WK 5
DE–8979 11
DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2010.
CLASSICAL AND STATISTICAL MECHANICS
(2008 onwards)
Time : Three hours Maximum: 100 Marks
Answer any FIVE questions.
Each question carries 20 marks.
1. (a) What are generalised co-ordinates? Explain. (5)
(b) Give the merits of Hamilton’s Principle. (5)
(c) Obtain Lagrange’s equation from D-Alebert’s principle.
(10)
2. (a) What are Poisson brackets? (5)
(b) Explain Routt’s procedure for handling cyclic
co-ordinates. (5)
(c) Derive the equation of motion under Poisson’s bracket.
(10)
3. (a) State and explain the principle of least action. (5)
(b) What are canonical transformations? (5)
(c) Discuss Hamilton Jacobi theory in detail. (10)
4. (a) Discuss the free vibrations of a linear triatomic molecule.
(5)
(b) Discuss the linear harmonic oscillator problem as an application of
action-angle variables. (5)
(c) Demonstrate the invariance of Poisson bracket with respect to canonical
transformation. (10)
1 DE–8979
WK 5
5. (a) Derive equations of motion under canonical transformation.
(5)
(b) Show that the transformation :
P
1 2
2
p q 2 and
Q tan 1 q / p is canonical. (7)
(c) Derive the equation of motion interms of Poisson bracket.
(8)
6. (a) What is meant by Euler angle? (5)
(b) Discuss the motion of a symmetric top. (5)
(c) Evaluate the normal modes of vibrations of a linear triatomic molecule.
(10)
7. (a) What is space phase? (5)
(b) Distinguish between mean velocity and root mean square velocity.
(5)
(c) Discuss how thermodynamic functions are calculated from partition
functions. (10)
8. (a) Explain microcanonical ensemble. (5)
(b) Discuss the application of microcanonical ensemble to ideal gas.
(10)
(c) State viral theorem. (5)
–––––––––––––––
DE–8980 12
DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2010.
MATHEMATICAL PHYSICS
(2008 onwards)
Time : Three hours Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
2 DE–8979
WK 5
1. (a) Explain Gram Schmidt’s orthogonalization process.
(7)
(b) State and establish Cayley Hamilton theorem. (5)
(c) Find the eigen values and eigen vectors of the matrix
2 2 3
M 2 1 6 . (8)
1 2
0
1 1 1
2. (a) Diagonalise the matrix A 0 2 1 .
(10)
4 4 3
(b) Define inner product and unitary vector space. (5)
(c) Show that m, n n, m . (5)
3. (a) Solve the Hermite differential equation. (10)
(b) Prove that integral
1
P x P x dx 0
1
n m if n m .
2
= if m n . (6)
2m 1
(c) Calculate the Hermite Polynomial of