </m:t></m:r><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>8πh</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>λ</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>c</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>" id="_x0000_i1034" style="height: 22.5pt; width: 30.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:%5CDOCUME%7E1%5CADMINI%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image005.png">
</v:imagedata></v:shape></span><!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--> B) <!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>QUOTE <span style='position:relative;
top:7.0pt;mso-text-raise:-7.0pt'><v:shape id="_x0000_i1035" type="#_x0000_t75"
style='width:27.75pt;height:22.5pt' equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?> <?mso-application progid="Word.Document"?> <w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="00213645"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00770500"/><wsp:rsid wsp:val="00770D3E"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009937B4"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A63572"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00B33934"/><wsp:rsid wsp:val="00BB2A3A"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00D839A5"/><wsp:rsid wsp:val="00D938DB"/><wsp:rsid wsp:val="00D973EE"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E2046E"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F11D28"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FE48FF"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="00B33934"><m:oMathPara><m:oMath><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>8Ï€</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>h</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>Ï…</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>c</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>">
<v:imagedata src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image006.png"
o:title="" chromakey="white"/>
</v:shape></span><span style='mso-spacerun:yes'> </span><span style='mso-element:
field-separator'></span><![endif]--><span style="position: relative; top: 7pt;"><v:shape equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<?mso-application progid="Word.Document"?>
<w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="00213645"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00770500"/><wsp:rsid wsp:val="00770D3E"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009937B4"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A63572"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00B33934"/><wsp:rsid wsp:val="00BB2A3A"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00D839A5"/><wsp:rsid wsp:val="00D938DB"/><wsp:rsid wsp:val="00D973EE"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E2046E"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F11D28"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FE48FF"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="00B33934"><m:oMathPara><m:oMath><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>8Ï€</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>h</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>Ï…</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/><w:i/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>c</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:nor/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>" id="_x0000_i1036" style="height: 22.5pt; width: 27.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:%5CDOCUME%7E1%5CADMINI%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image006.png">
</v:imagedata></v:shape></span><!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--> C) <!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>QUOTE <span style='position:relative;
top:7.0pt;mso-text-raise:-7.0pt'><v:shape id="_x0000_i1037" type="#_x0000_t75"
style='width:25.5pt;height:22.5pt' equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?> <?mso-application progid="Word.Document"?> <w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="00213645"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006B3E03"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00770500"/><wsp:rsid wsp:val="00770D3E"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009937B4"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A63572"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BB2A3A"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00D839A5"/><wsp:rsid wsp:val="00D938DB"/><wsp:rsid wsp:val="00D973EE"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E2046E"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F11D28"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FE48FF"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="006B3E03"><m:oMathPara><m:oMath><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>8Ï€h</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>Ï…</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>c</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>">
<v:imagedata src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image007.png"
o:title="" chromakey="white"/>
</v:shape></span><span style='mso-spacerun:yes'> </span><span style='mso-element:
field-separator'></span><![endif]--><span style="position: relative; top: 7pt;"><v:shape equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<?mso-application progid="Word.Document"?>
<w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="00213645"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006B3E03"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00770500"/><wsp:rsid wsp:val="00770D3E"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009937B4"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A63572"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BB2A3A"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00D839A5"/><wsp:rsid wsp:val="00D938DB"/><wsp:rsid wsp:val="00D973EE"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E2046E"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F11D28"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FE48FF"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="006B3E03"><m:oMathPara><m:oMath><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>8Ï€h</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>Ï…</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>c</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>" id="_x0000_i1038" style="height: 22.5pt; width: 25.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:%5CDOCUME%7E1%5CADMINI%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image007.png">
</v:imagedata></v:shape></span><!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--> D) <!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>QUOTE <span style='position:relative;
top:7.0pt;mso-text-raise:-7.0pt'><v:shape id="_x0000_i1039" type="#_x0000_t75"
style='width:25.5pt;height:22.5pt' equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?> <?mso-application progid="Word.Document"?> <w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="000132BA"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="00213645"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00770500"/><wsp:rsid wsp:val="00770D3E"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009937B4"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A63572"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BB2A3A"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00D839A5"/><wsp:rsid wsp:val="00D938DB"/><wsp:rsid wsp:val="00D973EE"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E2046E"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F11D28"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FE48FF"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="000132BA"><m:oMathPara><m:oMath><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>8πh</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>λ</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>c</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>">
<v:imagedata src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image008.png"
o:title="" chromakey="white"/>
</v:shape></span><span style='mso-spacerun:yes'> </span><span style='mso-element:
field-separator'></span><![endif]--><span style="position: relative; top: 7pt;"><v:shape equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<?mso-application progid="Word.Document"?>
<w:wordDocument xmlns:aml="http://schemas.microsoft.com/aml/2001/core" xmlns:dt="uuid:C2F41010-65B3-11d1-A29F-00AA00C14882" xmlns:ve="http://schemas.openxmlformats.org/markup-compatibility/2006" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:wx="http://schemas.microsoft.com/office/word/2003/auxHint" xmlns:wsp="http://schemas.microsoft.com/office/word/2003/wordml/sp2" xmlns:sl="http://schemas.microsoft.com/schemaLibrary/2003/core" w:macrosPresent="no" w:embeddedObjPresent="no" w:ocxPresent="no" xml:space="preserve"><w:ignoreSubtree w:val="http://schemas.microsoft.com/office/word/2003/wordml/sp2"/><o:DocumentProperties><o:Version>12</o:Version></o:DocumentProperties><w:docPr><w:view w:val="print"/><w:zoom w:percent="100"/><w:doNotEmbedSystemFonts/><w:defaultTabStop w:val="720"/><w:drawingGridHorizontalSpacing w:val="120"/><w:displayHorizontalDrawingGridEvery w:val="2"/><w:displayVerticalDrawingGridEvery w:val="2"/><w:punctuationKerning/><w:characterSpacingControl w:val="DontCompress"/><w:optimizeForBrowser/><w:relyOnVML/><w:allowPNG/><w:validateAgainstSchema/><w:saveInvalidXML w:val="off"/><w:ignoreMixedContent w:val="off"/><w:alwaysShowPlaceholderText w:val="off"/><w:compat><w:breakWrappedTables/><w:snapToGridInCell/><w:wrapTextWithPunct/><w:useAsianBreakRules/><w:dontGrowAutofit/></w:compat><wsp:rsids><wsp:rsidRoot wsp:val="003B558B"/><wsp:rsid wsp:val="000132BA"/><wsp:rsid wsp:val="00083B23"/><wsp:rsid wsp:val="000B1762"/><wsp:rsid wsp:val="00173ADF"/><wsp:rsid wsp:val="00206055"/><wsp:rsid wsp:val="00213645"/><wsp:rsid wsp:val="002A4C8D"/><wsp:rsid wsp:val="00305481"/><wsp:rsid wsp:val="00316C66"/><wsp:rsid wsp:val="003639B4"/><wsp:rsid wsp:val="003B558B"/><wsp:rsid wsp:val="00425085"/><wsp:rsid wsp:val="0043139D"/><wsp:rsid wsp:val="004C6621"/><wsp:rsid wsp:val="005948E5"/><wsp:rsid wsp:val="005D1EEA"/><wsp:rsid wsp:val="006659AE"/><wsp:rsid wsp:val="006A4E3D"/><wsp:rsid wsp:val="006D3935"/><wsp:rsid wsp:val="006E4872"/><wsp:rsid wsp:val="00770500"/><wsp:rsid wsp:val="00770D3E"/><wsp:rsid wsp:val="00774303"/><wsp:rsid wsp:val="007939AB"/><wsp:rsid wsp:val="007A2385"/><wsp:rsid wsp:val="007A7FAF"/><wsp:rsid wsp:val="007B2714"/><wsp:rsid wsp:val="007E3808"/><wsp:rsid wsp:val="00853410"/><wsp:rsid wsp:val="008543C2"/><wsp:rsid wsp:val="008720D3"/><wsp:rsid wsp:val="008A769A"/><wsp:rsid wsp:val="008E1D34"/><wsp:rsid wsp:val="008E6A73"/><wsp:rsid wsp:val="00951DC0"/><wsp:rsid wsp:val="009937B4"/><wsp:rsid wsp:val="009C1457"/><wsp:rsid wsp:val="00A13073"/><wsp:rsid wsp:val="00A63572"/><wsp:rsid wsp:val="00A778C2"/><wsp:rsid wsp:val="00B26E55"/><wsp:rsid wsp:val="00BB2A3A"/><wsp:rsid wsp:val="00BC5BCF"/><wsp:rsid wsp:val="00BE1BB1"/><wsp:rsid wsp:val="00C056EF"/><wsp:rsid wsp:val="00C6670F"/><wsp:rsid wsp:val="00D022EF"/><wsp:rsid wsp:val="00D062A3"/><wsp:rsid wsp:val="00D839A5"/><wsp:rsid wsp:val="00D938DB"/><wsp:rsid wsp:val="00D973EE"/><wsp:rsid wsp:val="00DB5B8F"/><wsp:rsid wsp:val="00E2046E"/><wsp:rsid wsp:val="00E33417"/><wsp:rsid wsp:val="00E90D65"/><wsp:rsid wsp:val="00EA344C"/><wsp:rsid wsp:val="00EE0AEB"/><wsp:rsid wsp:val="00F11D28"/><wsp:rsid wsp:val="00F4069C"/><wsp:rsid wsp:val="00F954E1"/><wsp:rsid wsp:val="00FB3E7E"/><wsp:rsid wsp:val="00FE48FF"/><wsp:rsid wsp:val="00FF1684"/></wsp:rsids></w:docPr><w:body><w:p wsp:rsidR="00000000" wsp:rsidRDefault="000132BA"><m:oMathPara><m:oMath><m:f><m:fPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>8πh</m:t></m:r><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>λ</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>3</m:t></m:r></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><m:ctrlPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr></m:ctrlPr></m:sSupPr><m:e><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>c</m:t></m:r></m:e><m:sup><m:r><m:rPr><m:sty m:val="p"/></m:rPr><w:rPr><w:rFonts w:ascii="Cambria Math" w:h-ansi="Cambria Math"/><wx:font wx:val="Cambria Math"/></w:rPr><m:t>2</m:t></m:r></m:sup></m:sSup></m:den></m:f></m:oMath></m:oMathPara></w:p><w:sectPr wsp:rsidR="00000000"><w:pgSz w:w="12240" w:h="15840"/><w:pgMar w:top="1440" w:right="1440" w:bottom="1440" w:left="1440" w:header="720" w:footer="720" w:gutter="0"/><w:cols w:space="720"/></w:sectPr></w:body></w:wordDocument>" id="_x0000_i1040" style="height: 22.5pt; width: 25.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:%5CDOCUME%7E1%5CADMINI%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image008.png">
</v:imagedata></v:shape></span><!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--> <b><o:p></o:p></b></div>
<div class="MsoNormal" style="text-align: justify;">
iv) Pumping process used in diode laser is </div>
<div class="MsoNormal" style="text-align: justify;">
A) Optical pumping B) Forward bias C) Electric discharge D) None of these</div>
<div class="MsoNormal" style="text-align: justify;">
(04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Obtain an expression for
energy density of radiation under equilibrium condition in terms of Einstein
coefficient. (07 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Describe the recording and
reconstruction processes in holography, with the help of suitable diagrams. (05 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. A ruby laser emits pulse of 20
ns duration with average power per pulse being 100 kW. If the number of photons
in each pulse is 6.981 × 10<sup>15</sup>, calculate the wavelength of photons. (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
</div>
<div class="MsoNormal" style="text-align: justify;">
<b>6</b> a. i) Superconductors are </div>
<div class="MsoNormal" style="text-align: justify;">
A) diamagnetic B) paramagnetic C)
ferromagnetic D) antiferromagnetic</div>
<div class="MsoNormal" style="text-align: justify;">
ii) In a single mode fiber, the diameter of
the core is nearly equal to </div>
<div class="MsoNormal" style="text-align: justify;">
A) 125 <span style="font-family: Symbol;">m</span>m B) 100 <span style="font-family: Symbol;">m</span>m C) 50 <span style="font-family: Symbol;">m</span>m D) 10 <span style="font-family: Symbol;">m</span>m</div>
<div class="MsoNormal" style="text-align: justify;">
iii) Attenuation in the optical fiber causes due to</div>
<div class="MsoNormal" style="text-align: justify;">
A) Absorption B) Scattering C) Dispersion D) All the three</div>
<div class="MsoNormal" style="text-align: justify;">
iv) Meissner effect will take place in
</div>
<div class="MsoNormal" style="text-align: justify;">
A) Solid B) Super conducting magnet C) Maglev vehicle D) MRI (04 Marks)</div>
<div class="MsoNoSpacing">
b. Obtain an expression for numerical aperture and arrive
the condition for propagation.<b> </b>(06
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Give a brief account of SQUID. (06 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. A fiber 500m long has an input
power of 8.6 mw and output power 7.5 mw. What is the loss specification in
cable? (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b>7</b> a. i) Four types of Bravais lattices are observed in </div>
<div class="MsoNormal" style="text-align: justify;">
A) Rhomohedral system B) Orthorhombic system</div>
<div class="MsoNormal" style="text-align: justify;">
C) Triclinic system D) Monoclinic system </div>
<div class="MsoNormal" style="text-align: justify;">
ii) A plane intercepts at a, b/2, 2c in a
simple cubic unit cell. The miller indices of the plane are</div>
<div class="MsoNormal" style="text-align: justify;">
A) (214) B) (241) C)
(421) D) (124)</div>
<div class="MsoNormal" style="text-align: justify;">
iii) The packing factor for fcc structure is</div>
<div class="MsoNormal" style="text-align: justify;">
A) 52% B) 68% C)
92% D) none of these</div>
<div class="MsoNormal" style="text-align: justify;">
iv) The miller indices of the plane parallel to the x and y axes
are </div>
<div class="MsoNormal" style="margin-left: 0.25in; text-align: justify;">
A) (100) B) (010) C) (001) D)
(111)<b> </b> (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. With a neat figure, explain the structure of diamond and show that atomic
packing factor of diamond is 0.34. (08 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. How do you find Miller indices
of a given plane? (04 Marks)<o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
d. The minimum order of Bragg’s
reflection occurs at an angle 20<sup><span style="font-size: 10pt;">0</span></sup>
in the plane [212]. Find the wavelength of X-ray if lattice constant is 3.615
Å. (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b>8</b> a. i) The state of matter around nanosize is known as </div>
<div class="MsoNormal" style="text-align: justify;">
A) solid state B) liquid state C) mesoscopic state D) macroscopic
state</div>
<div class="MsoNormal" style="text-align: justify;">
ii) In a carbon nanotubes, the bond between the carbon atoms is </div>
<div class="MsoNormal" style="text-align: justify;">
A) metallic B)
ionic C) covalent D) hydrogen</div>
<div class="MsoNormal" style="text-align: justify;">
iii) Elastic behavior of the liquid is characterized by its </div>
<div class="MsoNormal" style="text-align: justify;">
A) Young’s modulus B) Rigidity
modulus C) bulk modulus D)
Poisson’s ratio</div>
<div class="MsoNormal" style="text-align: justify;">
iv) Ultrasonic waves are produced by</div>
<div class="MsoNormal" style="text-align: justify;">
A) Electromagnetic induction B) Inverse piezoelectric effect </div>
<div class="MsoNormal" style="text-align: justify;">
C) Electronic tuning fork D)Piezoelectric effect (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Write a note on carbon
nanotubes. Discuss the various quantum
structures. (08 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Explain the principle and
method of nondestructive testing of material using ultrasonics.</div>
<div class="MsoNormal" style="margin-left: 5.5in; text-align: justify; text-indent: 0.5in;">
(08 Marks)</div>
<div class="MsoNormal" style="margin-left: 5.5in; text-align: justify; text-indent: 0.5in;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 6in; text-indent: 0.5in;">
<br /></div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com1tag:blogger.com,1999:blog-4803935933670175751.post-2939143869468679772012-08-10T05:45:00.004-07:002012-08-10T05:45:48.767-07:00VTU Engineering Physics Solution to problems-June2012 Question Paper<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">1(d) λ<sub>electron</sub>
= h/</span><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">Ö</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">2meV =0.91Å</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">λ<sub>object</sub> =
h/mv = 6.626 × 10<sup>-34</sup> m<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif";">2(d) P =
1/8<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif";">3 (d) n
= 1 </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">×
N<sub>A</sub> × D/A = 2.54 × 10 <sup>28<o:p></o:p></sup></span></div>
<div class="MsoNormal">
<span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">s</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> = n e<sup>2</sup></span><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">t</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> /m = 1.47 × 10<sup>7</sup> /</span><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">W</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">m<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">4(d) </span><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">e</span></span><sub><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">r
</span></sub><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">=
1.532<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">5 (d) λ = 632 nm<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">6 (d) N.A = 0.168<span style="mso-spacerun: yes;">
</span>V-number = 32<span style="mso-spacerun: yes;"> </span>Number of modes =
512<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">7 (d) λ = 2dsin</span><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">q</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">/n
= 1.348Å <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>E = h<sup>2</sup>/2m<sub>e</sub> λ<sup>2</sup>
= 1.33 × 10<sup>-17</sup> J<o:p></o:p></span></div>
</div>RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com1tag:blogger.com,1999:blog-4803935933670175751.post-57335023498059822022012-06-26T23:28:00.002-07:002012-06-26T23:28:38.187-07:0010 PHY 12/22 engineering physics June 2012 exam objective answer key<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal">
1a(i) C<span> </span>(ii)
B<span> </span>(iii) C<span> </span>(iv) C</div>
<div class="MsoNormal">
2a(i) A<span> </span>(ii)
A<span> </span>(iii) C<span> </span>(iv) A</div>
<div class="MsoNormal">
3a(i) C<span> </span>(ii)
C<span> </span>(iii) D<span> </span>(iv) D</div>
<div class="MsoNormal">
4a(i) C<span> </span>(ii)
C<span> </span>(iii) A<span> </span>(iv) C</div>
<div class="MsoNormal">
5a(i) B<span> </span>(ii)
C<span> </span>(iii) D<span> </span>(iv) B</div>
<div class="MsoNormal">
6a(i) A<span> </span>(ii)
B<span> </span>(iii) D<span> </span>(iv) D</div>
<div class="MsoNormal">
7a(i) C<span> </span>(ii)
B<span> </span>(iii) A<span> </span>(iv) A</div>
<div class="MsoNormal">
8a(i) C<span> </span>(ii)
A<span> </span>(iii) C<span> </span><span> </span>(iv)
C</div>
<div class="MsoNormal">
<br /></div>
</div>RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-81896270471760777342012-06-17T23:24:00.000-07:002012-06-17T23:24:29.887-07:00VTU Engineering Physics- Some tips-sure questions (Study the following portions-35 marks guarantee)<div dir="ltr" style="text-align: left;" trbidi="on">
<!--[if gte mso 9]><xml>
<o:OfficeDocumentSettings>
<o:RelyOnVML/>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;}
</style>
<![endif]-->
<br />
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: small;"><b><span style="font-family: "Times New Roman","serif"; line-height: 115%;">Unit 1-Davisson Germer
experiment/de-Broglie wavelength from group velocity</span></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: small;"><b><span style="font-family: "Times New Roman","serif"; line-height: 115%;">Unit
2-Wavefunction/particle in a potential well</span></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: small;"><b><span style="font-family: "Times New Roman","serif"; line-height: 115%;">Unit 3-Classical free
electron theory/ Quantum free electron theory</span></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: small;"><b><span style="font-family: "Times New Roman","serif"; line-height: 115%;">Unit 4- Internal
field/Claussius-Mussotti equation</span></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: small;"><b><span style="font-family: "Times New Roman","serif"; line-height: 115%;">Unit 5- Relation
between Einstein co-efficients/Semiconductor laser</span></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: small;"><b><span style="font-family: "Times New Roman","serif"; line-height: 115%;">Unit 6- BCS
theory/SQUID</span></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: small;"><b><span style="font-family: "Times New Roman","serif"; line-height: 115%;">Unit7-Expression for
interplanar spacing/Crystal structure of NaCl</span></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: small;"><b><span style="font-family: "Times New Roman","serif"; line-height: 115%;">Unit 8- Carbon
nanotubes/ultrasonic NDT</span></b></span></div>
</div>RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-27363707765414129082012-06-05T06:29:00.002-07:002012-06-05T06:29:58.880-07:00Material science nanomaterials<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Introduction
to nanoscience and nanotechnology</span></b><span style="font-family: "Times New Roman","serif";"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif";">Nanoscience
is the study of atoms and molecular structures whose size, at least in one
dimension is between 1-100 nm. Nanotechnology is the design and fabrication of
devices using such nanostructures. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Nanomaterials</span></b><span style="font-family: "Times New Roman","serif";"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Times New Roman","serif";">Size
a few nanometers to a few hundred nanometers. Both surface effects and size
effects plays crucial role in the properties of nanomaterials. Exhibit
properties strikingly different from those of bulk materials. The state of
matter around nanosize is referred to as mesoscopic state. The physics of
nanotechnology is also called as mesoscopic physics<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Shapes of
nanomaterials<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">Nanomaterials
are classified as quantum wells, quantum wires and quantum dots. In a three
dimensional structure, if one dimension, say thickness, is of nanosize, then
the structure is called quantum well. If two dimensions are of nanosize, then
it is called a quantum wire. If all the three dimensions are of nanosize, then
it is called quantum dot. The word
quantum is associated with the structures because the properties exhibited by
them are described by quantum mechanics. <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Density of states</span></b><span style="font-family: "Times New Roman","serif";"><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">The
density of states is defined as the number of available electron states per
unit volume per unit energy range centered at a certain energy level E.<b> <o:p></o:p></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Density of states
for nanostructures<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> For a quantum well, density of
states varies as a step function. <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> In a quantum wire, density of states
has peaks. <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> For quantum dots, permitted energy
values are almost discrete. <!--[if gte vml 1]><v:shapetype id="_x0000_t75"
coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe"
filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:486pt;
height:148.5pt;mso-position-horizontal-relative:char;
mso-position-vertical-relative:line' fillcolor="#bbe0e3">
<v:imagedata src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.png"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><img height="198" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image002.jpg" v:shapes="_x0000_i1025" width="648" /><!--[endif]--><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> </span><span style="font-family: 'Times New Roman', serif;"> </span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Nanomaterials-
examples<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> Fullerenes, carbon nanotubes and nanowires
are examples of inorganic nanomaterials.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> Artificially synthesized DNA strands are
examples of organic nanomaterials. <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Methods of
preparation of nanomaterials<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">There
exist many methods for the preparation of nanomaterials. These methods are
broadly classified into two: top-down approach and bottom-up approach. <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Top-down methods <o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">Milling
(mechanical grinding) and lithography are examples of top-down methods. During
milling, balls in the vial impart energy to powder material splitting them
further to nanoscale. Lithography deals with the nanoelectromechanical systems
which can be developed by using light, electron beam or ion beam. <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Bottom-up methods <o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">Wet
chemical methods, plasma chemical methods, sol gel methods, physical vapour
deposition, chemical vapour deposition, sputtering, Laser ablation, Molecular
beam epitaxy, thermolysis, electrodeposition, Self assembly method etc are
examples of bottom-up methods.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Wonders of nano
technology<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Fullerene and
carbon nanotubes<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Fullerene<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">Carbon
molecule having spherical, ellipsoidal or tubular form is known as fullerene.
Spherical fullerenes are called buckyballs and cylindrical fullerenes are
called buckytubes. In buckyball clusters, 20 to 60 carbon atoms are
accommodated. Nanotubes with small dimensions and megatubes with larger
dimensions are extensively used in electronics industry. Spherical particles
based on multiple carbon layers surrounding a buckyball core are known as
nano-onions. If two bucky balls are
linked by a carbon chain, it is called ‘linked ball and chain dimers’. <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Buckyball</span></b><span style="font-family: "Times New Roman","serif";">It
contains sixty carbon atoms with 20 hexagonal and 12 pentagonal faces
symmetrically arranged to form a molecular ball of carbon atoms. <!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:252.75pt;
height:198pt'>
<v:imagedata src="file:///C:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.emz"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><img height="264" src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_i1025" width="337" /><!--[endif]--><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Properties of
fullerene<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">Showing
aliphatic behaviour in chemical reactions. Sparingly
soluble in many solvents. Stable. If we heat fullerenes without air at very
high temperature, it turns into graphite. Thin layers of fullerenes are
coloured from yellow to yellow-green. Different species of fullerenes are
fullerites, fullerides, endohedral fullerenes, exohedral fullerenes,
heterofullerenes and metcars.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Carbon
nanotubes-Synthesis methods<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";"> Chemical vapour deposition, Carbon arc
methods and laser evaporation <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif";">Applications of
carbon nanotubes<o:p></o:p></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">1.In
the construction of electronic devices like transistors, logic gates etc.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">2.
In the construction of nanowires.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">3.
In flat panel displays.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">4.
In scanning probe microscopes. <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">5.
In fuel cells/batteries.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">6.
As catalysts in chemical reactions.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">7.
As chemical sensors.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif";">8.
In air pollution filters and water filters.<o:p></o:p></span></div>
</div>RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com2tag:blogger.com,1999:blog-4803935933670175751.post-76387999616381307892012-05-24T06:33:00.002-07:002012-05-24T06:33:11.657-07:00VTU Engineering Physics Examination details (MAY-JUNE 2012)<div dir="ltr" style="text-align: left;" trbidi="on">
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;}
</style>
<![endif]-->
<br />
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">14-06-2012 (Thursday)
9.30 AM – 12.30 PM 2006 Scheme (06 PHY 12/22)</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">20-06-2012 (Wednesday)
9.30 AM – 12.30 PM 2010 scheme (10 PHY 12/22)</span></div>
</div>RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com1tag:blogger.com,1999:blog-4803935933670175751.post-11171707496387537652012-05-09T05:37:00.003-07:002012-05-09T05:37:44.539-07:00VTU Engineering Physics-Some suggestions<div dir="ltr" style="text-align: left;" trbidi="on">
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:10.0pt;
font-family:"Calibri","sans-serif";}
</style>
<![endif]-->
<br />
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Modern Physics (Unit 1)
- Relatively simple unit. But some derivations you may find difficult to derive
during exam if not practiced “writing and study” many times.</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Quantum Mechanics (Unit
2) – only a few questions examiners can ask from this unit. Very easy and
understandable but problems sometimes may make you a bit nervous. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Electrical conductivity
in metals (Unit 3) – Very easy unit and some of the portions already covered
during your PUC. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Dielectric and magnetic
properties (Unit 4) – Many equations and some derivations may make you skip
this unit but just refer previous university question papers where you can find
only 4 questions which are always repeating.</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Laser (Unit 5) – It’s a
natural choice of all students since it is very easy to understand. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Optical fiber and
superconductivity (Unit 6) – Optical fiber part is very easy but you may find
some difficulty in grasping some superconductivity concepts.</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Crystal Physics (Unit
7) – Easy unit but if you are not good in drawings better avoid this. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Material science
(Unit8) – Very easy unit. Since this unit includes latest topic nanomaterials, a
threat of unexpected questions exist. Otherwise both nanomaterias and
ultrasonics are easy to handle.</span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Ranking based on
understandability and scoring scope</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">1. Laser</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">2. Electrical
conductivity in metals </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">3. Optical fibers and
superconductivity</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">4. Quantum Mechanics</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">5. Materials science</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">6. Modern physics</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">7. Crystal physics</span></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">8. Dielectric and
magnetic properties</span></div>
</div>RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-89023737562661139592012-04-30T05:28:00.001-07:002012-04-30T05:29:54.567-07:00First/Second Semester B.E. Degree Examination, June/July 2012 Engineering Physics-Model Question Paper<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<table align="left" border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 6.75pt; margin-right: 6.75pt; mso-border-alt: solid black .5pt; mso-border-insideh: .5pt solid black; mso-border-insidev: .5pt solid black; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-table-anchor-horizontal: page; mso-table-anchor-vertical: paragraph; mso-table-left: 98.1pt; mso-table-lspace: 9.0pt; mso-table-rspace: 9.0pt; mso-table-top: -1.45pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;">
<td style="border: solid black 1.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: .2in;" valign="top" width="19"><div class="MsoNormal" style="mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 98.15pt; mso-element-top: -1.45pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: justify;">
<br /></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: .2in;" valign="top" width="19"><div class="MsoNormal" style="mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 98.15pt; mso-element-top: -1.45pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: justify;">
<br /></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: .2in;" valign="top" width="19"><div class="MsoNormal" style="mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 98.15pt; mso-element-top: -1.45pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: justify;">
<br /></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: .2in;" valign="top" width="19"><div class="MsoNormal" style="mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 98.15pt; mso-element-top: -1.45pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: justify;">
<br /></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: .2in;" valign="top" width="19"><div class="MsoNormal" style="mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 98.15pt; mso-element-top: -1.45pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: justify;">
<br /></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: .2in;" valign="top" width="19"><div class="MsoNormal" style="mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 98.15pt; mso-element-top: -1.45pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: justify;">
<br /></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: .2in;" valign="top" width="19"><div class="MsoNormal" style="mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 98.15pt; mso-element-top: -1.45pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: justify;">
<br /></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: .2in;" valign="top" width="19"><div class="MsoNormal" style="mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 98.15pt; mso-element-top: -1.45pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: justify;">
<br /></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: .2in;" valign="top" width="19"><div class="MsoNormal" style="mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 98.15pt; mso-element-top: -1.45pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: justify;">
<br /></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: .2in;" valign="top" width="19"><div class="MsoNormal" style="mso-element-anchor-horizontal: page; mso-element-anchor-vertical: paragraph; mso-element-frame-hspace: 9.0pt; mso-element-left: 98.15pt; mso-element-top: -1.45pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: justify;">
<br /></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: 14pt;">USN 10PHY12/22 </span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 14pt;">First/Second Semester B.E. Degree Examination,
June/July 2012</span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 16pt;">Engineering Physics</span></b></div>
<div align="center" class="MsoNormal" style="text-align: center;">
Time: 3 hrs. Max.
Marks:100</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Note: 1. Answer any FIVE full
questions, choosing atleast two from each part.</div>
<div class="MsoNormal" style="text-align: justify;">
2. Answer all objective type
questions only in OMR sheet page 5 of the answer booklet.</div>
<div class="MsoNormal" style="text-align: justify;">
3. Answer to objective type questions
on sheets other than OMR will not be valued.</div>
<div class="MsoNormal" style="text-align: justify;">
4. Physical constants: h = 6.626×10<sup>-34</sup>
Js, c = 3×10<sup>8</sup> m/s, m<sub>e</sub> = 9.1×10<sup>-31</sup> kg, </div>
<div class="MsoNormal" style="text-align: justify;">
k
= 1.38×10<sup>-23</sup> J/K, ε<sub>0</sub> = 8.854×10<sup>-12</sup> F/m</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b style="mso-bidi-font-weight: normal;">PART-A</b><span style="font-size: 14pt;"></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
<b style="mso-bidi-font-weight: normal;">1 </b>a.
i) Experimental evidence for the existence of matter waves was first
provided by</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
A) de-Broglie B) Davisson and Germer
C) G.P.Thomson D)
Max Planck</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
ii) Recoil electron in compton
scattering carry maximum kinetic energy when x-ray scattering angle θ =</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
A) 180<sup>0</sup> B) 0<sup>0</sup> C) 90<sup>0 </sup> D) 65<sup>0</sup> </div>
<div class="MsoNormal" style="text-align: justify;">
iii) K<sub>e</sub>,K<sub>p</sub> and K<sub><span style="font-family: Symbol;">a</span> </sub>are respective energy of an e<sup>-</sup>, a proton and <span style="font-family: Symbol;">a</span>particle of same
de-Broglie wavelength. Then,</div>
<div class="MsoNormal" style="text-align: justify;">
A) K<sub>e</sub>>K<sub>p</sub>>K<sub><span style="font-family: Symbol;">a</span> </sub>B) K<sub>e</sub>>K<sub>p</sub><k< span=""><sub><span style="font-family: Symbol;">a</span> </sub> C) K<sub>e</sub><k<sub>p<k< span=""><sub><span style="font-family: Symbol;">a</span> </sub> D) K<sub>e</sub>=K<sub>p</sub>=
K<sub><span style="font-family: Symbol;">a</span> </sub></k<></k<sub></k<></div>
<div class="MsoNormal" style="text-align: justify;">
iv) de-Broglie wavelength associated
with a moving particle is independent of its </div>
<div class="MsoNormal" style="text-align: justify;">
A) mass B) charge C) velocity D) momentum<sub> </sub> (04
marks)</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
b. Show that group velocity is equal to
particle velocity. (04 Marks)</div>
<div class="MsoNoSpacing" style="text-align: justify;">
c. What is Planck’s radiation
law? Show how Wien’s law and
Rayleigh-Jean’s law can be
derived from it. <b style="mso-bidi-font-weight: normal;"> </b> (08 Marks)</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: -.1in; margin-right: -.1in; margin-top: 0in; text-align: justify;">
d. Calculate the momentum of the particle and
de-Broglie wavelength associated with an electron with a kinetic energy of 1.5
keV. (04 Marks)</div>
<div class="MsoNormal" style="margin-left: 6.0in; text-indent: .5in;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">2</b> a. i) The wavefunction for the motion of particles in one
dimensional potential box of length ‘a’ is given by </div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: Symbol;">y</span><sub>n</sub> = D sin n<span style="font-family: Symbol;">p</span>x/a
where ‘D’ is normalization constant. The value of ‘D’ is </div>
<div class="MsoNormal" style="text-align: justify;">
A) <span style="position: relative; top: 7pt;">
</span> B) <span style="position: relative; top: 10pt;">
</span> C) a D) <span style="position: relative; top: 10.5pt;">
</span> </div>
<div class="MsoNormal" style="text-align: justify;">
ii) The ground state energy of an electron
in an one dimensional infinite potential well of width 2Å is 16 </div>
<div class="MsoNormal" style="text-align: justify;">
eV. Its energy in third excited state
is</div>
<div class="MsoNormal" style="text-align: justify;">
A) 32 eV B)
64 eV C) 144 eV D) 256 eV</div>
<div class="MsoNormal" style="tab-stops: 305.25pt; text-align: justify;">
iii) According to Max Born approximation, <span style="font-family: Symbol;">|</span><span style="font-family: Symbol;">y</span><span style="font-family: Symbol;">|</span><sup>2</sup>
represents </div>
<div class="MsoNormal" style="text-align: justify;">
A) Energy density B) Particle density C) Probability density
D) Charge density</div>
<div class="MsoNormal" style="text-align: justify;">
iv) Schrödinger’s wave equation is
applicable for the particles with</div>
<div class="MsoNormal">
A) Constant
energy B) Variable energy C)
Only constant potential energy </div>
<div class="MsoNormal">
D) All of these (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Solve the Schrödinger’s wave equation for
allowed energy values in case of a particle in a potential box. (08
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. What is a wave function?
Explain the properties of a wave function. (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. Estimate the time spent by an
atom in the excited state during the excitation and de-excitation processes,
when a spectral line of wavelength 546 nm and width 10<sup>-14</sup> m is
emitted. (04 Marks)
</div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">3</b> a. i) The
mobility of electrons in a conductor is 4×10<sup>-3</sup> m<sup>2</sup>V<sup>-1</sup>s<sup>-1</sup>.
Then the drift velocity of the electron in the presence of applied electric
field of strength 100 Vm<sup>-1</sup> is</div>
<div class="MsoNormal" style="text-align: justify;">
A) 4 ms<sup>-1</sup> B) 10 ms<sup>-1</sup> C) 0.4 ms<sup>-1</sup> D) 0.04 ms<sup>-1</sup></div>
<div class="MsoNormal">
<span lang="SV"> </span>ii) Which one of the following is
correct for current density?</div>
<div class="MsoNormal" style="text-align: justify;">
A) J = neAv<sub>d</sub> B) J = neA/v<sub>d</sub> C) J = nev<sub>d</sub> D) J = 1/nev<sub>d<b> </b></sub></div>
<div class="MsoNormal">
iii) The
classical value of molar specific heat of a conductor is</div>
<div class="MsoNormal" style="text-align: justify;">
A) <sup>3</sup>/<sub>2</sub> R B) ½ R C) 3R D)
<sup>5</sup>/<sub>2</sub> R</div>
<div class="MsoNormal">
<span lang="IT"> </span>iv) The Fermi energy of a metal at
absolute zero temperature is proportional to</div>
<div class="MsoNormal" style="text-align: justify;">
A) n<sup>1/3</sup> B) n<sup>3/2</sup> C) n<sup>2/3</sup> D)
n<sup>2 </sup> (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Define relaxation time and
discuss the dependence of electrical resistivity of metals with temperature and
impurity. (06
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Explain how quantum free
electron theory succeeds in overcoming the drawbacks of classical free electron
theory. (06 marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. lculate the probability of an
electron occupying an energy level 0.02 eV above the Fermi level and 0.02 eV
below the Fermi level at 200 K. (04 marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">4</b> a. i) Orientation polarization occurs</div>
<div class="MsoNormal" style="text-align: justify;">
A) In all dielectrics B) in polar dielectrics C) in non-polar dielectrics </div>
<div class="MsoNormal" style="text-align: justify;">
D) in ionic dielectrics</div>
<div class="MsoNormal" style="text-align: justify;">
ii) The polarization produced in a
dielectric medium in the frequency range 1013 to 1016 Hz is </div>
<div class="MsoNormal" style="text-align: justify;">
A) electronic B) orientational C) space
charge D) ionic</div>
<div class="MsoNormal" style="text-align: justify;">
iii) The susceptibility of a diamagnetic material is</div>
<div class="MsoNormal" style="text-align: justify;">
A) Infinity B) positive C) zero D)
negative</div>
<div class="MsoNormal" style="text-align: justify;">
iv) In a magnetic material, the major contributor to magnetism is </div>
<div class="MsoNormal" style="text-align: justify;">
A) orbital motion of electrons B) nuclear spin</div>
<div class="MsoNormal" style="text-align: justify;">
C) spin motion of electrons D) none of these (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Derive the expression for
internal field in solids. (08 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. What are ferromagnetic
materials? Discuss the hysteresis of a ferromagnetic material. (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. A solid dielectric material
has electronic polarizability 7×10<sup>-40</sup> Fm<sup>2</sup>. If it is a
cubic structure, calculate the relative permittivity of the material. It has 3×
10<sup>28</sup> atoms/m<sup>3</sup>. (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<b style="mso-bidi-font-weight: normal;">PART-B</b></div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">5</b> a. Choose your answers for the following:</div>
<div class="MsoNormal" style="text-align: justify;">
i)<span style="color: #7030a0;"> </span>Quartz plates are fixed at the ends of the
discharge tube in a He-Ne laser so that </div>
<div class="MsoNormal" style="text-align: justify;">
A) there won’t be leakage of
gas B) the tube can
withstand high electric voltage</div>
<div class="MsoNormal" style="text-align: justify;">
C) the loses light can pass out
without any loss D) the emergency
light is polarized </div>
<div class="MsoNormal" style="text-align: justify;">
ii) The required condition to
achieve laser action in a system is</div>
<div class="MsoNormal" style="text-align: justify;">
A) state of population inversion B) existence of metastable state</div>
<div class="MsoNormal" style="text-align: justify;">
C) a resonant cavity D) all the three</div>
<div class="MsoNormal" style="text-align: justify;">
iii) 3D image of an object
constructed by hologram is the process of</div>
<div class="MsoNormal" style="text-align: justify;">
A) Intensity recording B) Phase
information recording </div>
<div class="MsoNormal" style="text-align: justify;">
C) Both phase and intensity
information recording </div>
<div class="MsoNormal" style="text-align: justify;">
D) Transmission and reflection
recording </div>
<div class="MsoNormal" style="text-align: justify;">
iv) The method used for the
measurement of pollutants in the atmosphere is </div>
<div class="MsoNormal" style="text-align: justify;">
A) Holography B) Lidar C) stimulated emission D)
coherence <b> </b>(04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Describe the construction and
working of semiconductor laser. (06 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Obtain an expression for
energy density of radiation under equilibrium condition in terms of Einstein
coefficient. (06
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. A ruby laser emits pulse of 20
ns duration with average power per pulse being 100 kW. If the number of photons
in each pulse is 6.981 × 10<sup>15</sup>, calculate the wavelength of photons.<b> </b>(04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">6</b> a. i) The temperature of a superconductor kept in a weak magnetic
field is reduced below critical </div>
<div class="MsoNormal" style="text-align: justify;">
temperature, then</div>
<div class="MsoNormal" style="text-align: justify;">
A) R=0;B≠0 B) R≠0;B=0 C) R≠0;B≠0 D) R=0;B=0</div>
<div class="MsoNormal" style="text-align: justify;">
ii) Meissner effect will take place in </div>
<div class="MsoNormal" style="text-align: justify;">
A) Solid B) Super conducting magnet
C) Maglev vehicle D) MRI.</div>
<div class="MsoNormal" style="text-align: justify;">
iii) In a single mode fiber, the diameter of the core is nearly equal
to </div>
<div class="MsoNormal" style="text-align: justify;">
A) 125 <span style="font-family: Symbol;">m</span>m B) 100 <span style="font-family: Symbol;">m</span>m C) 50 <span style="font-family: Symbol;">m</span>m D) 10 <span style="font-family: Symbol;">m</span>m</div>
<div class="MsoNormal" style="text-align: justify;">
iv) The numerical aperture of an optical fiber in air is 0.32. The
numerical aperture in water (n<sub>w</sub> = 4/3) is</div>
<div class="MsoNormal" style="text-align: justify;">
A) 0.43 B)
0.24 C) 0.64 D) 0.96 (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Explain BCS theory of
superconductivity. Give a brief account of SQUID. (07 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Describe the point to point
communication system, with the help of block diagram. (05 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. A fiber 500m long has an input
power of 8.6 mw and output power 7.5 mw. What is the loss specification in
cable? (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">7</b> a. i) The relation for angles between axes of a triclinic crystal
is</div>
<div class="MsoNormal" style="text-align: justify;">
A) <span style="font-family: Symbol;">a</span> = β = γ = 90<sup>0</sup> B) <span style="font-family: Symbol;">a</span> ≠ β ≠ γ = 90<sup>0</sup> C) <span style="font-family: Symbol;">a</span> ≠ β ≠ γ ≠ 90<sup>0</sup> D) <span style="font-family: Symbol;">a</span> = β = γ ≠ 90<sup>0</sup></div>
<div class="MsoNormal" style="text-align: justify;">
ii) The coordination number in case of
simple cubic crystal structure is </div>
<div class="MsoNormal" style="text-align: justify;">
A) 12 B) 8
C) 2 D) 6</div>
<div class="MsoNormal" style="text-align: justify;">
iii) The packing fraction of diamond
crystal structure is </div>
<div class="MsoNormal" style="text-align: justify;">
A) 34% B) 52% C) 68% D) 74% </div>
<div class="MsoNormal" style="text-align: justify;">
iv) In a simple cubic lattice the ratio d<sub>100</sub>:d<sub>110</sub>:d<sub>111</sub>
is</div>
<div class="MsoNormal" style="text-align: justify;">
A) 6:3:1 B) √3:√6:1
C) 6:3:√2 D) √6:√3:√2 (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Derive an expression for inter
planar spacing in terms of Miller indices. (06 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. With neat fig, explain crystal
structure of NaCl. (06 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. The minimum order of Bragg’s
reflection occurs at an angle 20<sup><span style="font-size: 10pt;">0</span></sup>
in the plane [212]. Find the wavelength of X-ray if lattice constant is 3.615
Å. (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;">8</b> a. i) In a carbon nanotube, the bond between the carbon atoms is</div>
<div class="MsoNormal" style="text-align: justify;">
A) Metallic B) ionic C)
covalent D) hydrogen</div>
<div class="MsoNormal" style="text-align: justify;">
ii) A constant testing of product without causing any damage is called</div>
<div class="MsoNormal" style="text-align: justify;">
A) minute testing B) destructive testing C) non-destructive testing D) random testing</div>
<div class="MsoNormal" style="text-align: justify;">
iii) Ultrasonic waves are used in</div>
<div class="MsoNormal" style="text-align: justify;">
A) LIDAR B) RADAR C) SONAR D) LASER</div>
<div class="MsoNormal" style="text-align: justify;">
iv) The typical size of nanomaterial is
between </div>
<div class="MsoNormal" style="text-align: justify;">
A) 1-10 nm B) 10-50 nm C) 1-100
nm D) 1-1000 nm (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
b. Explain density of states for
various quantum structures. (04 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
c. Write a note on carbon
nanotube. (04
Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
d. Explain the principle and
method of nondestructive testing of material using ultrasonics.</div>
<div class="MsoNormal" style="margin-left: 5.5in; text-align: justify; text-indent: .5in;">
(08 Marks)</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 6.0in; text-indent: .5in;">
<br /></div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-52521079262877639002012-01-18T05:03:00.001-08:002012-01-18T05:04:54.868-08:00Scheme of valuation (Enginering Physics VTU exam held on 16 January 2012)<!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:trackmoves/> <w:trackformatting/> <w:punctuationkerning/> <w:validateagainstschemas/> <w:saveifxmlinvalid>false</w:SaveIfXMLInvalid> <w:ignoremixedcontent>false</w:IgnoreMixedContent> <w:alwaysshowplaceholdertext>false</w:AlwaysShowPlaceholderText> <w:donotpromoteqf/> <w:lidthemeother>EN-US</w:LidThemeOther> <w:lidthemeasian>X-NONE</w:LidThemeAsian> <w:lidthemecomplexscript>X-NONE</w:LidThemeComplexScript> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> <w:dontgrowautofit/> <w:splitpgbreakandparamark/> <w:dontvertaligncellwithsp/> <w:dontbreakconstrainedforcedtables/> <w:dontvertalignintxbx/> <w:word11kerningpairs/> <w:cachedcolbalance/> </w:Compatibility> <m:mathpr> <m:mathfont val="Cambria Math"> <m:brkbin val="before"> <m:brkbinsub val="--"> <m:smallfrac val="off"> <m:dispdef/> <m:lmargin val="0"> <m:rmargin val="0"> <m:defjc val="centerGroup"> <m:wrapindent val="1440"> <m:intlim val="subSup"> <m:narylim val="undOvr"> </m:mathPr></w:WordDocument> </xml><![endif][if gte mso 9]><xml> <w:latentstyles deflockedstate="false" defunhidewhenused="true" defsemihidden="true" defqformat="false" defpriority="99" latentstylecount="267"> <w:lsdexception locked="false" priority="0" semihidden="false" unhidewhenused="false" qformat="true" name="Normal"> <w:lsdexception locked="false" priority="9" semihidden="false" unhidewhenused="false" qformat="true" name="heading 1"> <w:lsdexception locked="false" priority="9" qformat="true" name="heading 2"> <w:lsdexception locked="false" priority="9" qformat="true" name="heading 3"> <w:lsdexception locked="false" priority="9" qformat="true" name="heading 4"> <w:lsdexception locked="false" priority="9" qformat="true" name="heading 5"> <w:lsdexception locked="false" priority="9" qformat="true" name="heading 6"> <w:lsdexception locked="false" priority="9" qformat="true" name="heading 7"> <w:lsdexception locked="false" priority="9" qformat="true" name="heading 8"> <w:lsdexception locked="false" priority="9" qformat="true" name="heading 9"> <w:lsdexception locked="false" priority="39" name="toc 1"> <w:lsdexception locked="false" priority="39" name="toc 2"> <w:lsdexception locked="false" priority="39" name="toc 3"> <w:lsdexception locked="false" priority="39" name="toc 4"> <w:lsdexception locked="false" priority="39" name="toc 5"> <w:lsdexception locked="false" priority="39" name="toc 6"> <w:lsdexception locked="false" priority="39" name="toc 7"> <w:lsdexception locked="false" priority="39" name="toc 8"> <w:lsdexception locked="false" priority="39" name="toc 9"> <w:lsdexception locked="false" priority="35" qformat="true" name="caption"> <w:lsdexception locked="false" priority="10" semihidden="false" unhidewhenused="false" qformat="true" name="Title"> <w:lsdexception locked="false" priority="1" name="Default Paragraph Font"> <w:lsdexception locked="false" priority="11" semihidden="false" unhidewhenused="false" qformat="true" name="Subtitle"> <w:lsdexception locked="false" priority="22" semihidden="false" unhidewhenused="false" qformat="true" name="Strong"> <w:lsdexception locked="false" priority="20" semihidden="false" unhidewhenused="false" qformat="true" name="Emphasis"> <w:lsdexception locked="false" priority="59" semihidden="false" unhidewhenused="false" name="Table Grid"> <w:lsdexception locked="false" unhidewhenused="false" name="Placeholder Text"> <w:lsdexception locked="false" priority="1" semihidden="false" unhidewhenused="false" qformat="true" name="No Spacing"> <w:lsdexception locked="false" priority="60" semihidden="false" unhidewhenused="false" name="Light Shading"> <w:lsdexception locked="false" priority="61" semihidden="false" unhidewhenused="false" name="Light List"> <w:lsdexception locked="false" priority="62" semihidden="false" unhidewhenused="false" name="Light Grid"> <w:lsdexception locked="false" priority="63" semihidden="false" unhidewhenused="false" name="Medium Shading 1"> <w:lsdexception locked="false" priority="64" semihidden="false" unhidewhenused="false" name="Medium Shading 2"> <w:lsdexception locked="false" priority="65" semihidden="false" unhidewhenused="false" name="Medium List 1"> <w:lsdexception locked="false" priority="66" semihidden="false" unhidewhenused="false" name="Medium List 2"> <w:lsdexception locked="false" priority="67" semihidden="false" unhidewhenused="false" name="Medium Grid 1"> <w:lsdexception locked="false" priority="68" semihidden="false" unhidewhenused="false" name="Medium Grid 2"> <w:lsdexception locked="false" priority="69" semihidden="false" unhidewhenused="false" name="Medium Grid 3"> <w:lsdexception locked="false" priority="70" semihidden="false" unhidewhenused="false" name="Dark List"> <w:lsdexception locked="false" priority="71" semihidden="false" unhidewhenused="false" name="Colorful Shading"> <w:lsdexception locked="false" priority="72" semihidden="false" unhidewhenused="false" name="Colorful List"> <w:lsdexception locked="false" priority="73" semihidden="false" unhidewhenused="false" name="Colorful Grid"> <w:lsdexception locked="false" priority="60" semihidden="false" unhidewhenused="false" name="Light Shading Accent 1"> <w:lsdexception locked="false" priority="61" semihidden="false" unhidewhenused="false" name="Light List Accent 1"> <w:lsdexception locked="false" priority="62" semihidden="false" unhidewhenused="false" name="Light Grid Accent 1"> <w:lsdexception locked="false" priority="63" semihidden="false" unhidewhenused="false" name="Medium Shading 1 Accent 1"> <w:lsdexception locked="false" priority="64" semihidden="false" unhidewhenused="false" name="Medium Shading 2 Accent 1"> <w:lsdexception locked="false" priority="65" semihidden="false" unhidewhenused="false" name="Medium List 1 Accent 1"> <w:lsdexception locked="false" unhidewhenused="false" name="Revision"> <w:lsdexception locked="false" priority="34" semihidden="false" unhidewhenused="false" qformat="true" name="List Paragraph"> <w:lsdexception locked="false" priority="29" semihidden="false" unhidewhenused="false" qformat="true" name="Quote"> <w:lsdexception locked="false" priority="30" semihidden="false" unhidewhenused="false" qformat="true" name="Intense Quote"> <w:lsdexception locked="false" priority="66" semihidden="false" unhidewhenused="false" name="Medium List 2 Accent 1"> <w:lsdexception locked="false" priority="67" semihidden="false" unhidewhenused="false" name="Medium Grid 1 Accent 1"> <w:lsdexception locked="false" priority="68" semihidden="false" unhidewhenused="false" name="Medium Grid 2 Accent 1"> <w:lsdexception locked="false" priority="69" semihidden="false" unhidewhenused="false" name="Medium Grid 3 Accent 1"> <w:lsdexception locked="false" priority="70" semihidden="false" unhidewhenused="false" name="Dark List Accent 1"> <w:lsdexception locked="false" priority="71" semihidden="false" unhidewhenused="false" name="Colorful Shading Accent 1"> <w:lsdexception locked="false" priority="72" semihidden="false" unhidewhenused="false" name="Colorful List Accent 1"> <w:lsdexception locked="false" priority="73" semihidden="false" unhidewhenused="false" name="Colorful Grid Accent 1"> <w:lsdexception locked="false" priority="60" semihidden="false" unhidewhenused="false" name="Light Shading Accent 2"> <w:lsdexception locked="false" priority="61" semihidden="false" unhidewhenused="false" name="Light List Accent 2"> <w:lsdexception locked="false" priority="62" semihidden="false" unhidewhenused="false" name="Light Grid Accent 2"> <w:lsdexception locked="false" priority="63" semihidden="false" unhidewhenused="false" name="Medium Shading 1 Accent 2"> <w:lsdexception locked="false" priority="64" semihidden="false" unhidewhenused="false" name="Medium Shading 2 Accent 2"> <w:lsdexception locked="false" priority="65" semihidden="false" unhidewhenused="false" name="Medium List 1 Accent 2"> <w:lsdexception locked="false" priority="66" semihidden="false" unhidewhenused="false" name="Medium List 2 Accent 2"> <w:lsdexception locked="false" priority="67" semihidden="false" unhidewhenused="false" name="Medium Grid 1 Accent 2"> <w:lsdexception locked="false" priority="68" semihidden="false" unhidewhenused="false" name="Medium Grid 2 Accent 2"> <w:lsdexception locked="false" priority="69" semihidden="false" unhidewhenused="false" name="Medium Grid 3 Accent 2"> <w:lsdexception locked="false" priority="70" semihidden="false" unhidewhenused="false" name="Dark List Accent 2"> <w:lsdexception locked="false" priority="71" semihidden="false" unhidewhenused="false" name="Colorful Shading Accent 2"> <w:lsdexception locked="false" priority="72" semihidden="false" unhidewhenused="false" name="Colorful List Accent 2"> <w:lsdexception locked="false" priority="73" semihidden="false" unhidewhenused="false" name="Colorful Grid Accent 2"> <w:lsdexception locked="false" priority="60" semihidden="false" unhidewhenused="false" name="Light Shading Accent 3"> <w:lsdexception locked="false" priority="61" semihidden="false" unhidewhenused="false" name="Light List Accent 3"> <w:lsdexception locked="false" priority="62" semihidden="false" unhidewhenused="false" name="Light Grid Accent 3"> <w:lsdexception locked="false" priority="63" semihidden="false" unhidewhenused="false" name="Medium Shading 1 Accent 3"> <w:lsdexception locked="false" priority="64" semihidden="false" unhidewhenused="false" name="Medium Shading 2 Accent 3"> <w:lsdexception locked="false" priority="65" semihidden="false" unhidewhenused="false" name="Medium List 1 Accent 3"> <w:lsdexception locked="false" priority="66" semihidden="false" unhidewhenused="false" name="Medium List 2 Accent 3"> <w:lsdexception locked="false" priority="67" semihidden="false" unhidewhenused="false" name="Medium Grid 1 Accent 3"> <w:lsdexception locked="false" priority="68" semihidden="false" unhidewhenused="false" name="Medium Grid 2 Accent 3"> <w:lsdexception locked="false" priority="69" semihidden="false" unhidewhenused="false" name="Medium Grid 3 Accent 3"> <w:lsdexception locked="false" priority="70" semihidden="false" unhidewhenused="false" name="Dark List Accent 3"> <w:lsdexception locked="false" priority="71" semihidden="false" unhidewhenused="false" name="Colorful Shading Accent 3"> <w:lsdexception locked="false" priority="72" semihidden="false" unhidewhenused="false" name="Colorful List Accent 3"> <w:lsdexception locked="false" priority="73" semihidden="false" unhidewhenused="false" name="Colorful Grid Accent 3"> <w:lsdexception locked="false" priority="60" semihidden="false" unhidewhenused="false" name="Light Shading Accent 4"> <w:lsdexception locked="false" priority="61" semihidden="false" unhidewhenused="false" name="Light List Accent 4"> <w:lsdexception locked="false" priority="62" semihidden="false" unhidewhenused="false" name="Light Grid Accent 4"> <w:lsdexception locked="false" priority="63" semihidden="false" unhidewhenused="false" name="Medium Shading 1 Accent 4"> <w:lsdexception locked="false" priority="64" semihidden="false" unhidewhenused="false" name="Medium Shading 2 Accent 4"> <w:lsdexception locked="false" priority="65" semihidden="false" unhidewhenused="false" name="Medium List 1 Accent 4"> <w:lsdexception locked="false" priority="66" semihidden="false" unhidewhenused="false" name="Medium List 2 Accent 4"> <w:lsdexception locked="false" priority="67" semihidden="false" unhidewhenused="false" name="Medium Grid 1 Accent 4"> <w:lsdexception locked="false" priority="68" semihidden="false" unhidewhenused="false" name="Medium Grid 2 Accent 4"> <w:lsdexception locked="false" priority="69" semihidden="false" unhidewhenused="false" name="Medium Grid 3 Accent 4"> <w:lsdexception locked="false" priority="70" semihidden="false" unhidewhenused="false" name="Dark List Accent 4"> <w:lsdexception locked="false" priority="71" semihidden="false" unhidewhenused="false" name="Colorful Shading Accent 4"> <w:lsdexception locked="false" priority="72" semihidden="false" unhidewhenused="false" name="Colorful List Accent 4"> <w:lsdexception locked="false" priority="73" semihidden="false" unhidewhenused="false" name="Colorful Grid Accent 4"> <w:lsdexception locked="false" priority="60" semihidden="false" unhidewhenused="false" name="Light Shading Accent 5"> <w:lsdexception locked="false" priority="61" semihidden="false" unhidewhenused="false" name="Light List Accent 5"> <w:lsdexception locked="false" priority="62" semihidden="false" unhidewhenused="false" name="Light Grid Accent 5"> <w:lsdexception locked="false" priority="63" semihidden="false" unhidewhenused="false" name="Medium Shading 1 Accent 5"> <w:lsdexception locked="false" priority="64" semihidden="false" unhidewhenused="false" name="Medium Shading 2 Accent 5"> <w:lsdexception locked="false" priority="65" semihidden="false" unhidewhenused="false" name="Medium List 1 Accent 5"> <w:lsdexception locked="false" priority="66" semihidden="false" unhidewhenused="false" name="Medium List 2 Accent 5"> <w:lsdexception locked="false" priority="67" semihidden="false" unhidewhenused="false" name="Medium Grid 1 Accent 5"> <w:lsdexception locked="false" priority="68" semihidden="false" unhidewhenused="false" name="Medium Grid 2 Accent 5"> <w:lsdexception locked="false" priority="69" semihidden="false" unhidewhenused="false" name="Medium Grid 3 Accent 5"> <w:lsdexception locked="false" priority="70" semihidden="false" unhidewhenused="false" name="Dark List Accent 5"> <w:lsdexception locked="false" priority="71" semihidden="false" unhidewhenused="false" name="Colorful Shading Accent 5"> <w:lsdexception locked="false" priority="72" semihidden="false" unhidewhenused="false" name="Colorful List Accent 5"> <w:lsdexception locked="false" priority="73" semihidden="false" unhidewhenused="false" name="Colorful Grid Accent 5"> <w:lsdexception locked="false" priority="60" semihidden="false" unhidewhenused="false" name="Light Shading Accent 6"> <w:lsdexception locked="false" priority="61" semihidden="false" unhidewhenused="false" name="Light List Accent 6"> <w:lsdexception locked="false" priority="62" semihidden="false" unhidewhenused="false" name="Light Grid Accent 6"> <w:lsdexception locked="false" priority="63" semihidden="false" unhidewhenused="false" name="Medium Shading 1 Accent 6"> <w:lsdexception locked="false" priority="64" semihidden="false" unhidewhenused="false" name="Medium Shading 2 Accent 6"> <w:lsdexception locked="false" priority="65" semihidden="false" unhidewhenused="false" name="Medium List 1 Accent 6"> <w:lsdexception locked="false" priority="66" semihidden="false" unhidewhenused="false" name="Medium List 2 Accent 6"> <w:lsdexception locked="false" priority="67" semihidden="false" unhidewhenused="false" name="Medium Grid 1 Accent 6"> <w:lsdexception locked="false" priority="68" semihidden="false" unhidewhenused="false" name="Medium Grid 2 Accent 6"> <w:lsdexception locked="false" priority="69" semihidden="false" unhidewhenused="false" name="Medium Grid 3 Accent 6"> <w:lsdexception locked="false" priority="70" semihidden="false" unhidewhenused="false" name="Dark List Accent 6"> <w:lsdexception locked="false" priority="71" semihidden="false" unhidewhenused="false" name="Colorful Shading Accent 6"> <w:lsdexception locked="false" priority="72" semihidden="false" unhidewhenused="false" name="Colorful List Accent 6"> <w:lsdexception locked="false" priority="73" semihidden="false" unhidewhenused="false" name="Colorful Grid Accent 6"> <w:lsdexception locked="false" priority="19" semihidden="false" unhidewhenused="false" qformat="true" name="Subtle Emphasis"> <w:lsdexception locked="false" priority="21" semihidden="false" unhidewhenused="false" qformat="true" name="Intense Emphasis"> <w:lsdexception locked="false" priority="31" semihidden="false" unhidewhenused="false" qformat="true" name="Subtle Reference"> <w:lsdexception locked="false" priority="32" semihidden="false" unhidewhenused="false" qformat="true" name="Intense Reference"> <w:lsdexception locked="false" priority="33" semihidden="false" unhidewhenused="false" qformat="true" name="Book Title"> <w:lsdexception locked="false" priority="37" name="Bibliography"> <w:lsdexception locked="false" priority="39" qformat="true" name="TOC Heading"> </w:LatentStyles> </xml><![endif][if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin-top:0in; mso-para-margin-right:0in; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0in; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin;} </style> <![endif]--> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify;font-family:times new roman;"><span style="font-size:130%;"><span style="font-size:12pt;">1<span style="font-weight: bold;"> a (i) A (ii) A (iii) C (iv) B (c) 0.08 eV</span></span></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify; font-weight: bold;font-family:times new roman;"><span style="font-size:130%;"><span style="font-size:12pt;">2 a (i) D<span style="mso-tab-count: 1"> </span> (ii) B<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:2"> </span>(iii) C<span style="mso-tab-count: 2"> </span> (iv) B<span style="mso-tab-count:2"> </span> (d) 5.78 X 10<sup>4</sup> m/s</span></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify; font-weight: bold;font-family:times new roman;"><span style="font-size:130%;"><span style="font-size:12pt;">3 a (i) A<span style="mso-tab-count: 1"> </span> (ii) D <span style="mso-tab-count:2"> </span>(iii) A <span style="mso-tab-count:2"> </span><span style="mso-spacerun:yes"> </span>(iv) C<span style="mso-tab-count:2"> </span> (d) 1.39 x 10<sup>6</sup>m/s<span style="mso-spacerun:yes"> </span>5.52 x 10<sup>-8</sup> m/s</span></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify; font-weight: bold;font-family:times new roman;"><span style="font-size:130%;"><span style="font-size:12pt;">4 a (i) C<span style="mso-tab-count: 1"> </span> (ii) A<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:2"> </span>(iii) C <span style="mso-tab-count: 2"> </span><span style="mso-spacerun:yes"> </span>(iv) A <span style="mso-tab-count:2"> </span><span style="mso-spacerun:yes"> </span>(c) 3.035 x 10<sup>-40</sup></span></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify; font-weight: bold;font-family:times new roman;"><span style="font-size:130%;"><span style="font-size:12pt;">5 a (i) B<span style="mso-tab-count: 1"> </span> (ii) B<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span><span style="mso-tab-count:1"> </span>(iii) A <span style="mso-tab-count:2"> </span><span style="mso-spacerun:yes"> </span>(iv) D <span style="mso-tab-count:2"> </span><span style="mso-spacerun:yes"> </span>(d) 1.43 x 10<sup>16</sup></span></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify; font-weight: bold;font-family:times new roman;"><span style="font-size:130%;"><span style="font-size:12pt;">6 a (i) A<span style="mso-tab-count: 1"> </span> (ii) B<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:2"> </span>(iii) C <span style="mso-tab-count: 2"> </span><span style="mso-spacerun:yes"> </span>(iv) B <span style="mso-tab-count:2"> </span><span style="mso-spacerun:yes"> </span>(d) 0.0345<span style="mso-spacerun:yes"> </span>53<span style="mso-spacerun:yes"> </span>1404</span></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify; font-weight: bold;font-family:times new roman;"><span style="font-size:130%;"><span style="font-size:12pt;">7 a (i) D<span style="mso-tab-count: 1"> </span> (ii) A<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:2"> </span>(iii) B <span style="mso-tab-count: 2"> </span><span style="mso-spacerun:yes"> </span>(iv) C<span style="mso-tab-count:2"> </span> (c) (100), (010) and (001)</span></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify; font-weight: bold;font-family:times new roman;"><span style="font-size:130%;"><span style="font-size:12pt;">8 a (i) B<span style="mso-tab-count: 1"> </span> (ii) D<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:2"> </span>(iii) D<span style="mso-tab-count: 2"> </span> (iv) C<span style="mso-tab-count:2"> </span> </span></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify; font-weight: bold;"><span style="font-size:130%;"><span style="font-family:"Times New Roman","serif"; mso-fareast-Times New Roman"font-family:";font-size:12.0pt;" > </span></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify; font-weight: bold;"><span style="font-size:130%;"><span style="font-family:"Times New Roman","serif"; mso-fareast-Times New Roman"font-family:";font-size:12.0pt;" > </span></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal; text-align: justify; font-weight: bold;"><span style="font-size:130%;"><span style="font-family:"Times New Roman","serif"; mso-fareast-Times New Roman"font-family:";font-size:12.0pt;" > </span></span></p>RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-90004286745520441402011-12-15T05:38:00.000-08:002012-01-04T05:33:31.720-08:00vtu engineering physics First/Second Semester B.E. Degree Examination, January 2012<p class="MsoNormal" style="text-align: center;"><span style="font-size:14.0pt">USN<span style="mso-spacerun:yes"> </span><span style="mso-tab-count: 5"></span>10PHY12/22<span style="mso-spacerun:yes"> </span><o:p></o:p></span></p> <p class="MsoNormal" align="center" style="text-align:center"><span style="font-size:14.0pt">First/Second Semester B.E. Degree Examination, January 2012<o:p></o:p></span></p> <p class="MsoNormal" align="center" style="text-align:center"><b style="mso-bidi-font-weight: normal"><span style="font-size:16.0pt">Engineering Physics<o:p></o:p></span></b></p> <p class="MsoNormal" align="center" style="text-align:center">Time: 3 hrs.<span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span><span style="mso-tab-count:9"> </span>Max. Marks:100</p> <p class="MsoNormal" align="center" style="text-align:center"><o:p> </o:p></p> <p class="MsoNormal" style="text-align:justify">Note: 1. Answer any FIVE full questions, choosing atleast two from each part.</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>2. Answer all objective type questions only in OMR sheet page 5 of the answer booklet.</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>3. Answer to objective type questions on sheets other than OMR will not be valued.</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>4. Physical constants: h = 6.626×10<sup>-34</sup> Js, c = 3×10<sup>8</sup> m/s, m<sub>e</sub> = 9.1×10<sup>-31</sup> kg, </p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>k = 1.38×10<sup>-23</sup> J/K, ε<sub>0</sub> = 8.854×10<sup>-12</sup> F/m</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span></p> <p class="MsoNormal" align="center" style="text-align:center"><b style="mso-bidi-font-weight: normal">PART-A</b><span style="font-size:14.0pt"><o:p></o:p></span></p> <p class="MsoNormal" style="text-align:justify"><b>1 a.<span style="mso-spacerun:yes"> </span>i) Electrons behaves as a wave because they can be </b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) Diffracted by a crystal<span style="mso-tab-count:2"> </span>B) Deflected by magnetic field<span style="mso-tab-count:3"> </span></b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>C) Deflected by electric field<span style="mso-tab-count:2"> </span>D) Ionise a gas</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>ii) Blackbody radiation spectrum, maximum intensity is shifting towards </b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) shorter wavelength<span style="mso-spacerun:yes"> </span>B) longer wavelength<span style="mso-spacerun:yes"> </span>C) no change<span style="mso-spacerun:yes"> </span>D) none of these</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>ii) We do not observe wave nature of macroparticles because</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) their wavelengths are very large<span style="mso-tab-count:1"> </span> B) their wavelengths are very negligibly small</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>C) their velocities are smaller<span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>D) their velocities are larger</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>iv) de-Broglie wavelength of an electron accelerated by a potential of 60 V is </b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) 1.85 Å<span style="mso-spacerun:yes"> </span>B) 1.58 Å<span style="mso-spacerun:yes"> </span>C) 1.589 Å<span style="mso-spacerun:yes"> </span>D) 1.57 Å<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:2"></span>(04 marks)</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>b. Describe Davisson-Germer experiment to prove the dual nature of matter waves. <span style="mso-tab-count:2"> </span>(08marks)</b></p> <p class="MsoNormal"><b><span style="mso-spacerun:yes"> </span>c. Define phase velocity and group velocity. Show that group velocity is equal to particle velocity. <span style="text-indent: 0.5in; ">(08 marks)</span></b></p> <p class="MsoNormal" style="margin-left:6.0in;text-indent:.5in"><o:p> </o:p></p> <p class="MsoNormal" style="text-align:justify"><b style="mso-bidi-font-weight: normal">2</b> a. i) If E<sub>1</sub> is the energy of the lowest state of a one dimensional potential box of length ‘a’ and E<sub>2</sub> is the </p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>energy of the lowest state when the length of the box is halved, then</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) E<sub>2</sub> = E<sub>1</sub> <span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>B) E<sub>2</sub> = 2E<sub>2</sub><span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>C) E<sub>2</sub> = E<sub>1</sub>/2<span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>D) E<sub>2</sub> = 4E<sub>1<o:p></o:p></sub></p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>ii) The wavefunction is acceptable if it is</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) Finite everywhere<span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>B) Continuous everywhere<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span></p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>C) Single valued everywhere<span style="mso-spacerun:yes"> </span>D) All of these<span style="mso-spacerun:yes"> </span></p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>iii) For a particle in an infinite potential well in its 1<sup>st</sup> excited state, the probability of finding the particle </p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>at the center of box is</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) 0<span style="mso-spacerun:yes"> </span>B) 0.25<span style="mso-spacerun:yes"> </span>C) 0.5<span style="mso-spacerun:yes"> </span>D) 0.1</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>iv) Schrödinger’s wave equation is applicable for the particles with</p> <p class="MsoNormal"><span style="mso-spacerun:yes"> </span>A) Constant energy<span style="mso-spacerun:yes"> </span>B) Variable energy<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span>C) Only constant potential energy<span style="mso-spacerun:yes"> </span>D) All of these</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-tab-count:13"> </span>(04 Marks)</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>b. State and explain Heisenberg’s uncertainty principle and prove that nuclei do not contain electron.</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-tab-count:13"> </span>(06 Marks)</p> <p class="MsoNormal" style="text-align:justify">c. Set up time independent one dimensional Schrödinger wave equation.<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:4"> </span>(06 Marks)</p> <p class="MsoNormal" style="text-align:justify">d. An electron is bound in one dimensional potential well of width 0.18 nm. Find the energy value in eV of </p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>the second excited state.<span style="mso-tab-count:4"> </span><span style="mso-spacerun:yes"> </span>(04 Marks)</p> <p class="MsoNormal" style="text-align:justify"><o:p> </o:p></p> <p class="MsoNormal" style="text-align:justify"><b>3 a. i) The value of Fermi distribution function at absolute zero (T= 0 K) is 1, under the condition</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) E = E<sub>F</sub> <span style="mso-tab-count:2"> </span>B) E > E<sub>F</sub><span style="mso-tab-count:2"> </span>C) E >> E<sub>F</sub><span style="mso-tab-count:2"> </span>D) E < E<sub>F</sub></b></p> <p class="MsoNormal" style="text-align:justify"><b><span lang="SV" style="mso-ansi-language: SV"><span style="mso-spacerun:yes"> </span></span>ii) Mobility of electron is </b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) Reciprocal of conductivity<span style="mso-tab-count:1"> </span> B) Flow of electrons per unit</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>C) Reciprocal of resistivity <span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>D) Average electron drift velocity per unit electric field</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>iii) According to quantum free electron theory, the energy level in a metal are</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) Continuous<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span>B) Discrete<span style="mso-tab-count:1"> </span>C) Overlapping<span style="mso-tab-count:1"> </span>D) None</b></p> <p class="MsoNormal" style="text-align:justify"><b><span lang="IT" style="mso-ansi-language: IT"><span style="mso-spacerun:yes"> </span></span>iv) For ordinary metals, the resistivity versus temperature curve at T = 0, </b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) has a positive intercept<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:3"> </span>B) has a negative intercept </b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>C) goes through the origin<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:3"> </span>D) none of these<span style="mso-tab-count:4"> </span>(04 Marks)</b></p> <p class="MsoNormal" style="text-align:justify"><b>b. Define relaxation time and discuss the dependence of electrical resistivity of metals with temperature and impurity. <span style="mso-tab-count:4"> </span><span style="mso-tab-count:8"> </span>(06 Marks)</b></p> <p class="MsoNormal" style="text-align:justify"><b>c. Explain how quantum free electron theory succeeds in overcoming the drawbacks of classical free electron theory. <span style="mso-tab-count:4"> </span><span style="mso-tab-count:7"> </span>(06 marks)</b></p> <p class="MsoNormal" style="text-align:justify"><b>d. A uniform silver wire has resistivity 1.54×10<sup>-8</sup> ohm-m at room temperature for an electric field 2 v/m.<span style="mso-spacerun:yes"> </span>Calculate relaxation time and drift velocity of the electrons, assuming that there are 5.8×10<sup>22</sup> conduction electrons per cm<sup>3 </sup>of the material.<span style="mso-tab-count: 5"> </span><span style="mso-tab-count:4"> </span>(04 marks)</b></p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span></p> <p class="MsoNormal" style="text-align:justify"><b style="mso-bidi-font-weight: normal">4</b> a. i) Orientation polarization occurs</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) In all dielectrics<span style="mso-spacerun:yes"> </span>B) in polar dielectrics<span style="mso-tab-count:1"> </span>C) in non-polar dielectrics<span style="mso-tab-count:1"> </span>D) in ionic dielectrics</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>ii) Ultrasonic waves can be produced by</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) Photoelectric effect method<span style="mso-tab-count:1"> </span>B) Inverse piezoelectric effect method </p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>C) Dielectric heating method<span style="mso-tab-count:2"> </span>D) High energy ball milling method</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>iii) The susceptibility of a diamagnetic material is</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) Infinity<span style="mso-tab-count: 1"> </span>B) positive<span style="mso-tab-count:1"> </span>C) zero<span style="mso-tab-count:2"> </span>D) negative</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>iv) In a magnetic material, the major contributor to magnetism is </p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) orbital motion of electrons<span style="mso-tab-count:2"> </span>B) nuclear spin</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>C) spin motion of electrons<span style="mso-tab-count:2"> </span>D) none of these<span style="mso-tab-count:5"> </span>(04 Marks)</p> <p class="MsoNormal" style="text-align:justify">b. What is meant by polarization mechanism in dielectrics? Discuss any three different polarization mechanisms in dielectrics and their frequency dependence.<span style="mso-tab-count:6"> </span>(08 Marks)</p> <p class="MsoNormal" style="text-align:justify">c. What are soft magnetic materials? Discuss their properties.<span style="mso-tab-count:5"> </span>(04 Marks)</p> <p class="MsoNormal" style="text-align:justify">d. The relative permittivity of sulphur is 4. Calculate its atomic polarizability. Given that sulphur is in cubic form and has a density of 20180 kg/cubic meter and atomic weight of 32.<span style="mso-tab-count:4"> </span>(04 Marks)</p> <p class="MsoNormal" style="text-align:justify"><o:p> </o:p></p> <p class="MsoNormal" align="center" style="text-align:center"><b style="mso-bidi-font-weight: normal">PART-B<o:p></o:p></b></p> <p class="MsoNormal" style="text-align:justify"><o:p> </o:p></p> <p class="MsoNormal" style="text-align:justify"><b>5 a. i) The life time of an atom in the excited state is of the order of</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) Millisecond<span style="mso-tab-count: 1"> </span><span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span>B) Few seconds<span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>C) Nano seconds <span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>D) Unlimited</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>ii) Pumping process used in diode laser is </b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) Optical pumping<span style="mso-spacerun:yes"> </span>B) Forward bias<span style="mso-spacerun:yes"> </span>C) Electric discharge<span style="mso-spacerun:yes"> </span>D) None of these</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>iii) Emission of a photon by an excited atom due to interaction of external energy is called</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) Spontaneous emission<span style="mso-spacerun:yes"> </span>B) Stimulated emission <span style="mso-spacerun:yes"> </span>C) Induced absorption<span style="mso-spacerun:yes"> </span>D) Light amplification</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>iv) In He-Ne laser, the ratio of He-Ne gas molecules in the order</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) 1:10<span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span><span style="mso-tab-count: 1"> </span><span style="mso-spacerun:yes"> </span>B) 10:1<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>C) 1:1<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>D) 1:2<span style="mso-tab-count:3"> </span>(04 Marks)</b></p> <p class="MsoNormal" style="text-align:justify"><b>b. Obtain an expression for energy density of radiation under equilibrium condition in terms of Einstein<span style="mso-spacerun:yes"> </span></b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>coefficient.<span style="mso-tab-count: 11"> </span>(07 Marks)</b></p> <p class="MsoNormal" style="text-align:justify"><b>c. Describe the recording and reconstruction processes in holography, with the help of suitable diagrams.<span style="mso-tab-count:2"> </span><span style="mso-tab-count:12"> </span>(05 Marks)</b></p> <p class="MsoNormal" style="text-align:justify"><b>d. Calculate on the basis of Einstein’s theory the number of photons emitted per second by He-Ne laser </b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>source emitting light of wavelength 6328Å with an optical power 10 mW. <span style="mso-tab-count:3"> </span>(04 Marks)</b></p> <p class="MsoNormal" style="text-align:justify"><span style="mso-tab-count:1"> </span></p> <p class="MsoNormal" style="text-align:justify"><b style="mso-bidi-font-weight: normal">6</b> a. i) The critical temperature of mercury is </p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) 4.2 K<span style="mso-tab-count: 1"> </span><span style="mso-spacerun:yes"> </span>B) 6.2 K<span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>C) 7.8 K<span style="mso-tab-count: 1"> </span><span style="mso-spacerun:yes"> </span>D) 20 K</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>ii) A superconducting material, on being subjected to the critical field, changes to</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) Critical conductivity<span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>B) Superconducting which is independent of temp</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>C) Normal state<span style="mso-tab-count: 2"> </span><span style="mso-spacerun:yes"> </span>D) Remains uninfluenced</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>iii) In a single mode fiber, the diameter of the core is nearly equal to<span style="mso-spacerun:yes"> </span></p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) 125 <span style="font-family:Symbol; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"; mso-char-type:symbol;mso-symbol-font-family:Symbol"><span style="mso-char-type: symbol;mso-symbol-font-family:Symbol">m</span></span>m <span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span>B) 100 <span style="font-family:Symbol; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"; mso-char-type:symbol;mso-symbol-font-family:Symbol"><span style="mso-char-type: symbol;mso-symbol-font-family:Symbol">m</span></span>m<span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span>C) 50 <span style="font-family:Symbol; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"; mso-char-type:symbol;mso-symbol-font-family:Symbol"><span style="mso-char-type: symbol;mso-symbol-font-family:Symbol">m</span></span>m<span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span>D) 10 <span style="font-family:Symbol; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"; mso-char-type:symbol;mso-symbol-font-family:Symbol"><span style="mso-char-type: symbol;mso-symbol-font-family:Symbol">m</span></span>m</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>iv) The width of the energy gap of the superconductor is maximum at </p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>A) T<sub>c</sub><span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span>B) 0K<span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span>C) T<sub>c</sub>/2<span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span>D) T<sub>c</sub>/3<span style="mso-tab-count: 2"> </span>(04 Marks)</p> <p class="MsoNormal" style="text-align:justify">b. Give a brief account of SQUID.<span style="mso-tab-count:9"> </span>(06 Marks)</p> <p class="MsoNormal" style="text-align:justify">c. What are the different types of attenuation losses in an optical fiber?<span style="mso-tab-count:4"> </span>(06 Marks)</p> <p class="MsoNormal" style="text-align:justify">d. An optical fiber has core R.I. 1.5 and R.I. of cladding 3% less than the core index. Calculate the numerical </p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>aperture, angle of acceptance and internal critical acceptance angle.<span style="mso-tab-count:4"> </span>(04 Marks)</p> <p class="MsoNormal" style="text-align:justify"><o:p> </o:p></p> <p class="MsoNormal" style="text-align:justify"><b>7 a. i) Which one of the following Bravais lattices is not found in cubic crystal?</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) Simple cubic<span style="mso-tab-count: 1"> </span><span style="mso-spacerun:yes"> </span>B) Face centered<span style="mso-tab-count:1"> </span> C) Body centered<span style="mso-tab-count: 1"> </span>D) Base centered</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>ii) A plane intercepts at a, b/2, 2c in a simple cubic unit cell. The miller indices of the plane are</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) (214)<span style="mso-tab-count: 1"> </span><span style="mso-spacerun:yes"> </span>B) (241)<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span>C) (421)<span style="mso-tab-count:1"> </span>D) (124)</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>iii) The coordination number for a face centered cubic lattice is</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>A) 12<span style="mso-tab-count:2"> </span>B) 8<span style="mso-tab-count:2"> </span>C) 6<span style="mso-tab-count:2"> </span>D) 26</b></p> <p class="MsoNormal" style="text-align:justify"><b><span style="mso-spacerun:yes"> </span>iv) Atomic packing fraction<span style="mso-spacerun:yes"> </span>of diamond crystal structure is </b></p> <p class="MsoNormal" style="margin-left:.25in;text-align:justify"><b><span style="mso-spacerun:yes"> </span>A)0.68<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:2"> </span>B) 0.74 <span style="mso-tab-count:1"> </span>C) 0.52<span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span>D) 0.34<span style="mso-tab-count:5"> </span>(04 Marks)</b></p> <p class="MsoNormal" style="text-align:justify"><b>b. Derive an expression for inter planar spacing in terms of Miller indices.<span style="mso-tab-count:4"> </span>(06 Marks)</b></p> <p class="MsoNormal" style="text-align:justify"><b>c. Derive Bragg’s law for X-ray diffraction. State one of the applications of X-ray diffraction technique.<span style="mso-tab-count:2"> </span><span style="mso-tab-count:12"> </span>(06 Marks)</b></p> <p class="MsoNormal" style="text-align:justify"><b>d. Calculate the glancing angle for incidence of X-rays of wavelength 0.58Å on the plane (132) of NaCl which results in second order diffraction maxima taking the lattice as 3.81Å<span style="mso-tab-count:3"> </span>(04 Marks)</b></p> <p class="MsoNormal" style="text-align:justify"><o:p> </o:p></p> <p class="MsoNormal" style="text-align:justify"><b style="mso-bidi-font-weight: normal">8</b> a. i) In a carbon nanotube, the bond between the carbon atoms is</p> <p class="MsoNormal" style="text-align:justify">A) Metallic<span style="mso-tab-count:1"> </span>B) ionic<span style="mso-tab-count:1"> </span>C) covalent<span style="mso-tab-count:1"> </span>D) hydrogen</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>ii) A bulk material reduced in two directions is known as</p> <p class="MsoNormal" style="text-align:justify">A)<span style="mso-spacerun:yes"> </span>Quantum wire<span style="mso-tab-count:1"> </span>B) Quantum dot <span style="mso-tab-count:1"> </span>C) Quantum well<span style="mso-tab-count:1"> </span>D) Thin film</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>iii) Ultrasonic waves are used in</p> <p class="MsoNormal" style="text-align:justify">A) LIDAR<span style="mso-tab-count: 1"> </span>B) RADAR <span style="mso-tab-count:1"> </span>C) SONAR<span style="mso-tab-count:1"> </span>D) LASER</p> <p class="MsoNormal" style="text-align:justify"><span style="mso-spacerun:yes"> </span>iv) Which one is not the property of ultrasonic waves</p> <p class="MsoNormal" style="text-align:justify">A) Produce heat while passing through a medium.<span style="mso-tab-count:1"> </span>B) Can penetrate large distances through matter</p> <p class="MsoNormal" style="text-align:justify">C) Require a material medium for propagation<span style="mso-tab-count:1"> </span>D) Undergo polarization like light waves.<span style="mso-tab-count:1"> </span>(04 Marks)</p> <p class="MsoNormal" style="text-align:justify">b. Explain density of states for various quantum structures.<span style="mso-tab-count:6"> </span>(08 Marks)</p> <p class="MsoNormal" style="text-align:justify">c. Explain the principle and method of nondestructive testing of material using ultrasonics. <span style="mso-tab-count:1"> </span>(08 Marks)</p>RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0tag:blogger.com,1999:blog-4803935933670175751.post-67857738658229312382008-07-25T06:11:00.000-07:002011-08-23T06:20:10.656-07:00MODERN PHYSICS<div align="justify"><span style="font-size:180%;">VTU Model Question Paper
<br /></span>1.a. I If the momentum of a particle is increased to four times, the de-Broglie wavelength is
<br />A) become twice B) become for times C) become one-fourth D) become half
<br />II Blackbody radiation spectrum, maximum intensity is shifting towards
<br />A) shorter wavelength B) longer wavelength C) no change D) none of these
<br />III Group velocity of wave is equal to
<br />A) V phase B) V particle C) Velocity of light D) none of these
<br />IV de-Broglie wavelength of an electron accelerated by a potential of 60 V is
<br />A) 1.85 Å B) 1.58 Å C) 1.589 Å D) 1.57 Å
<br />b. Describe Davisson-Germer experiment to prove the dual nature of matter waves.
<br />c. Explain phase velocity and Group velocity. Derive de-broglie wavelength using Group velocity. (4+8+8)
<br />
<br /><span style="font-size:180%;">Dec 08/ Jan 09</span>
<br />1 a. 1) The de-Broglie wavelength associated with an electron of mass m and accelerated by a potential V is
<br />
<br />2) Davisson and Germer were the first to demonstrate :
<br />i) The straight line propagation of light ii) The diffraction of photons
<br />iii) The effective mass of electron iv) None of these
<br />3) Electrons behaves as waves because they can be :
<br />i) Deflected by an electric field ii) Diffracted by a crystal
<br />iii) Deflected by magnetic field iv) They ionize a gas
<br />4) In Davisson-Germer experiment, the hump is most prominent when the electron is accelerated by
<br />i) 34 volts ii) 54 volts iii) 60 volts iv) 80 volts (04 Marks)
<br />b. Define phase velocity and group velocity. Show that group velocity is same as particle velocity. (08 Marks)
<br />c. Derive de-Broglie wavelength using Group velocity. (04 Marks)
<br />d. Compare the energy of a photon with that of a neutron when both are associated with wavelength of 1 Å. Given that mass of neutron is 1.678 × 10 -27 kg. (04 Marks)
<br />
<br />
<br /><span style="font-size:180%;">June-July 2009</span>
<br />1 a. i) An electron and a proton are accelerated through same potential. The ratio of de-Broglie wavelength e/p is
<br />
<br />ii) Wavefunction associated with a material particle is
<br />A) Single valued B) Finite C) Continuous D) ALL the above
<br />iii) In a blackbody radiation spectrum, the maximum energy peaks shift towards the shorter wavelength side with the increase in temperature. This confirms
<br />A) Stefan’s law B) Wein’s law C) Rayleigh-Jean’s law
<br />D) Planck’s law
<br />iv) The group velocity of the particle is 3×106 m/s, whose phase velocity is
<br />A) 6.06×106 m/s B) 3×1010 m/s C) 3 nm/s D) 1.5×1010 m/s (04 Marks)
<br />b. Describe Davisson and Germer experiment for confirmation of deBroglie hypothesis.
<br />(08 Marks)
<br />c. Explain phase and group velocity. Calculate the de-Broglie wavelength of a bullet of mass 5 gm moving with a velocity 20 km/hr. (08 Marks)
<br />
<br /><span style="font-size:180%;">Dec.09/Jan.10</span>
<br />1 a. i) Wien’s law is deduced from Planck’s radiation formula under the condition of
<br />A) Very small wavelength and temperature B) Large wavelength and temperature
<br />C) Small wavelength and high temperature D) Large wavelength and small temperature
<br />ii) The Compton wavelength is given by
<br />A) h/m0C2 B) h2/m0C2 C) h/m0C D) h2/2m0C
<br />iii) Which of the following relations can be used to determine de-Broglie wavelength associated with a particle?
<br />
<br />iv) If the group velocity of a particle is 3×106 m/s, its phase velocity is
<br />A) 100 m/s B) 3×106 m/s C) 3×108 m/s D) 3×1010 m/s
<br />(04 Marks)
<br />b. What is Planck’s radiation law? Show how Wien’s law and Rayleigh-Jean’s law can be derived from it. (06 Marks)
<br />c. Define group velocity. Derive relation between group velocity and phase velocity.
<br />(06 Marks)
<br />d. A fast moving neutron is found to be have a associated de-Broglie wavelength 2Å. Find its kinetic energy and group velocity of the de-Broglie waves. (04 Marks)
<br />
<br /><span style="font-size:180%;">May/June 2010</span>
<br />1 a. i) In a blackbody radiation spectrum, the Wien’s distribution law is applicable only for
<br />A) Longer wavelength B) Shorter wavelength C) Entire wavelength
<br />D) None of these
<br />ii) The de-Broglie wavelength associated with an electron of mass m and accelerated by a potential V is
<br />
<br />iii) Electrons behaves as a wave because they can be
<br />A) Diffracted by a crystal B) Deflected by magnetic field
<br />C) Deflected by electric field D) Ionise a gas
<br />iv) If the group velocity of de-Broglie wave is 4×108 m/sec, its phase velocity is
<br />A) 12×108 m/sec B) 2.25×108 m/sec C) 5.33×108 m/sec D) 1.33×108 m/sec
<br />(04 Marks)
<br />b. Explain duality of matter waves. (04 Marks)
<br />c. Define phase velocity and group velocity. Show that group velocity is equal to particle velocity. (08 Marks)
<br />d. Calculate the momentum of the particle and de-Broglie wavelength associated with an electron with a kinetic energy of 1.5 keV. (04 Marks)
<br /><span style="font-size:180%;">January 2011</span>
<br />1 a. Choose your answers for the following:
<br />i) Green light incident on a surface releases photoelectrons from the surface. If now blue light is incident on the same surface, the velocity of electrons
<br />A) increases B) decreases C) remains same D) becomes zero
<br />ii) Rayleigh-Jean’s theory of radiations agree with experimental results for
<br />A) all wavelengths B) shorter wavelengths only C) longer wavelengths only
<br />D) middle order wavelengths only
<br />iii) The de-Broglie wavelength of an electron accelerated to a potential difference of 100 volts is
<br />A) 1.2Å B) 10Å C) 100Å D) 12Å
<br />iv) The wave nature associated with electrons in motion was verified by
<br />A) photoelectric effect B) Compton effect C) diffraction by crystals
<br />D) Raman effect (04 Marks)
<br />b. State and explain de-Broglie’s hypothesis. (04 Marks)
<br />c. Define phase velocity and group velocity. Obtain the relation between group velocity and particle velocity. Obtain the expression for de-Broglie wavelength using group velocity. (08 Marks)
<br />d. Find the kinetic energy and group velocity of an electron with de-Broglie wavelength of 0.2 nm.
<br />
<br /><strong><span style="font-size:85%;">Introduction to blackbody radiation spectrum</span></strong>
<br /><span style="font-size:85%;">An object which absorbs all radiation that is incident on it is called a blackbody. A perfect blackbody is an assumption and we can have objects that are only close to a blackbody. A blackbody, on heating, can emit all radiations it has absorbed and is called blackbody radiation. Figure shows the energy distribution curves in which energy density E (energy emitted by the blackbody per unit area of the surface) is plotted as a function of wavelength at different temperatures of the blackbody.
<br /></span>
<br /></div><span style="font-size:85%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0fq83WnU3y3dGmr5flFRCFEaUhyg_QbTC4NieVQtiZoQwm_sdWbzoMtwu_uwtBCXewxy6UZYVayAEJuEVCwmRNyN0ZyN50UGa7mscvrS9VOr5UHSSxfFscaSxuywVp-yvxZpeyzaenk4/s1600-h/1.bmp"><img style="WIDTH: 325px; HEIGHT: 210px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276318953778939778" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0fq83WnU3y3dGmr5flFRCFEaUhyg_QbTC4NieVQtiZoQwm_sdWbzoMtwu_uwtBCXewxy6UZYVayAEJuEVCwmRNyN0ZyN50UGa7mscvrS9VOr5UHSSxfFscaSxuywVp-yvxZpeyzaenk4/s400/1.bmp" /></a></span>
<br />
<br />
<br /><span style="font-size:85%;">The important points that can be noted down from these curves are
<br />1. All curves shows a peak suggesting that the emitted intensity is maximum at a particular wavelength.
<br />2. An increase in temperature results in an increase in the energy emitted.3 .As the temperature increases, the peak shifts to lower wavelength. </span>
<br />
<br />
<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy-K7e6x7dDky8aQArGjoJRX-fAyiuHCq_F6h6DnLbDl47gSolyMNe6MwKjzZoKjNESk4mTx4ZfpOW7Kx_xzqDqFGjTh2PO-x248tmAVfs5AxC7QR72HbjfP6Df-f2E4LIGb0BTUFRPYI/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 104px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276318531908434290" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy-K7e6x7dDky8aQArGjoJRX-fAyiuHCq_F6h6DnLbDl47gSolyMNe6MwKjzZoKjNESk4mTx4ZfpOW7Kx_xzqDqFGjTh2PO-x248tmAVfs5AxC7QR72HbjfP6Df-f2E4LIGb0BTUFRPYI/s400/1.bmp" /></a>
<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5nuWX2UERzqkNIJT5ajEg9yK3sLPx_LT3JDOdHgNpzhAMOeSzMFdy3nb_3Rrnja7Xyka5MEh6zYJyPqaSC3-MIe97aWzu9VVz_ns0EMUsVSPOZFLGXccWieE8SH54mWPd5_vI1bs5LR0/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 311px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276318299089102994" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5nuWX2UERzqkNIJT5ajEg9yK3sLPx_LT3JDOdHgNpzhAMOeSzMFdy3nb_3Rrnja7Xyka5MEh6zYJyPqaSC3-MIe97aWzu9VVz_ns0EMUsVSPOZFLGXccWieE8SH54mWPd5_vI1bs5LR0/s400/1.bmp" /></a>
<br />
<br />
<br />
<br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZIPrkR9E6Pix_rJ9i0NL9Sdx9HukSOAeDzRjroZGn5eA1ZfZ80B3IXcNFS8111yp_NC7Ge9BJd4Q3nqApG1S9skEEgb8SoRzlqWS3YoJHVnZjBF74ULLzdQxXlpnT13o5kSAOuYSonZg/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 270px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276318013390662578" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZIPrkR9E6Pix_rJ9i0NL9Sdx9HukSOAeDzRjroZGn5eA1ZfZ80B3IXcNFS8111yp_NC7Ge9BJd4Q3nqApG1S9skEEgb8SoRzlqWS3YoJHVnZjBF74ULLzdQxXlpnT13o5kSAOuYSonZg/s400/1.bmp" /></a>
<br />
<br />
<br />
<br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRN1rEIzO14HfzOH3hkxtjYBTsqNJyJIw4XQg3TMOBKpPUJx58l6wTNjrFFdLcvB4UBPjfZ6Sg3Ef8kfa7TBvn0wakJ_ebqdZkaFKSEc97ZqydqXcH9HqxqFy7DnFvcjZeHRiI_OnY7D8/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 336px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276317582431828802" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRN1rEIzO14HfzOH3hkxtjYBTsqNJyJIw4XQg3TMOBKpPUJx58l6wTNjrFFdLcvB4UBPjfZ6Sg3Ef8kfa7TBvn0wakJ_ebqdZkaFKSEc97ZqydqXcH9HqxqFy7DnFvcjZeHRiI_OnY7D8/s400/1.bmp" /></a>
<br />
<br />
<br />
<br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiul9-9HyXVO7BHb34e2Uq3HlBml9LzoS8KvAh6vJfmoob7NcW0IG6PtFsBWylO1TDiq3w_Zpw-r6ZewHd-JfexT_4upWZehcJXc-2ycNO_x6yazTjnkeBqq8iAf5TmoALB8EqB2C2BTV4/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 200px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276317228563708242" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiul9-9HyXVO7BHb34e2Uq3HlBml9LzoS8KvAh6vJfmoob7NcW0IG6PtFsBWylO1TDiq3w_Zpw-r6ZewHd-JfexT_4upWZehcJXc-2ycNO_x6yazTjnkeBqq8iAf5TmoALB8EqB2C2BTV4/s400/1.bmp" /></a>
<br />
<br />
<br />
<br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGjSIXZDbDdIDHEMsiMNBI9fQ7hnJRTeDkN9j190BrzIFvxtt1WjwTzqDLFWBIVGWbFhGKCuemEdoKV2l_hH3zg_6BAjgufo1j5c-kew0u6Z7PnxD6XRLOCuu2e4foZkkHgF1o2Kk6TE0/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 375px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276316962956926290" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGjSIXZDbDdIDHEMsiMNBI9fQ7hnJRTeDkN9j190BrzIFvxtt1WjwTzqDLFWBIVGWbFhGKCuemEdoKV2l_hH3zg_6BAjgufo1j5c-kew0u6Z7PnxD6XRLOCuu2e4foZkkHgF1o2Kk6TE0/s400/1.bmp" /></a>
<br />
<br />
<br />
<br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggpLzLnWpHPMNu8Nd7TrVPcMPDPHK8MBLAKlSUdjp-gz1X9QJA7BLEYT8zvrlar5kqh6jGzonRORBpcDQ6dyhQoJnVfJrh5__6jWuqVdd7YdEPOFcvK30ZuHRfqyC04VRUd5pVCT-4cSo/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 90px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276316554508311426" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggpLzLnWpHPMNu8Nd7TrVPcMPDPHK8MBLAKlSUdjp-gz1X9QJA7BLEYT8zvrlar5kqh6jGzonRORBpcDQ6dyhQoJnVfJrh5__6jWuqVdd7YdEPOFcvK30ZuHRfqyC04VRUd5pVCT-4cSo/s400/1.bmp" /></a>
<br />
<br />
<br />
<br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTi5i47tGQVTgT4frCH3xnd7PpdXJm18j-S0p_vIxhRr3JeUKA6I2pM0tQeMbSTrwGpIIvrRe-dp_Nuj2JTexaDnPzzt22jJWV7nu2LhYdG3vjPSn6JYgzV6241bCltp22D1ptkhV0kqQ/s1600-h/1.bmp"><img style="WIDTH: 259px; HEIGHT: 136px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276316378652043778" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTi5i47tGQVTgT4frCH3xnd7PpdXJm18j-S0p_vIxhRr3JeUKA6I2pM0tQeMbSTrwGpIIvrRe-dp_Nuj2JTexaDnPzzt22jJWV7nu2LhYdG3vjPSn6JYgzV6241bCltp22D1ptkhV0kqQ/s400/1.bmp" /></a>
<br />
<br />
<br />
<br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSHQ3OYNF6EZecR3MGUE2ajBXii1K5vqctITyYMtbBW22E630GjfozOK7TcByUN5GZLGoyky0fPyMa-rn19DEU2Bkln2vzg2p1OBgqvn5SkWb-xT4dnMELVY7Y-9FKKe-5gvoeLWH7bbg/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 390px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276315920317648482" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSHQ3OYNF6EZecR3MGUE2ajBXii1K5vqctITyYMtbBW22E630GjfozOK7TcByUN5GZLGoyky0fPyMa-rn19DEU2Bkln2vzg2p1OBgqvn5SkWb-xT4dnMELVY7Y-9FKKe-5gvoeLWH7bbg/s400/1.bmp" /></a>
<br />
<br />
<br /><div>
<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2KBJhqMYNSFCxif30RrDOVb0HEmJgTA6crBvxCtccjFmgtAmWm4Y_5S-exu_NeiAbffiRHwWal4TNjJIw5Cjcp5d4-ICSEeXXTl0Z8kt_-qEowrOp_pX04ST-S6iLCZuBfHgEpcTo4Lw/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 152px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276315464273585778" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2KBJhqMYNSFCxif30RrDOVb0HEmJgTA6crBvxCtccjFmgtAmWm4Y_5S-exu_NeiAbffiRHwWal4TNjJIw5Cjcp5d4-ICSEeXXTl0Z8kt_-qEowrOp_pX04ST-S6iLCZuBfHgEpcTo4Lw/s400/1.bmp" /></a></div>
<br />
<br />
<br /><div><span style="font-size:85%;"><strong>Davisson-Germer experiment
<br /></strong>The electron diffraction experimental setup used by Davisson and Germer to verify de-Broglie’s hypothesis is as shown:
<br /></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifsnTPP-PwnRD5eLr0zpq1BfowurHpoP0nIu1WNEUiA_RMgshv4ztO7fXs35B0YebyMqzYSMWSpCokAP5hyphenhyphen-6eoR2kfid_PPLNeTAv6yPPCV47n53b305Hr7WNRBASf3YESBqpNtYkT9U/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 162px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276315020367789890" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifsnTPP-PwnRD5eLr0zpq1BfowurHpoP0nIu1WNEUiA_RMgshv4ztO7fXs35B0YebyMqzYSMWSpCokAP5hyphenhyphen-6eoR2kfid_PPLNeTAv6yPPCV47n53b305Hr7WNRBASf3YESBqpNtYkT9U/s400/1.bmp" /></a>
<br />
<br />
<br />
<br /><div><span style="font-size:85%;">The filament F is heated to produce electrons via thermionic emission. These electrons are passed through a narrow aperture forming a fine beam of accelerated electrons. The electron beam was then made to incident on a single crystalline sample of Nickel. The electrons scattered at different angles were counted using a detector. The experiment was repeated by recording the scattered electron intensities at various positions of the detector.
<br />A sharp maximum occurred in electron density at an angle of 500 with the incident beam for an accelerating potential of 54 V. The angle of incidence corresponding to this is 250 and from figure, glancing angle (angle of diffraction) is 650. From X-ray diffraction experiment, spacing of the planes responsible for diffraction was found to be 0.091 nm.
<br />Assuming first order diffraction, Bragg’s law can be written as,
<br />l = 2d sinq = 2×0.091×10-9×sin65 = 0.165 nm.
<br />By de-Broglie relation,
<br />l = h/(2meV)1/2 = (6.626×10-34) / (2×9.1×10-31×1.6×10-19×54)1/2 = 0.167 nm.
<br />Thus Davisson and Germer experiment directly verifies the de-Broglie hypothesis.</span></div>
<br />
<br /><div><span style="font-size:85%;"><strong>Characteristic properties of matter waves
<br /></strong>1. Matter waves are associated with moving particle.
<br />2. Wavelength of matter waves is inversely proportional to the velocity with which the particle is moving (l = h/mv). Hence a particle at rest has an infinite wavelength.
<br />3. Wavelength of matter waves is inversely proportional to the mass of the particle. Hence wavelike behaviour of heavier bodies is not very evident whereas wave nature of subatomic particles could be observed experimentally.
<br />4. Wavefunction is used to define a matter wave which is related to the probability of finding a particle at any place at any instant.
<br />5. Matter waves are represented by a wave packet made up of a group of waves of slightly differing wavelengths. Hence we talk of group velocity of matter waves rather than the phase velocity (velocity of a single wave). The group velocity can be shown to be equal to the particle velocity. </span>
<br /></div>
<br />
<br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj90kbkBoHrU3Kv7CGHsN4NKz0pX14_JVM590V-iP3os2_RdiBIQQEPURXF3RLMxHXoNltWFP2_NpX8nDX18xkCbe7Rl9PgCDj-DJ4QYiagfpEy0hl-GWjzAr2czapK24yob5pCWOKRGiU/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 146px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276313821990832338" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj90kbkBoHrU3Kv7CGHsN4NKz0pX14_JVM590V-iP3os2_RdiBIQQEPURXF3RLMxHXoNltWFP2_NpX8nDX18xkCbe7Rl9PgCDj-DJ4QYiagfpEy0hl-GWjzAr2czapK24yob5pCWOKRGiU/s400/1.bmp" /></a>
<br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPC1oM98mgU0fx8-vrWwTxveo7cpdFCGJJpVnsJyPBaPx-TvLhcFRfKjlriKs0QjgaZjxgZ9R15jsOhAgrJBF67BTITYVQo7Yfo9DrvjC4uzcksCNgnITCH4KJAdnfPwu0dLJxFMlNyA4/s1600-h/1.bmp"><img style="WIDTH: 382px; HEIGHT: 400px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276313444142172770" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPC1oM98mgU0fx8-vrWwTxveo7cpdFCGJJpVnsJyPBaPx-TvLhcFRfKjlriKs0QjgaZjxgZ9R15jsOhAgrJBF67BTITYVQo7Yfo9DrvjC4uzcksCNgnITCH4KJAdnfPwu0dLJxFMlNyA4/s400/1.bmp" /></a>
<br />
<br />
<br /><div>
<br />
<br /><div>
<br />
<br /><div></div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoUDom9hUeH6r718XjbD9eyP50y3Z8qGanW-NtfhA4lOK_S9hxsFfvceraotiWipYNDSpeSUaho6y2HNGJ4o3S7YX-y41E4N3U5iXWohAM5ZHVeP-uOfeyx3sDX9w8pxAR61HGs06w1CA/s1600-h/1.bmp"><img style="WIDTH: 292px; HEIGHT: 293px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276312950337295746" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoUDom9hUeH6r718XjbD9eyP50y3Z8qGanW-NtfhA4lOK_S9hxsFfvceraotiWipYNDSpeSUaho6y2HNGJ4o3S7YX-y41E4N3U5iXWohAM5ZHVeP-uOfeyx3sDX9w8pxAR61HGs06w1CA/s400/1.bmp" /></a>
<br />
<br />
<br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIxtX8f9pDNfbdHYSJ2OMp0JFjdRTmMreSMNTRg5nwOP1Tu4M-anTnVrH3IVmXp5oBcveyep-aI38XEVv9xjxyYc0VV7MjCi38OMlOgS0htLDVKrIH7_lmUSoO88m10Y7rbm_eGO_6fw8/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 396px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276312489687759810" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIxtX8f9pDNfbdHYSJ2OMp0JFjdRTmMreSMNTRg5nwOP1Tu4M-anTnVrH3IVmXp5oBcveyep-aI38XEVv9xjxyYc0VV7MjCi38OMlOgS0htLDVKrIH7_lmUSoO88m10Y7rbm_eGO_6fw8/s400/1.bmp" /></a></div>
<br />
<br />
<br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj072keDH2NsZI7MvjbFwuXqk5ODDE4MUYlDoUSWgLct0OvahB3Hg5WY116MLaHYC8dWsjhrG534jk4ePpYlI551x3luC9q7Gu9niptdQMxSXL89DSLRBlND6SPTEcD-u7XDzCfD2K6y2M/s1600-h/1.bmp"><img style="WIDTH: 400px; HEIGHT: 319px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5276311946339092674" border="0" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj072keDH2NsZI7MvjbFwuXqk5ODDE4MUYlDoUSWgLct0OvahB3Hg5WY116MLaHYC8dWsjhrG534jk4ePpYlI551x3luC9q7Gu9niptdQMxSXL89DSLRBlND6SPTEcD-u7XDzCfD2K6y2M/s400/1.bmp" /></a></div></div></div></div></div></div></div></div></div></div></div></div>
<br />RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com6tag:blogger.com,1999:blog-4803935933670175751.post-14068426866266602032008-07-25T06:10:00.002-07:002011-11-12T05:39:10.523-08:00Quantum Mechanics<div align="justify"><span style="font-family:times new roman;font-size:130%;"><span style="font-size:180%;">VTU Model question paper</span><br />2 a I The product of uncertainty between energy and time is<br />A) ≥h/2p B) ≥h/4p C) h/2p D)≤h/4p<br />II According to Max Born approximation, y2 represents<br />A) Energy density B) Particle density C) Probability density D) Charge density<br />III The first permitted energy level is called<br />A) Excited energy level B) Zero point energy C) Ground level D) None of these<br />IV) The wavefunction associated with a material particle is<br />A) Finite B) Continuous C) Single valued D) All the above<br />b. Set up time independent one dimensional Schrödinger wave equation.<br />c. What are eigen values and eigen function<br />d. Compute first three permitted energy values for an electron in a box of width 4Å.<br />(4+6+6+4)<br /><span style="font-size:180%;">Dec08/Jan09<br /></span>2 a 1) The product of uncertainty between angular momentum and angular displacement is<br />A) ≥h/2p B) ≥h/4p C) h/2p D)≤h/4p<br />2) Kinetic energy of electron acclerated by a voltage 50 Volts<br />A) 50 eV B) 10 eV C) 5 eV D) 15 eV<br />3) The energy of the lowest state in one dimensional potential box of length ‘a’ is<br />A) Zero B) 2h2/8ma2 C) h2/8ma2 D) h/8ma2<br />4) The wavefunction for the motion of particles in one dimensional potential box of length ‘a’ is given by yn = D sin npx/a where ‘D’ is normalization constant. The value of ‘D’ is<br />(04 Marks)<br />b. Set up time independent one dimensional Schrödinger wave equation. (06 Marks)<br />c. Write the physical significance of wavefunction. (04 Marks)<br />d. A quantum particle confined to one dimensional box of width ‘a’ is in its first excited state. What is the probability of finding the particle over an interval of (a/2) marked symmetrically at the centre of the box? (06 Marks)<br /><br /><span style="font-size:180%;">June-July 2009</span><br />2 a i) According to Max Born approximation, y2 represents<br />A) Energy density B) Particle density C) Probability density D) Charge density<br />ii) An electron has a speed of 100 m/s, accurate to 0.005%. The uncertainty in its position is<br />A) 0.01 m B) 0.0115 m C) 0.024 m D) 0.04 m<br />iii) An electron is moving in a box of length ‘a’. If ‘y1’ is the wavefunction at x = a/4 with n = 1 and y2 at x = a for n = 2, then y2/y1 is<br />iv) The lowest quantized energy of a particle of mass ‘m’ in a box of length ‘L’ is given by<br />A) Zero B) h2/8mL2 C) 2h2/8mL2 D) h2/2mL2 (04 Marks)<br />b. Explain Heisenberg’s uncertainty principle. Give its physical significance. (06 Marks)<br />c. Set up time independent one dimensional Schrödinger wave equation. (06 Marks)<br />d. A quantum particle confined to one dimensional box of width ‘a’ is in its first excited state. What is the probability of finding the particle over an interval of (a/2) marked symmetrically at the centre of the box? (04 Marks)<br /><br /><span style="font-size:180%;">Dec 09/ Jan 10</span><br />2 a i) The normalization of wavefunction is always possible, if<br />A) y y* dx = infinite B) y y* dx = finite<br />C) y y* dx =0 D) All of those<br />ii) Schrödinger’s wave equation is applicable for the particles with<br />A) Constant energy B) Variable energy C) Only constant potential energy<br />D) All of these<br />iii) The ground state energy of an electron in an infinite well is 5.6 meV. If the width of the well is doubled, the ground state energy is<br />A) 9.92×10-23 J B) 4.48× 10-22 J C) 2.24×10-22 J D) None of these<br />iv) The wavefunction is acceptable if it is<br />A) Finite everywhere B) Continuous everywhere C) Single valued everywhere<br />D) All of these (04 Marks)<br />b. State Heisenberg’s uncertainty principle and discuss its physical significance.<br />(06 Marks)<br />c. Solve the Scrodinger’s wave equation for allowed energy values in case of a particle in a potential box. (10 Marks)<br /><span style="font-size:180%;"><br />May/June 2010</span><br />2 a i) If free electron exists in a nucleus, its energy value must have a minimum energy of about<br />A) 4 MeV B) 20 MeV C) 20 KeV D) 10 KeV<br />ii) According to Max Born approximation, y2 represents<br />A) Energy density B) Particle density C) Probability density D) Charge density<br />iii) If E1 is the energy of the lowest state of a one dimensional potential box of length ‘a’ and E2 is the energy of the lowest state when the length of the box is halved, then<br />A) E2 = E1 B) E2 = 2E2 C) E2 = E1/2 D) E2 = 4E1<br />iv) ) The wavefunction for the motion of particles in one dimensional potential box of length ‘a’ is given by yn = A sin npx/a where ‘A’ is normalization constant. The value of ‘A’ is<br />(04 Marks)<br />b. State and explain Heisenberg’s uncertainty principle and prove that nuclei do not contain electron. (08 marks)<br />c. Discuss the wavefunctions and probability density for particle in an infinite potential well for first two states. (04 Marks)<br />d. An electron is bound in one dimensional potential well of width 0.18 nm. Find the energy value in eV of the second excited state. (04 Marks)<br /><br /><span style="font-size:180%;">January 2011</span><br />2 a. Choose your answers for the following:<br />i) The uncertainty in the determination of position of an electron is h/3p. Then, the uncertainty in the determination of its momentum is<br />A) ¾ B) ¼ C) 4/3 D) 3<br />ii) The probability of locating a particle is maximum<br />A) at the centre of the wavepacket B) at the nodes of the wavepacket<br />C) cannot be determined D) none of these<br />iii) In Davisson and Germer experiment, when 54 volts was applied to electrons, the pronounced scattering direction was found to be at<br />A) 900 B) 1200 C) 500 D) none of these<br />iv) The ground state energy of an electron in an one dimensional infinite potential well of width 2Å is 16 eV. Its energy in third excited state is<br />A) 32 eV B) 64 eV C) 144 eV D) 256 eV (04 Marks)<br />b. State and explain Heisenberg’s uncertainty principle (04 Marks)<br />c. Find the eigen value and eigen functions for an electron in one dimensional potential well of infinite height. (08 Marks)<br />d. Estimate the time spent by an atom in the excited state during the excitation and de-excitation processes, when a spectral line of wavelength 546 nm and width 10-14 m is emitted. (04 marks)</span><br /><p class="MsoNormal" align="center" style="margin-bottom:0in;margin-bottom:.0001pt; text-align:center;line-height:normal"><b><span style="font-family: 'Times New Roman', serif; "><span class="Apple-style-span" >June/July 2011</span><span class="Apple-style-span" ><o:p></o:p></span></span></b></p> <p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height: normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><o:p> </o:p></span><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><span> </span>2 a. i) An electron is moving in a box of length ‘a’. If ‘</span><span style="font-size:12.0pt;font-family:Symbol; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"; mso-char-type:symbol;mso-symbol-font-family:Symbol"><span>y</span></span><sub><span style="font-size:12.0pt;font-family:"Times New Roman","serif"">1</span></sub><span style="font-size:12.0pt;font-family:"Times New Roman","serif"">’ is the wavefunction at x = a/4 with n = 1 and </span><span style="font-size:12.0pt; font-family:Symbol;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman";mso-char-type:symbol;mso-symbol-font-family:Symbol"><span>y</span></span><sub><span style="font-size:12.0pt;font-family:"Times New Roman","serif"">2</span></sub><span style="font-size:12.0pt;font-family:"Times New Roman","serif""> at x = a for n = 2, then </span><span style="font-size:12.0pt;font-family:Symbol;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-char-type:symbol; mso-symbol-font-family:Symbol"><span>y</span></span><sub><span style="font-size:12.0pt;font-family:"Times New Roman","serif"">2</span></sub><span style="font-size:12.0pt;font-family:"Times New Roman","serif"">/</span><span style="font-size:12.0pt;font-family:Symbol;mso-ascii-font-family:"Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-font-family: Symbol"><span>y</span></span><sub><span style="font-size:12.0pt;font-family:"Times New Roman","serif"">1</span></sub><span style="font-size:12.0pt;font-family:"Times New Roman","serif""> is</span></p><p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;line-height: normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><span> </span>A) </span><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><span style="position:relative;top:8.5pt;mso-text-raise:-8.5pt"><img width="13" height="31" src="file:///C:/DOCUME~1/admin/LOCALS~1/Temp/msohtmlclip1/01/clip_image002.gif" shapes="_x0000_i1025" /></span></span><span style="font-size: 12.0pt;font-family:"Times New Roman","serif""><span> </span>B) </span><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><span style="position:relative;top:12.0pt;mso-text-raise:-12.0pt"><img width="17" height="38" src="file:///C:/DOCUME~1/admin/LOCALS~1/Temp/msohtmlclip1/01/clip_image004.gif" shapes="_x0000_i1026" /></span></span><span style="font-size: 12.0pt;font-family:"Times New Roman","serif""><span> </span>C) 0<span> </span>D) </span><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><span style="position:relative;top:4.5pt;mso-text-raise:-4.5pt"><img width="10" height="20" src="file:///C:/DOCUME~1/admin/LOCALS~1/Temp/msohtmlclip1/01/clip_image006.gif" shapes="_x0000_i1027" /></span></span></p> <p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;text-align: justify;line-height:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><span> </span>ii) For a particle in an infinite potential well in its 1<sup>st</sup> excited state, the probability of finding the particle at the center of box is<o:p></o:p></span></p> <p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;text-align: justify;line-height:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><span> </span>A) 0<span> </span>B) 0.25<span> </span>C) 0.5<span> </span>D) 0.1<o:p></o:p></span></p> <p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;text-align: justify;line-height:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><span> </span>iii) To become a nuclear constituent, the K.R of e<sup>-</sup> must be of the order of<o:p></o:p></span></p> <p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;text-align: justify;line-height:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><span> </span>A) 20MeV<span> </span><span> </span>B) 2MeV<span> </span>C) 20eV<span> </span>D) Zero<o:p></o:p></span></p> <p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;text-align: justify;line-height:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><span> </span>iv)<span> </span>An electron has speed of 100ms<sup>-1</sup> accurate to 0.05%. The uncertainty in its position is<o:p></o:p></span></p> <p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;text-align: justify;line-height:normal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif"">A) 0.01m<span> </span>B) 0.0115m<span> </span>C) 0.024m<span> </span><span> </span>D) 0.04m<span> </span>(04 Marks)<o:p></o:p></span></p> <p class="MsoNoSpacing" style="text-align:justify"><span> </span>b. What is a wave function? Explain the properties of a wave function.<span> </span>(04 Marks)</p> <p class="MsoNoSpacing" style="text-align:justify"><span> </span>c. Derive the expression for energy Eigen value for an electron in potential well of infinite depth.<span> </span><span> </span>(06 Marks) </p> <p class="MsoNoSpacing" style="text-align:justify"><span> </span>d. A quantum particle confined to one dimensional box of width ‘a’ is in its first excited state. What is the probability of finding the particle over an interval of (<!--[if supportFields]><span style="'mso-element:field-begin'"></span> QUOTE <span style="'position:relative;"><![if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75" style="'width:15.75pt;height:18.75pt'" equationxml="" version=""1.0"" encoding=""UTF-8"" standalone=""yes"?"> <?mso-application progid="Word.Document"?> <w:worddocument aml=""http://schemas.microsoft.com/aml/2001/core"" dt=""uuid:C2F41010-65B3-11d1-A29F-00AA00C14882"" ve=""http://schemas.openxmlformats.org/markup-compatibility/2006"" o=""urn:schemas-microsoft-com:office:office"" m=""http://schemas.openxmlformats.org/officeDocument/2006/math"" v=""urn:schemas-microsoft-com:vml"" w10=""urn:schemas-microsoft-com:office:word"" w=""http://schemas.microsoft.com/office/word/2003/wordml"" wx=""http://schemas.microsoft.com/office/word/2003/auxHint"" wsp=""http://schemas.microsoft.com/office/word/2003/wordml/sp2"" sl=""http://schemas.microsoft.com/schemaLibrary/2003/core"" macrospresent=""no"" embeddedobjpresent=""no"" ocxpresent=""no"" space=""preserve""><w:ignoresubtree val=""http://schemas.microsoft.com/office/word/2003/wordml/sp2"/"><o:documentproperties><o:version>12</o:Version></o:DocumentProperties><w:docpr><w:view val=""print"/"><w:zoom percent=""100"/"><w:donotembedsystemfonts/><w:defaulttabstop val=""720"/"><w:drawinggridhorizontalspacing val=""110"/"><w:displayhorizontaldrawinggridevery val=""2"/"><w:displayverticaldrawinggridevery val=""2"/"><w:punctuationkerning/><w:characterspacingcontrol val=""DontCompress"/"><w:optimizeforbrowser/><w:validateagainstschema/><w:saveinvalidxml val=""off"/"><w:ignoremixedcontent val=""off"/"><w:alwaysshowplaceholdertext val=""off"/"><w:compat><w:breakwrappedtables/><w:snaptogridincell/><w:wraptextwithpunct/><w:useasianbreakrules/><w:dontgrowautofit/></w:compat><wsp:rsids><wsp:rsidroot val=""00FB3236"/"><wsp:rsid val=""0003025E"/"><wsp:rsid val=""00087E47"/"><wsp:rsid val=""000A3BE7"/"><wsp:rsid val=""000C34A6"/"><wsp:rsid val=""000D0CB2"/"><wsp:rsid val=""000D6390"/"><wsp:rsid val=""00104EF5"/"><wsp:rsid val=""001337A6"/"><wsp:rsid val=""00174EFF"/"><wsp:rsid val=""00190605"/"><wsp:rsid val=""001A425B"/"><wsp:rsid val=""001A5C49"/"><wsp:rsid val=""001B7732"/"><wsp:rsid val=""001D025F"/"><wsp:rsid val=""001F2FD9"/"><wsp:rsid val=""00206055"/"><wsp:rsid val=""00304A3F"/"><wsp:rsid val=""0030724E"/"><wsp:rsid val=""00341B3E"/"><wsp:rsid val=""00377E1A"/"><wsp:rsid val=""003856A3"/"><wsp:rsid val=""003A2F12"/"><wsp:rsid val=""003F78A0"/"><wsp:rsid val=""0040530E"/"><wsp:rsid val=""0042258D"/"><wsp:rsid val=""00453F35"/"><wsp:rsid val=""0048694D"/"><wsp:rsid val=""0050423D"/"><wsp:rsid val=""00512BAF"/"><wsp:rsid val=""00522A48"/"><wsp:rsid val=""00525674"/"><wsp:rsid val=""005321C6"/"><wsp:rsid val=""0059273E"/"><wsp:rsid val=""005B5B91"/"><wsp:rsid val=""005C48F7"/"><wsp:rsid val=""005D7B2B"/"><wsp:rsid val=""00613340"/"><wsp:rsid val=""006173A7"/"><wsp:rsid val=""0066159D"/"><wsp:rsid val=""006751AC"/"><wsp:rsid val=""00697603"/"><wsp:rsid val=""006B4921"/"><wsp:rsid val=""006F5D1A"/"><wsp:rsid val=""00737DE6"/"><wsp:rsid val=""0087096B"/"><wsp:rsid val=""008D17BD"/"><wsp:rsid val=""008D5330"/"><wsp:rsid val=""00972F42"/"><wsp:rsid val=""00983744"/"><wsp:rsid val=""009D1221"/"><wsp:rsid val=""009F74D9"/"><wsp:rsid val=""00A17F73"/"><wsp:rsid val=""00A63CF6"/"><wsp:rsid val=""00A71B5D"/"><wsp:rsid val=""00A728AC"/"><wsp:rsid val=""00A74532"/"><wsp:rsid val=""00A832B3"/"><wsp:rsid val=""00A87FD6"/"><wsp:rsid val=""00A944C9"/"><wsp:rsid val=""00AD0807"/"><wsp:rsid val=""00B201C8"/"><wsp:rsid val=""00BD695D"/"><wsp:rsid val=""00C21300"/"><wsp:rsid val=""00C250BB"/"><wsp:rsid val=""00C43F54"/"><wsp:rsid val=""00CA0CAF"/"><wsp:rsid val=""00CC6A9B"/"><wsp:rsid val=""00CD1847"/"><wsp:rsid val=""00CD6733"/"><wsp:rsid val=""00CE2542"/"><wsp:rsid val=""00D00B25"/"><wsp:rsid val=""00D1147F"/"><wsp:rsid val=""00D16319"/"><wsp:rsid val=""00D66ADF"/"><wsp:rsid val=""00DC5B86"/"><wsp:rsid val=""00E57CA4"/"><wsp:rsid val=""00E703FA"/"><wsp:rsid val=""00E7397D"/"><wsp:rsid val=""00E94474"/"><wsp:rsid val=""00EB1669"/"><wsp:rsid val=""00EC1562"/"><wsp:rsid val=""00EF5C3F"/"><wsp:rsid val=""00F12CFC"/"><wsp:rsid val=""00F13BDB"/"><wsp:rsid val=""00F14302"/"><wsp:rsid val=""00F227AC"/"><wsp:rsid val=""00F31204"/"><wsp:rsid val=""00F37AEA"/"><wsp:rsid val=""00FB3236"/"></wsp:rsids></w:docPr><w:body><w:p rsidr=""00000000"" rsidrdefault=""00512BAF""><m:omathpara><m:omath><m:r><w:rpr><w:rfonts ascii=""Cambria" ansi=""Cambria"><wx:font val=""Cambria"><w:i/></w:rPr><m:t> </m:t></m:r><m:f><m:fpr><m:ctrlpr><w:rpr><w:rfonts ascii=""Cambria" ansi=""Cambria"><wx:font val=""Cambria"><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rpr><w:rfonts ascii=""Cambria" ansi=""Cambria"><wx:font val=""Cambria"><w:i/></w:rPr><m:t>a</m:t></m:r></m:num><m:den><m:r><w:rpr><w:rfonts ascii=""Cambria" ansi=""Cambria"><wx:font val=""Cambria"><w:i/></w:rPr><m:t>2</m:t></m:r></m:den></m:f><m:r><w:rpr><w:rfonts ascii=""Cambria" ansi=""Cambria"><wx:font val=""Cambria"><w:i/></w:rPr><m:t> )</m:t></m:r></m:oMath></m:oMathPara></w:p><w:sectpr rsidr=""00000000""><w:pgsz w=""12240"" h=""15840"/"><w:pgmar top=""1440"" right=""1440"" bottom=""1440"" left=""1440"" header=""720"" footer=""720"" gutter=""0"/"><w:cols space=""720"/"></w:sectPr></w:body></w:wordDocument>"> <v:imagedata src="file:///C:\DOCUME~1\admin\LOCALS~1\Temp\msohtmlclip1\01\clip_image007.png" title="" chromakey="white"> </v:shape><![endif]><![if !vml]><img width="21" height="25" src="file:///C:\DOCUME~1\admin\LOCALS~1\Temp\msohtmlclip1\01\clip_image008.gif" shapes="_x0000_i1032" /><![endif]></span><span style="'mso-spacerun:yes'"> </span><span style="'mso-element:field-separator'"></span><![endif]--><span style="position:relative;top:7.0pt;mso-text-raise:-7.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1028" type="#_x0000_t75" style="'width:15.75pt;height:18.75pt'" equationxml="" version=""1.0"" encoding=""UTF-8"" standalone=""yes"?"> <?mso-application progid="Word.Document"?> <w:worddocument aml=""http://schemas.microsoft.com/aml/2001/core"" dt=""uuid:C2F41010-65B3-11d1-A29F-00AA00C14882"" ve=""http://schemas.openxmlformats.org/markup-compatibility/2006"" o=""urn:schemas-microsoft-com:office:office"" m=""http://schemas.openxmlformats.org/officeDocument/2006/math"" v=""urn:schemas-microsoft-com:vml"" w10=""urn:schemas-microsoft-com:office:word"" w=""http://schemas.microsoft.com/office/word/2003/wordml"" wx=""http://schemas.microsoft.com/office/word/2003/auxHint"" wsp=""http://schemas.microsoft.com/office/word/2003/wordml/sp2"" sl=""http://schemas.microsoft.com/schemaLibrary/2003/core"" macrospresent=""no"" embeddedobjpresent=""no"" ocxpresent=""no"" space=""preserve""><w:ignoresubtree val=""http://schemas.microsoft.com/office/word/2003/wordml/sp2"/"><o:documentproperties><o:version>12</o:Version></o:DocumentProperties><w:docpr><w:view val=""print"/"><w:zoom percent=""100"/"><w:donotembedsystemfonts/><w:defaulttabstop val=""720"/"><w:drawinggridhorizontalspacing val=""110"/"><w:displayhorizontaldrawinggridevery val=""2"/"><w:displayverticaldrawinggridevery val=""2"/"><w:punctuationkerning/><w:characterspacingcontrol val=""DontCompress"/"><w:optimizeforbrowser/><w:validateagainstschema/><w:saveinvalidxml val=""off"/"><w:ignoremixedcontent val=""off"/"><w:alwaysshowplaceholdertext val=""off"/"><w:compat><w:breakwrappedtables/><w:snaptogridincell/><w:wraptextwithpunct/><w:useasianbreakrules/><w:dontgrowautofit/></w:compat><wsp:rsids><wsp:rsidroot val=""00FB3236"/"><wsp:rsid val=""0003025E"/"><wsp:rsid val=""00087E47"/"><wsp:rsid val=""000A3BE7"/"><wsp:rsid val=""000C34A6"/"><wsp:rsid val=""000D0CB2"/"><wsp:rsid val=""000D6390"/"><wsp:rsid val=""00104EF5"/"><wsp:rsid val=""001337A6"/"><wsp:rsid val=""00174EFF"/"><wsp:rsid val=""00190605"/"><wsp:rsid val=""001A425B"/"><wsp:rsid val=""001A5C49"/"><wsp:rsid val=""001B7732"/"><wsp:rsid val=""001D025F"/"><wsp:rsid val=""001F2FD9"/"><wsp:rsid val=""00206055"/"><wsp:rsid val=""00304A3F"/"><wsp:rsid val=""0030724E"/"><wsp:rsid val=""00341B3E"/"><wsp:rsid val=""00377E1A"/"><wsp:rsid val=""003856A3"/"><wsp:rsid val=""003A2F12"/"><wsp:rsid val=""003F78A0"/"><wsp:rsid val=""0040530E"/"><wsp:rsid val=""0042258D"/"><wsp:rsid val=""00453F35"/"><wsp:rsid val=""0048694D"/"><wsp:rsid val=""0050423D"/"><wsp:rsid val=""00512BAF"/"><wsp:rsid val=""00522A48"/"><wsp:rsid val=""00525674"/"><wsp:rsid val=""005321C6"/"><wsp:rsid val=""0059273E"/"><wsp:rsid val=""005B5B91"/"><wsp:rsid val=""005C48F7"/"><wsp:rsid val=""005D7B2B"/"><wsp:rsid val=""00613340"/"><wsp:rsid val=""006173A7"/"><wsp:rsid val=""0066159D"/"><wsp:rsid val=""006751AC"/"><wsp:rsid val=""00697603"/"><wsp:rsid val=""006B4921"/"><wsp:rsid val=""006F5D1A"/"><wsp:rsid val=""00737DE6"/"><wsp:rsid val=""0087096B"/"><wsp:rsid val=""008D17BD"/"><wsp:rsid val=""008D5330"/"><wsp:rsid val=""00972F42"/"><wsp:rsid val=""00983744"/"><wsp:rsid val=""009D1221"/"><wsp:rsid val=""009F74D9"/"><wsp:rsid val=""00A17F73"/"><wsp:rsid val=""00A63CF6"/"><wsp:rsid val=""00A71B5D"/"><wsp:rsid val=""00A728AC"/"><wsp:rsid val=""00A74532"/"><wsp:rsid val=""00A832B3"/"><wsp:rsid val=""00A87FD6"/"><wsp:rsid val=""00A944C9"/"><wsp:rsid val=""00AD0807"/"><wsp:rsid val=""00B201C8"/"><wsp:rsid val=""00BD695D"/"><wsp:rsid val=""00C21300"/"><wsp:rsid val=""00C250BB"/"><wsp:rsid val=""00C43F54"/"><wsp:rsid val=""00CA0CAF"/"><wsp:rsid val=""00CC6A9B"/"><wsp:rsid val=""00CD1847"/"><wsp:rsid val=""00CD6733"/"><wsp:rsid val=""00CE2542"/"><wsp:rsid val=""00D00B25"/"><wsp:rsid val=""00D1147F"/"><wsp:rsid val=""00D16319"/"><wsp:rsid val=""00D66ADF"/"><wsp:rsid val=""00DC5B86"/"><wsp:rsid val=""00E57CA4"/"><wsp:rsid val=""00E703FA"/"><wsp:rsid val=""00E7397D"/"><wsp:rsid val=""00E94474"/"><wsp:rsid val=""00EB1669"/"><wsp:rsid val=""00EC1562"/"><wsp:rsid val=""00EF5C3F"/"><wsp:rsid val=""00F12CFC"/"><wsp:rsid val=""00F13BDB"/"><wsp:rsid val=""00F14302"/"><wsp:rsid val=""00F227AC"/"><wsp:rsid val=""00F31204"/"><wsp:rsid val=""00F37AEA"/"><wsp:rsid val=""00FB3236"/"></wsp:rsids></w:docPr><w:body><w:p rsidr=""00000000"" rsidrdefault=""00512BAF""><m:omathpara><m:omath><m:r><w:rpr><w:rfonts ascii=""Cambria" ansi=""Cambria"><wx:font val=""Cambria"><w:i/></w:rPr><m:t> </m:t></m:r><m:f><m:fpr><m:ctrlpr><w:rpr><w:rfonts ascii=""Cambria" ansi=""Cambria"><wx:font val=""Cambria"><w:i/></w:rPr></m:ctrlPr></m:fPr><m:num><m:r><w:rpr><w:rfonts ascii=""Cambria" ansi=""Cambria"><wx:font val=""Cambria"><w:i/></w:rPr><m:t>a</m:t></m:r></m:num><m:den><m:r><w:rpr><w:rfonts ascii=""Cambria" ansi=""Cambria"><wx:font val=""Cambria"><w:i/></w:rPr><m:t>2</m:t></m:r></m:den></m:f><m:r><w:rpr><w:rfonts ascii=""Cambria" ansi=""Cambria"><wx:font val=""Cambria"><w:i/></w:rPr><m:t> )</m:t></m:r></m:oMath></m:oMathPara></w:p><w:sectpr rsidr=""00000000""><w:pgsz w=""12240"" h=""15840"/"><w:pgmar top=""1440"" right=""1440"" bottom=""1440"" left=""1440"" header=""720"" footer=""720"" gutter=""0"/"><w:cols space=""720"/"></w:sectPr></w:body></w:wordDocument>"> <v:imagedata src="file:///C:\DOCUME~1\admin\LOCALS~1\Temp\msohtmlclip1\01\clip_image007.png" title="" chromakey="white"> </v:shape><![endif]--><!--[if !vml]--><img width="21" height="25" src="file:///C:/DOCUME~1/admin/LOCALS~1/Temp/msohtmlclip1/01/clip_image008.gif" shapes="_x0000_i1028" /><!--[endif]--></span><!--[if supportFields]><span style="'mso-element:field-end'"></span><![endif]--><span> </span>marked symmetrically at the centre of box.<span> </span>(06 Marks)</p> <p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;text-align: justify;line-height:normal"><span class="Apple-style-span" ><br /></span></p></div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPOdQ0e8u-iVBEKVQTs488o8yVhZDDI_wG0XYQItrQ419vt1G9jZHzGCA5fWf_-NahIeQMwKfbpD7Sm0-U1bZVIWBF6Nrj2eONB9_iLYbSmH7dTqTuaoR61I-1lr7CIAwYK1wnQF3VvW0/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490673673015580402" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 262px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPOdQ0e8u-iVBEKVQTs488o8yVhZDDI_wG0XYQItrQ419vt1G9jZHzGCA5fWf_-NahIeQMwKfbpD7Sm0-U1bZVIWBF6Nrj2eONB9_iLYbSmH7dTqTuaoR61I-1lr7CIAwYK1wnQF3VvW0/s400/sds.bmp" border="0" /></a><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF5bVtWWI11QsksiVoHxC6Mp_AKQfvcaby53DXpZ68dbUA-oShZwep5GqnHvcq7OA0JvI2597Shs0utebaffhSCum9UGjWP0_4B9NmIs_NDXe1_2bHxwhHij9ScLY_FubKSKXI4ynuETQ/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490673394053678034" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 329px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF5bVtWWI11QsksiVoHxC6Mp_AKQfvcaby53DXpZ68dbUA-oShZwep5GqnHvcq7OA0JvI2597Shs0utebaffhSCum9UGjWP0_4B9NmIs_NDXe1_2bHxwhHij9ScLY_FubKSKXI4ynuETQ/s400/sds.bmp" border="0" /></a><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXAkQW_SU-4VB5jNpcAEq8jEpph-W-VZCh0DaTUpaWdKXocMpfCslm-AfbwY7AXURjmgoKfMqXC_gMAdv6liVZTaAmSF2MipmovJeWtFzPPk5ypk3Ykah9zXCOeo8Dka1MelfbNVjYz6Y/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490673038417007330" style="WIDTH: 374px; CURSOR: hand; HEIGHT: 400px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXAkQW_SU-4VB5jNpcAEq8jEpph-W-VZCh0DaTUpaWdKXocMpfCslm-AfbwY7AXURjmgoKfMqXC_gMAdv6liVZTaAmSF2MipmovJeWtFzPPk5ypk3Ykah9zXCOeo8Dka1MelfbNVjYz6Y/s400/sds.bmp" border="0" /></a><br /><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEig1X-JhhdkU5baUNC-FKxG9hJFuYWEOWoki55p5iqaVWqOuU27ko2TVhEPx6NGWs3-WHbAEiqAOvZbiGsTpKC6jnips3mvKzfM1AIuMEgo-UDhIqBUbxguj1OmhTqgPphybNbBanNJsiQ/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490672686952146370" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 382px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEig1X-JhhdkU5baUNC-FKxG9hJFuYWEOWoki55p5iqaVWqOuU27ko2TVhEPx6NGWs3-WHbAEiqAOvZbiGsTpKC6jnips3mvKzfM1AIuMEgo-UDhIqBUbxguj1OmhTqgPphybNbBanNJsiQ/s400/sds.bmp" border="0" /></a><br /><br /><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6h3nDsc-vPp7m4ZnwvjJWRdeyvvIcxw7Yb1sR8mpUXGu-fwVnLtjI93q0lxdG3OwGzTTF-nTszYiKcg4H27bZDkuPfY9s0L8dM6sTDh8iSouGHlTMQXLAmUkwzmDQSgolb2LGiakeXrU/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490672288353267762" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 311px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6h3nDsc-vPp7m4ZnwvjJWRdeyvvIcxw7Yb1sR8mpUXGu-fwVnLtjI93q0lxdG3OwGzTTF-nTszYiKcg4H27bZDkuPfY9s0L8dM6sTDh8iSouGHlTMQXLAmUkwzmDQSgolb2LGiakeXrU/s400/sds.bmp" border="0" /></a><br /><br /><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXPaG1D19RdK6fPZVuUJ4sP42-OABmelsAMHI95fZx0dh9AWJfq6e3YIp5iYbzF9R4haLq8YmLgibh4GJz2h9tHqa8ZG2WabuFkiL_vs7gSdZFNnNnkdvCjj62OW1ozdQi_ot_BWgecZk/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490671971765490562" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 367px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXPaG1D19RdK6fPZVuUJ4sP42-OABmelsAMHI95fZx0dh9AWJfq6e3YIp5iYbzF9R4haLq8YmLgibh4GJz2h9tHqa8ZG2WabuFkiL_vs7gSdZFNnNnkdvCjj62OW1ozdQi_ot_BWgecZk/s400/sds.bmp" border="0" /></a><br /><br /><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6H40lgJfDYUzMlhpWDedSZfvAv2OMSP1Z0REn-4adkzucHGk8TNwwEZXggTIpCTVKWbBUTZc0ByfvEbcA2LVPew6SQbHGgNsgUw0aLLzG62IYgNh92SpxsLmQ0hE9yDSeWhFw7E_LdNo/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490671599429170738" style="WIDTH: 355px; CURSOR: hand; HEIGHT: 400px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6H40lgJfDYUzMlhpWDedSZfvAv2OMSP1Z0REn-4adkzucHGk8TNwwEZXggTIpCTVKWbBUTZc0ByfvEbcA2LVPew6SQbHGgNsgUw0aLLzG62IYgNh92SpxsLmQ0hE9yDSeWhFw7E_LdNo/s400/sds.bmp" border="0" /></a><br /><br /><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6Zg2e4fDEm7kELW-xTZ1a-JxPimhibwbgS3TPHxjXdbpx2a2lkYlL3ukCjg00MqiijzMDiH2mJhLWJkuJlI6isKqOYp6-NcJuKEUQ6lWdMl_cnsDxloZpGi5Is52VYAWNxBdkysR86K8/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490671341681145650" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 190px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6Zg2e4fDEm7kELW-xTZ1a-JxPimhibwbgS3TPHxjXdbpx2a2lkYlL3ukCjg00MqiijzMDiH2mJhLWJkuJlI6isKqOYp6-NcJuKEUQ6lWdMl_cnsDxloZpGi5Is52VYAWNxBdkysR86K8/s400/sds.bmp" border="0" /></a><br /><br /><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjh9eMGd4_untRceQtwTEOZ3hVu-oDB9TyRURoa3vI3IvExawcznknRpXlB-FLeVGTOLAO8I0-n-WE627fRwo5I43Hvs8-SdGLhJOFgX4bEDdcqI4JIyhsLrMvim2g5agmoIjon1Ugcos/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490671019925142338" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 346px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjh9eMGd4_untRceQtwTEOZ3hVu-oDB9TyRURoa3vI3IvExawcznknRpXlB-FLeVGTOLAO8I0-n-WE627fRwo5I43Hvs8-SdGLhJOFgX4bEDdcqI4JIyhsLrMvim2g5agmoIjon1Ugcos/s400/sds.bmp" border="0" /></a><br /><br /><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB9uftCk5gMjdWFMk4fZbAuEcsA2aNZvH_3_f9yT-DdOXMQsRS21nTbTP0-0dBPZgNrAZHfNiySXkmJeXhZR5PdCDqfd80rwKXz3UlcuCoUlu5MQg1dYhO4FD2xV2rwg5epXkIMkfxTCI/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490670646581918562" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 285px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB9uftCk5gMjdWFMk4fZbAuEcsA2aNZvH_3_f9yT-DdOXMQsRS21nTbTP0-0dBPZgNrAZHfNiySXkmJeXhZR5PdCDqfd80rwKXz3UlcuCoUlu5MQg1dYhO4FD2xV2rwg5epXkIMkfxTCI/s400/sds.bmp" border="0" /></a><br /><br /><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq8i55fMinXiuK9z0U3E53OKDjjeCqeDAX0b5-UU7AN0aC2MVttyZkhqKwjS2GzJ4XkpyGRI4GzWjdcO4z0esVCDUL-tRmDTabsngujhe9-Iv4frxiw-zjAaQ_fs76RHk40vKeQRW4qK4/s1600/sds.bmp"><img id="BLOGGER_PHOTO_ID_5490670367398929442" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 157px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq8i55fMinXiuK9z0U3E53OKDjjeCqeDAX0b5-UU7AN0aC2MVttyZkhqKwjS2GzJ4XkpyGRI4GzWjdcO4z0esVCDUL-tRmDTabsngujhe9-Iv4frxiw-zjAaQ_fs76RHk40vKeQRW4qK4/s400/sds.bmp" border="0" /></a><br /><br /><div><br /><div></div></div></div></div></div></div></div></div></div></div>RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com2tag:blogger.com,1999:blog-4803935933670175751.post-87526603343944718932008-07-25T06:10:00.001-07:002012-11-29T04:48:04.654-08:00CLASSICAL FREE ELECTRON THEORY OF METALS<div dir="ltr" style="text-align: left;" trbidi="on">
<div align="justify">
<b><span style="font-size: 180%;">VTU Model Question paper</span><br />3.a.I In a metal, if the temperature is increased, then resistivity<br />A) Increases B) decreases C) remains same D) none of these<br />II The T > 0K probability of occupancy of Fermi level is<br />A) 75% B) 90% C) 100% D) 50%<br />III The electron mobility in metals is given by<br />A) vd/V B) vd/E C) vd/L D) vd/t<br />IV The Fermi factor for E = EF at any temperature is<br />A) 1 B) ½ C) 0 D) 2<br />b. Define drift velocity, mobility and relaxation time for free electron, derive the expression for conductivity in metals.<br />c. The Fermi level in Silver is 5.5 eV. What is the energies for which the probabilities of occupancy at 300 K are 0.99 and 0.01. (4+10+6)<br /><span style="font-size: 180%;">December 08 / January 09</span><br />3 a. 1) If the mobility of electron in a metal increases, the resistivity<br />i) Decreases ii) Increases iii) Remains constant iv) none of these.<br />2) Ohms law relates to the electric field E, conductivity s and current density J as<br />i) J = E/s ii) J = sE2 iii) J = s/E iv) J = sE<br />3) The average drift velocity vd of electrons in a metal is related to the electric field and collision time t as<br />4) Experimentally specific heat at constant volume Cv is given by<br />i) 3/2 R ii) 10 -4 RT iii) 2/3 R iv) 10 -4 R (04 Marks)<br />b.Write down the assumptions of classical free electron theory. (04 Marks)<br />c.Explain failure of classical free electron theory (06 Marks)<br />d.<a href="http://www.blogger.com/blogger.g?blogID=4803935933670175751" name="OLE_LINK2">Find the temperature at which there is 1% probability that a state with an energy 0.5 eV above Fermi energy is occupied. </a>(06 Marks)<br /><span style="font-size: 180%;">June-July 2009</span><br />3 a. i) If the mobility of the electron is 7 × 10-3 m2/vs, when accelerated by a field 1v/cm, the vd is given by<br />A) 7 × 10-3 m/s B) 0.7 m/s C) 7 × 10 -2 m/s D) 0.007 m/s<br />ii) The temperature dependence for electrical resistivity of metal is<br />A) r µ 1/T B) r µ 1/ÖT C) rµÖT D) rµ T<br />iii) The fermi factor for E = EF at T > 0K is<br />A) 1 B) ½ C) 0 D) 2<br />iv)According to quantum free electron theory, the energy level in a metal are<br />A) Continuous B) Discrete C) Overlapping D) None (04 Marks)<br />b.Derive an expression for density of states for conduction electron for unit volume of metal. (08 Marks)<br />c.Discuss the various drawbacks of classical free electron theory of metals. What are the assumptions made in quantum theory to overcome (08 Marks)<br /><span style="font-size: 180%;">December 09 / January 10</span><br />3 a. i) For ordinary metals, the resistivity versus temperature curve at T = 0,<br />A) has a positive intercept B) has a negative intercept<br />C) goes through the origin D) none of these<br />ii) Which one of the following is correct for current density<br />A) J = neAvd B) J = neA/vd C) J = nevd D) J = 1/nevd<br />iii) The value of Fermi distribution function at absolute zero (T= 0 K) is 1, under the condition<br />A) E = EF B) E > EF C) E >> EF D) E < EF<br />iv) If the Fermi energy of silver is 5.5 eV, the Fermi velocity of conduction electron is<br />A) 0.98 × 106 m/s B) 1.39 × 106 m/s C) 2.46 × 105 m/s D) None of these (04 Marks)<br />b. Describe how quantum free electron theory has been successful in overcoming the failures of classical free electron theory. (06 Marks)<br />c. What is Fermi energy? Discuss variation of Fermi factor with energy and temperature. (06 Marks)<br />d. Calculate the probability of an electron occupying an energy level 0.02 eV above the Fermi level at 200 K, in a material. (04 Marks)<br /><span style="font-size: 180%;">May/June 2010</span><br />3 a i) The collision time and root mean square velocity of an electron at room temperature are 3×10-14 sec and 1×105 m/s respectively. The classical value of mean free path of the electron is<br />A) 3×10-19 nm B) 3Å C) 3 nm D) 17.3 nm<br />ii) Mobility of electron is<br />A) Reciprocal of conductivity B) Flow of electrons per unit<br />C) Reciprocal of resistivity D) Average electron drift velocity per unit electric field<br />iii) The quantum mechanical expression for electrical conductivity is<br />A) s = m*vF/ne2lF B) s = ne2lF/m2vF C) s = m*vF/n2e2lF D) s = m*/ne2lF<br />iv) If the Fermi energy of metal at 00 K is 5 eV, f(E) for Fermi energy at T>00K is<br />A) 0.5 eV B) 1 eV C) 0.75 eV D) 0 eV (04 Marks)<br />b. Define relaxation time and discuss the dependence of electrical resistivity of metals with temperature and impurity. (06 Marks)<br />c. Explain how quantum free electron theory succeeds in overcoming the drawbacks of classical free electron theory. (06 marks)<br />d. A uniform silver wire has resistivity 1.54×10-8 ohm-m at room temperature for an electric field 2 v/m. Calculate relaxation time and drift velocity of the electrons, assuming that there are 5.8×1022 conduction electrons per cm3 of the material. (04 marks)<br /><span style="font-size: 180%;">January 2011</span><br />3 a. Choose your answers for the following:<br />i) The mobility of electrons in a conductor is 4×10-3 m2V-1s-1. Then the drift velocity of the electron in the presence of applied electric field of strength 100 Vm-1 is<br />A) 4 ms-1 B) 10 ms-1 C) 0.4 ms-1 D) 0.04 ms-1<br />ii) The classical value of molar specific heat of a conductor is<br />A) 3/2 R B) ½ R C) 3R D) 5/2 R<br />iii) The Fermi energy of a metal at absolute zero temperature is proportional to<br />A) n1/3 B) n3/2 C) n2/3 D) n2<br />iv) At 50K, the probability of finding an electron at Fermi energy is ½. The probability of finding electron at the same energy level at 100 K is<br />A) 1 B) zero C) ¼ D) ½ (04 Marks)<br />b. Obtain the expression for electrical conductivity on the basis of free electron theory of metals. (08 Marks)<br />c. Explain Fermi energy and Fermi factor. (04 Marks)<br />d. Calculate the probability of an electron occupying an energy level 0.02 eV above the Fermi level and 0.02 eV below the Fermi level at 200 K. (04 Marks)</b><br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: large;"><b><span style="font-family: "Times New Roman","serif"; line-height: 115%;">December
2011</span></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">3 a. Choose your
answers for the following:</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">i) For ordinary metals,
resistivity versus temperature curve at T = 0K</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">A) has a positive
intercept B) has a negative
intercept C) goes through the
origin D) none of these</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">ii)At T> 0K,
probability of occupancy of Fermi level is</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">A) 75% B) 90%
C) 100% D) 50%</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">iii) If the mobility of
electron in a metal increases, the resistivity</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">A) decreases B)increases C) remains constant D) none of these </span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">iv) The dependence of
mean free path λ on temperature T is </span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">A) λ </span><span style="font-family: Symbol; font-size: small; line-height: 115%;">µ</span><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;"> T
B) λ </span><span style="font-family: Symbol; font-size: small; line-height: 115%;">µ</span><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;"> </span><span style="font-family: Symbol; font-size: small; line-height: 115%;">Ö</span><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">T
C) λ </span><span style="font-family: Symbol; font-size: small; line-height: 115%;">µ</span><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;"> 1/ T D) λ </span><span style="font-family: Symbol; font-size: small; line-height: 115%;">µ</span><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">
1/</span><span style="font-family: Symbol; font-size: small; line-height: 115%;">Ö</span><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">T (04 Marks)</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">b. Using the free
electron theory, derive an expression for electrical conductivity in metals.
(05 Marks)</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">c. Explain Fermi energy
and Fermi factor. (06 Marks)</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">d. Calculate the Fermi
velocity and mean free path for the conduction electrons in silve, given that
its Fermi energy is 5.5eV and the relaxation time for electrons is 3.97×10<sup>-14</sup>
s. (05 Marks)</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<span style="font-size: large;"><b><span style="font-family: "Times New Roman","serif"; line-height: 115%;">June
2012</span></b></span></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">3 a. Choose your
answers for the following:</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">i) In classical free
electron theory, the electric field due to ion cores</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">A) is neglected B) is assumed to be periodic C) is assumed to be a constant D) None of these</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">ii) Mobility of
electron is </span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">A) reciprocal of
electrical conductivity B) acceleration
of electron per unit electric field C)
average drift velocity per unit electric field
D) None of these </span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">iii) If E<sub>F</sub>
is the Fermi energy at absolute zero, then mean energy of the electron at
absolute zero is</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">A) Ē = 1.5 E<sub>F</sub> B) Ē = 2/3 E<sub>F </sub>C) Ē = 2/5 E<sub>F</sub> D) Ē = 3/5 E<sub>F</sub></span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">iv) The resistivity of
metals is due to scattering of electron by</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">A) phonons B) lattice imperfection C) impurities D) All of these (04 Marks)</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">b. Explain the terms</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">i) Relaxation time ii)
Mean collision time iii) Drift
velocity (06 Marks)</span></b></div>
<div class="MsoNormal" style="text-align: justify;">
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">c. Define Fermi energy.
Discuss the Fermi factor f(σ) for cases EF</span></b></div>
<b><span style="font-size: small;">, E>E<sub>F</sub>
at T=0, E=E<sub>F</sub> at T≠0.</span><span style="font-size: small;"> (05
Marks)</span></b>
<br />
<b><span style="font-family: "Times New Roman","serif"; font-size: small; line-height: 115%;">d. Calculate the
conductivity of sodium. Given τ<sub>m</sub> = 2×10<sup>-14</sup> s. Density of
sodium is 971 kg/m<sup>3</sup>. Its atomic weight is 23 and has one conduction
electron/atom. (05 Marks)</span></b><span style="font-size: large;"><b></b></span></div>
<div align="justify">
<b>Free electron concept</b>All metal atoms consist of valence electrons which are responsible for electrical conduction. Valence electrons are loosely bound to the nucleus. When a large number of atoms join to form a metal, the boundaries of the neighbouring atoms overlap, and thus, valence electrons can move easily throughout the body of the metal. These electrons are called free electrons or conduction electrons which account for properties such as electrical conductivity, thermal conductivity, opacity, surface luster etc.<br />
<b>Classical free electron theory</b>This theory was developed by Drude and Lorentz and hence is also known as Drude-Lorentz theory. According to this theory, a metal consists of electrons which are free to move about in the body of the metal like molecules of a gas in a container.<br />
<b>Assumptions</b>1. A metal is imagined as a structure of 3-dimensional array of ions between which, there are freely moving valence electrons (conduction electrons) confined to the body of the material.<br />
2. Mutual repulsion between electrons is ignored and hence potential energy is taken as zero. Therefore the total energy of the electron is equal to its kinetic energy.<br />
3. The free electrons are treated as equivalent to gas molecules and thus they are assumed to obey the laws of kinetic theory of gases. In the absence of field, the energy associated with each electron at a temperature T is given by 3/2 kT.<br />
<b>4. Drift velocity</b>If no electric field is applied on a conductor, the free electrons move in random directions. They collide with each other and also with the positive ions. Since the motion is completely random, average velocity in any direction is zero. If a constant electric field is established inside a conductor, the electrons experience a force F = -eE due to which they move in the direction opposite to direction of the field. These electrons undergo frequent collisions with positive ions. In each such collision, direction of motion of electrons undergoes random changes. As a result, in addition to the random motion, the electrons are subjected to a very slow directional motion. This motion is called drift and the average velocity of this motion is called drift velocity vd.</div>
<br />
<div align="justify">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpyQkwSh1CGYxg3z0JekpRKflQawR4nFFe4wO9mIb9UGtmiJo_9y-n6w6p117Xo_L89C6kjZ9YrRU1rfyoHXiLwYGThxcxmpAG_p-KX4M-HUF8MOVxwCm5zY2POqLtwuMp2gxCWMvPi6A/s1600-h/ferr.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5278899673404952914" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpyQkwSh1CGYxg3z0JekpRKflQawR4nFFe4wO9mIb9UGtmiJo_9y-n6w6p117Xo_L89C6kjZ9YrRU1rfyoHXiLwYGThxcxmpAG_p-KX4M-HUF8MOVxwCm5zY2POqLtwuMp2gxCWMvPi6A/s400/ferr.bmp" style="cursor: hand; height: 210px; width: 400px;" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwvtt7kmXyjmEfdlkUVwqMxJnVNrHEOp4vXqUqMfjAUN33w5t8I9Ul_Vk0E_u0SAZvS-P6KWYVFebbo-qDGbnDvv7irPpokcywB8OU5e3Xg95k9tsXtsC3tfxbuYXZolnKFUIE42v-ZDs/s1600-h/ferr.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5278899234289814290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwvtt7kmXyjmEfdlkUVwqMxJnVNrHEOp4vXqUqMfjAUN33w5t8I9Ul_Vk0E_u0SAZvS-P6KWYVFebbo-qDGbnDvv7irPpokcywB8OU5e3Xg95k9tsXtsC3tfxbuYXZolnKFUIE42v-ZDs/s400/ferr.bmp" style="cursor: hand; height: 400px; width: 354px;" /></a></div>
<br />
<div align="justify">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv8GVZ5cqJ1c0i6DgAmhtgX0njzWhCUBIQrlbcRcH1vvYJyZ_c6mq5Cy7abBGS1uYCLUdvhIK_CJaCLt3ut-YWtHfDGoa-51rXUdKrO3Ctk1mAB_MfG3OAapE7umWcNvE1gruCgfxpV3A/s1600-h/ferr.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5278898688217683938" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv8GVZ5cqJ1c0i6DgAmhtgX0njzWhCUBIQrlbcRcH1vvYJyZ_c6mq5Cy7abBGS1uYCLUdvhIK_CJaCLt3ut-YWtHfDGoa-51rXUdKrO3Ctk1mAB_MfG3OAapE7umWcNvE1gruCgfxpV3A/s400/ferr.bmp" style="cursor: hand; height: 400px; width: 358px;" /></a></div>
<br />
<div align="justify">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDBK-04RHlPK7F-n5TI1VAffssHHF3ELg9sXnbfoclZPPUgJdud8vRGOfbra0Mb-p-t_0-h9tEhYTs1bfN8PDFVcbR_Mk8QhCC1AP46tuyKGWniT2VOLcQ5jrysl9zXiDPPC-ckxuBOvQ/s1600-h/ferr.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5278896980507887618" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDBK-04RHlPK7F-n5TI1VAffssHHF3ELg9sXnbfoclZPPUgJdud8vRGOfbra0Mb-p-t_0-h9tEhYTs1bfN8PDFVcbR_Mk8QhCC1AP46tuyKGWniT2VOLcQ5jrysl9zXiDPPC-ckxuBOvQ/s400/ferr.bmp" style="cursor: hand; height: 376px; width: 400px;" /></a><br />
5. Positive Hall co-efficient of Zinc<br />
Metals are expected to exhibit negative Hall co-efficient since current carriers in them are electrons. The free electron theory cannot explain why Zinc and some other metals have positive Hall co-efficient.<br />
6. The free electron theory cannot explain the classification of materials into conductors, semiconductors and insulators.<br />
7. This theory fails to explain ferromagnetism, superconductivity, photoelectric effect, Compton effect and blackbody radiation.<br />
<b>Quantum free electron theory</b><br />
Classical free electron theory could not explain many physical properties. In classical free electron theory, we use Maxwell-Boltzman statistics which permits all the free electrons to gain energy. In 1928, Sommerfeld developed a new theory, in which he retained some of the features of classical free electron theory and included quantum mechanical concepts and Fermi-Dirac statistics to the free electrons in the metal. This theory is called quantum free electron theory. Quantum free electron theory permits only a fraction of electrons to gain energy. The main <b>assumptions</b> of this theory are:<br />
1. The energy values of conduction electrons are quantized and are realized in terms of a set of energy levels.<br />
2. The distribution of electrons in various allowed energy levels takes place according to Pauli’s exclusion principle.<br />
3. The electrons move in a constant potential inside the metal and are confined within defined boundaries.<br />
4. The attraction between the electrons and the lattice ions and the repulsion between the electrons themselves are ignored. </div>
<br />
<div align="justify">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgp9owh-bmv1wwpH6zPDy6vaD2jTtfU1SctA8H3mhBQTH628rIM-eAQCvRLpgmz23DbD8VO3BBR97PDtf26wqEhqQlzAGibsZjGBLAlmce67s8SlN1fJUYdzbhWlvQ6PmI0WoFW8E-arE/s1600-h/ferr.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5278896228929544834" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgp9owh-bmv1wwpH6zPDy6vaD2jTtfU1SctA8H3mhBQTH628rIM-eAQCvRLpgmz23DbD8VO3BBR97PDtf26wqEhqQlzAGibsZjGBLAlmce67s8SlN1fJUYdzbhWlvQ6PmI0WoFW8E-arE/s400/ferr.bmp" style="cursor: hand; height: 400px; width: 308px;" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgv5d8h2WmtOAO9obBogtCPc389ESrSwsANOZ7IOL8kGQbiR3PnKYxbdo4vjCaJw2BsflpAgacpaBXZG7Iie_DmAc2_KlKbQgVhq7Q_iZoyukMEZRzxEG9WwgzqcXKe0WP2GdIjA5BtY4g/s1600-h/ferr.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5278895568007976418" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgv5d8h2WmtOAO9obBogtCPc389ESrSwsANOZ7IOL8kGQbiR3PnKYxbdo4vjCaJw2BsflpAgacpaBXZG7Iie_DmAc2_KlKbQgVhq7Q_iZoyukMEZRzxEG9WwgzqcXKe0WP2GdIjA5BtY4g/s400/ferr.bmp" style="cursor: hand; height: 400px; width: 268px;" /></a></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjdomEJ22S-dnu_bMvVDy8g682xcMAlv7Ao9f0qjSbELAuCVNsnjI0Y_2dUbkzm5GOfb4F4uLHj9WeM4iDzJ6f16X44rA0cIshkg5qlW4n9ou6X3SKMkpK3QAJiMtP7pGCz7CAUHDx4s0/s1600-h/ferr.bmp"></a><br />
<div align="justify">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhklTYyUA_wpNSeC0ompJAyhhktYjU08MbhKRrKiENhj9vWokTgBkpZZadKjfR-5020JJ9LwfbcA7AtxUJG64Dc35SFPghMN8XNpDMFFZEjqJ-MPhYr34Jtq7O0FFGrDhPMrlI4viAEY30/s1600-h/ferr.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5278895016751954882" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhklTYyUA_wpNSeC0ompJAyhhktYjU08MbhKRrKiENhj9vWokTgBkpZZadKjfR-5020JJ9LwfbcA7AtxUJG64Dc35SFPghMN8XNpDMFFZEjqJ-MPhYr34Jtq7O0FFGrDhPMrlI4viAEY30/s400/ferr.bmp" style="cursor: hand; height: 208px; width: 322px;" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_qi0unS_syTmjijx0I3rwBFmH2_hqigNlB54VA6_AzEesbRUao5Kq1auV7cnE36fYeSbb1d412dRF7MZuFlJEpAXhhNcgjNKpRl9YegtvCnQ-jUCW-Il4V2EaaJ5RiyDKDBUA9Nb7_c/s1600-h/ferr.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5278894669109578194" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV_qi0unS_syTmjijx0I3rwBFmH2_hqigNlB54VA6_AzEesbRUao5Kq1auV7cnE36fYeSbb1d412dRF7MZuFlJEpAXhhNcgjNKpRl9YegtvCnQ-jUCW-Il4V2EaaJ5RiyDKDBUA9Nb7_c/s400/ferr.bmp" style="cursor: hand; height: 274px; width: 400px;" /></a><br />
<b>Classical free electron theory and quantum free electron theory-Comparison<br />Similarities</b>1. Valence electrons are treated as gas molecules are treated as gas molecules of an ideal gas which are free to move throughout the body of the solid.<br />
2. The mutual repulsion between the electrons and the force of attraction between the electrons and ions are considered insignificant.<br />
<b>Differences</b><br />
1. According to classical free electron theory, free electrons obey Maxwell-Boltzman statistics. According to quantum free electron theory, free electrons obey Fermi-Dirac statistics.<br />
2. According to classical free electron theory, free electrons can possess any energy values and it is possible that many electrons possessing same energy. According to quantum free electron theory, free electrons can occupy certain energy levels with discrete energy values and they obey Pauli’s exclusion principle. Hence no two electrons possess same energy.<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1Sik7t1wkr21w-oBRHX3D6B8ew2E1-4ddmSTeYFbQTuSDzE_6HnvWJvgrUulSMs78toANSxGqMneJrrG0_wL6LWbcRw4xaBHzg8VNmspOPf5i8jUS_VddI0eTtKddOGQJoG0oRtDhtyU/s1600-h/ferr.bmp"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5278893505452729554" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1Sik7t1wkr21w-oBRHX3D6B8ew2E1-4ddmSTeYFbQTuSDzE_6HnvWJvgrUulSMs78toANSxGqMneJrrG0_wL6LWbcRw4xaBHzg8VNmspOPf5i8jUS_VddI0eTtKddOGQJoG0oRtDhtyU/s400/ferr.bmp" style="cursor: hand; height: 400px; width: 295px;" /></a></div>
<br />
<div align="justify">
<b>Demerits of quantum free electron theory</b><br />
1. It fails to explain properties of metal alloys.<br />
2. It fails to explain why only some solids are metals and others are either semiconductors or insulators.</div>
</div>
RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com2tag:blogger.com,1999:blog-4803935933670175751.post-88811999743416894192008-07-25T06:09:00.003-07:002010-04-30T23:30:27.400-07:00Dielectric and Magnetic properties of materials<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiReIfJ4WjfnpQem9etsTF3gxgdogiIzkEGnkjVlVn83U8V5a0Vfb36COYw4KHmtcecNxQkGR6tCZ7oT1FXr9fH3IoO1_9GhxC4b6XnxKIP2hIhwvVbgcStXk4B3c3nbTuQbFs_AE28Wuk/s1600/untitled.bmp"><img id="BLOGGER_PHOTO_ID_5466185017889515698" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 382px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiReIfJ4WjfnpQem9etsTF3gxgdogiIzkEGnkjVlVn83U8V5a0Vfb36COYw4KHmtcecNxQkGR6tCZ7oT1FXr9fH3IoO1_9GhxC4b6XnxKIP2hIhwvVbgcStXk4B3c3nbTuQbFs_AE28Wuk/s400/untitled.bmp" border="0" /></a><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiq3XfQtbyCsllD_wsybnK89mnpKkQxx9NGLSxTfQFDr_x2lORr4ZJEt8EFNqih7SSWWBws-3gzcECSkfbvstK0FOHPT6qLR8Zh1W0v-9CrALc_YM6rRA4ExGNMpD1d43h1J7O4xvqit0/s1600/untitled.bmp"><img id="BLOGGER_PHOTO_ID_5466184583615776258" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 281px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiq3XfQtbyCsllD_wsybnK89mnpKkQxx9NGLSxTfQFDr_x2lORr4ZJEt8EFNqih7SSWWBws-3gzcECSkfbvstK0FOHPT6qLR8Zh1W0v-9CrALc_YM6rRA4ExGNMpD1d43h1J7O4xvqit0/s400/untitled.bmp" border="0" /></a><br /><br /><div><br /><br /><br /><div align="justify"><span style="font-size:130%;"><strong>Dielectric loss</strong><br />When a dielectric material is subjected to an ac field, a part of the energy is lost each time the field changes its direction. This is due to the fact that each time the field is reversed, the direction of the dipoles has to change. In this process, a loss of energy due to friction occurs. This energy loss appears in the form of heat. This energy loss depends on the frequency of ac field.<br /><strong>Important applications of dielectric materials</strong><br />1. As insulating materials<br />2. In capacitors<br />3. Dielectric ceramic materials are used in high voltage power lines<br />4. Liquid dielectrics such as petroleum oil are used in transformers for cooling, circuit breakers and in cables.<br />5. In dielectric heating devices<br />6. Non linear dielectrics (piezoelectrics and ferroelectrics where er depend on the intensity of the applied electric field) are used in many applications.<br /><strong>Ferro electricity (Qualitative)<br /></strong>Dielectric materials which possess electric polarization even in the absence of electric field (spontaneous polarization) are known as ferroelectric materials. They exhibit electrical hysteresis for the variation of polarization P with the applied electric field E analogous to the way ferromagnetic material exhibit magnetic hysteresis for variation of B with H.<br /></span></div><br /><br /><br /><div align="justify"><span style="font-size:130%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9evvwb46RmTeDpcwUkJXlAb2zDzOTQB1O9IrVlvJzQUX1jcCmI6UZPNEVdO5973pYM2y7hMN873WN6ICR8H6jTp5mTZSWJcessY6C5v3rBgY7xILGoTf4dTYy0-MVpE2tR9LfhETYTIA/s1600/untitled.bmp"><img id="BLOGGER_PHOTO_ID_5466183826011030386" style="WIDTH: 339px; CURSOR: hand; HEIGHT: 383px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9evvwb46RmTeDpcwUkJXlAb2zDzOTQB1O9IrVlvJzQUX1jcCmI6UZPNEVdO5973pYM2y7hMN873WN6ICR8H6jTp5mTZSWJcessY6C5v3rBgY7xILGoTf4dTYy0-MVpE2tR9LfhETYTIA/s400/untitled.bmp" border="0" /></a></span></div><br /><br /><br /><div align="justify"><span style="font-size:130%;">Ferroelectric materials possess very high values of er of the order of 1000 to 10000. In ferroelectric materials the value of er changes with temperature according to the relation, er = C/T-TC above TC, where TC is called Curie temperature. This is known as Curie-Wiess law of ferroelectrics. Rochelle salt, BaTiO3 and PbTiO3 are examples of ferroelectric materials. These materials are widely used in capacitors, electronic circuits and in memory devices.<br /><strong>Piezoelectricity (Qualitative)</strong><br />When one pair of opposite faces of certain asymmetric crystals such as quartz crystal is compressed, opposite electric charges appear on the other pair of opposite faces of the crystal. On application of tension, the polarities of the charges reversed. This phenomenon of the development of charges as a result of the mechanical deformation is known as piezoelectric effect. Crystals which exhibit this property are called piezoelectric crystals. Quartz, ammonium phosphate and lead zirconate titanate are examples of piezoelectric materials.<br />The converse of piezoelectric effect is also true. If an electric field is applied across one pair of faces of piezoelectric crystal, it gets deformed along the direction of the other opposite pair of faces. If an ac field is applied, crystal vibrates with the frequency of the field. This effect is also called inverse piezoelectric effect which is used for the production of ultrasonic waves. Piezoelectric materials are also used in gas igniters, vibrators, sensors, detectors and in printer heads.</span></div><br /><br /><br /><div><br /></div><br /><br /><br /><div align="justify"><span style="font-size:130%;"><strong>Langevin’s theory of Diamagnetism (Qualitative treatment)<br /></strong>Diamagnetic materials are those which acquire feeble magnetism opposite to the applied magnetic field. i.e., they exhibit negative susceptibility. The order of susceptibility is around 10-6. Copper, Bismuth, Lead, Zinc, Inert gases etc. are examples.<br />Here all the electrons rotating in clockwise direction will have magnetic moment in one direction and the remaining electrons which rotate in the anticlockwise direction will have magnetic moment in opposite direction. Thus net magnetic moment in any direction must be zero.<br />When magnetic field is applied, the electrons rotating in clockwise direction will experience a Lorentz force directed radially outwards. Now to maintain equilibrium, electrons reduce its velocity which results in the reduction of magnetic moment in the direction of applied magnetic field.<br />Meanwhile the electrons which revolve in the anticlockwise direction will experience a force directing radially inwards. Now to maintain equilibrium, electrons increase its velocity which results in an increase of magnetic moment in a direction opposite to the magnetic field.</span> </div><br /><br /><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTiKUTD2Zllb-5C6AruiHqb-P4fTJISfxS8QScCxSgeGTCbY1sBh6JdkvJKdHwzePBy69f84XzSjPGJ6TWduJM1bYzHeV4vKxR73ubaoPE0vFOvnL7dfsvvjqOQrigte-GJhkq6BYEN30/s1600/untitled.bmp"><img id="BLOGGER_PHOTO_ID_5466183133617262418" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 226px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTiKUTD2Zllb-5C6AruiHqb-P4fTJISfxS8QScCxSgeGTCbY1sBh6JdkvJKdHwzePBy69f84XzSjPGJ6TWduJM1bYzHeV4vKxR73ubaoPE0vFOvnL7dfsvvjqOQrigte-GJhkq6BYEN30/s400/untitled.bmp" border="0" /></a><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh6GEyTZyp1Rao2k-LOXANlwtfG7HtXKuloUV-Hy9B7PSF9sOggMa4AzglOuCT2djpg0UCIQYb673OyQlkwqRZPwyUi-RN8nbcSgIkvnGjGiXHHznX6dYjGmwoqa_cnkBJAjS8jdSYo8o/s1600/untitled.bmp"><img id="BLOGGER_PHOTO_ID_5466182942798286658" style="WIDTH: 301px; CURSOR: hand; HEIGHT: 400px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgh6GEyTZyp1Rao2k-LOXANlwtfG7HtXKuloUV-Hy9B7PSF9sOggMa4AzglOuCT2djpg0UCIQYb673OyQlkwqRZPwyUi-RN8nbcSgIkvnGjGiXHHznX6dYjGmwoqa_cnkBJAjS8jdSYo8o/s400/untitled.bmp" border="0" /></a><br /><br /><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiShAO4F480dZPzwENYIjnrHZ05DWineKBMrPsIv_zXRzdEs_vGgIqwF9GL4DeaPqpCyDEaPHCkeDb96VaHsQ0PKQNqN3vV-F1wJDf-eJfSsVMet36s5tpAAfS0D1x1KzDt3mtInxHoI3E/s1600/untitled.bmp"><img id="BLOGGER_PHOTO_ID_5466182417524640018" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 383px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiShAO4F480dZPzwENYIjnrHZ05DWineKBMrPsIv_zXRzdEs_vGgIqwF9GL4DeaPqpCyDEaPHCkeDb96VaHsQ0PKQNqN3vV-F1wJDf-eJfSsVMet36s5tpAAfS0D1x1KzDt3mtInxHoI3E/s400/untitled.bmp" border="0" /></a><br /><br /><br /><br /></div><br /><br /><br /><div><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnjyKnHCc2JiTRN8lrEY2V3RAlaO0V7gVL24Z6i5ljwWSy17zci09EytKbIK9uwGxM4-leBA6E_3psdC2Dio8JMeDL_N0jfY-oUkvz3wOVlL30QbXy-HJH3_Zi-gLXr_hNp_ebwCytr0w/s1600/untitled.bmp"><img id="BLOGGER_PHOTO_ID_5466182122326425698" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 191px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnjyKnHCc2JiTRN8lrEY2V3RAlaO0V7gVL24Z6i5ljwWSy17zci09EytKbIK9uwGxM4-leBA6E_3psdC2Dio8JMeDL_N0jfY-oUkvz3wOVlL30QbXy-HJH3_Zi-gLXr_hNp_ebwCytr0w/s400/untitled.bmp" border="0" /></a><br /><br /><br /><br /><br /><br /><br /><br /><div align="justify"><span style="font-size:130%;">The entire ferromagnetic volume splits into a large number of small regions of spontaneous magnetization. These regions are called domains. In the absence of magnetic field, the relative orientation of the magnetic moments of various domains will be completely random, and thus the resultant magnetic moment of the material as a whole turns out to be zero.<br /><strong>Antiferromagnetism and ferrimagnetism</strong><br />When the magnetic moments of sublattices in a crystal unit cell are equal in magnitude but opposite in direction, they cancel each other giving rise to antiferromagnetism. Their susceptibility is of the order of 10-3 to 10-5. MnO is an example for antiferromagnetic material. If the temperature of the antiferromagnetic material is raised above Neel temperature, material becomes paramagnetic.<br />When the magnetic moments of sublattices in a crystal unit cell are not exactly equal in magnitude and oriented in opposite in direction, the crystal possess a net resultant magnetic moment. This type of materials is called ferromagnetic materials whose saturation magnetization value is not as high as for ferromagnetic materials. Ferrites are examples for ferrimagnetic material.<br /><strong>Ferrites<br /></strong>Ferrites are mixed metal oxides with the general formula MFe2O4 or MO Fe2O3. By varying composition, we can appreciably vary the magnetic and other properties of ferrite materials. Metal ions can occupy tetrahedral A sites (surrounded by 4 oxygen ions) or octahedral B sites (surrounded by 6 oxygen ions). In ZnFe2O4 and CdFe2O4 F3+ ions occupy octahedral sites and Zn2+/Cd2+ ions occupy tetrahedral sites. They are called normal spinel ferrites. In NiFe2O4, CoFe2O4 and CuFe2O4, Fe3+ ions occupy both octahedral and tetrahedral sites while Ni2+, Co2+ and Cu2+ ions occupy octahedral sites. Hence they are called inverse spinel ferrites.<br /><strong>B-H graph in ferromagnetic materials</strong><br />When a ferromagnetic material is taken through a cycle of magnetization, a curve as shown below is obtained. This curve is known as hysteresis curve (B-H curve).</span> </div><br /><br /><br /><br /><br /><br /><br /><br /><div align="justify"><span style="font-size:130%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhE7DrWzyBcSfrRXtaZQ2sfD8_01TrIfpAGuodXVpkb8dUE6JpQw9xNQBvIcm03sWL7DsBwkAeXbm9THh_NZlNOvzuIxqdkzY4JeyIgpjwvS8Tslo4ow3SLnPMsp30gNUy1dk8c2uXJd5E/s1600/untitled.bmp"><img id="BLOGGER_PHOTO_ID_5466181723157438274" style="WIDTH: 400px; CURSOR: hand; HEIGHT: 384px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhE7DrWzyBcSfrRXtaZQ2sfD8_01TrIfpAGuodXVpkb8dUE6JpQw9xNQBvIcm03sWL7DsBwkAeXbm9THh_NZlNOvzuIxqdkzY4JeyIgpjwvS8Tslo4ow3SLnPMsp30gNUy1dk8c2uXJd5E/s400/untitled.bmp" border="0" /></a></span></div><br /><br /><br /><br /><br /><br /><br /><br /><div align="justify"><span style="font-size:130%;">When a magnetic field H is applied to a ferromagnetic material, the magnetic flux density B (or magnetisation M) will vary. As the magnetic field is increased, the flux density (or magnetisation) increases and reaches a saturation value Bs (or Ms). When the field intensity is reduced to zero, the flux density will not become zero, but will have a finite value which is called remanent flux density Br ( or remanent magnetisation Mr). This remanent flux density may be reduced to zero by applying a magnetic field in the opposite direction. The field Hc required to reduce the flux density to zero is called the coercive field.<br /><strong>Soft and hard magnetic materials</strong><br />Magnetic materials which are easily magnetized and demagnetized are known as soft magnetic materials. They are characterized by thin hysteresis loop (loop area small) with low coercive field, low hysteresis loss and high initial permeability. All these properties are by virtue of the domain wall motion that occurs easily in soft magnetic materials. Permalloy, Silicon-Iron alloy and ferrites are examples.<br />Hard magnetic materials are those which have a high resistance to demagnetization. They are characterized by large hysteresis loop (loop are large) with high coercive field, high hysteresis loss and low initial permeability. In these materials, domain walls are highly immobile. Alnico alloy, Invar, Platinum-Cobalt alloy etc. are examples.</span><br /></div><br /><br /><br /><br /><br /><br /><br /><br /><div><br /></div><br /><br /><br /><br /><br /><br /><br /><br /><div align="justify"></div><br /><br /><br /><br /><br /><br /><br /><br /><div><br /></div><br /><br /><br /><br /><br /><br /><br /><br /><div align="justify"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsnpHp0bSlnovC4ggmZ9rRO8zzEsxUwlMMfmvdxVz24kj66TXL1LYkbP08khPUwTiPd3kM0qmLRWdDgK8xsjrlm6ZSkhyphenhyphennJGN_xyfUfzbmpnZgB0Yuki7PGty2o-UFQL9nmPclQWEH-d0/s1600/untitled.bmp"><img id="BLOGGER_PHOTO_ID_5466181079568755122" style="WIDTH: 324px; CURSOR: hand; HEIGHT: 400px" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsnpHp0bSlnovC4ggmZ9rRO8zzEsxUwlMMfmvdxVz24kj66TXL1LYkbP08khPUwTiPd3kM0qmLRWdDgK8xsjrlm6ZSkhyphenhyphennJGN_xyfUfzbmpnZgB0Yuki7PGty2o-UFQL9nmPclQWEH-d0/s400/untitled.bmp" border="0" /></a><br /></div><br /><br /><br /><br /><br /><br /><br /><br /><div><br /></div><br /><br /><br /><br /><br /><br /><br /><br /><p align="justify"><span style="font-size:130%;"><strong>Applications of magnetic materials</strong><br />High resistivity soft magnetic materials are used in the transformer cores since in ac conditions hysteresis loss factor and eddy current loss are important and for high resistivity soft magnetic materials these factors are low. Ferrites are used for high frequency applications. Hard magnetic materials are used in fabrication of permanent magnets. Magnetic materials are also used in memory devices, loud speakers, generators, switching devices, tape-recorders, telephones, electrical instruments, TV tubes etc.<br /></p></span></div></div></div>RAMACHANDRA KAMATHhttp://www.blogger.com/profile/17621852569091514783noreply@blogger.com0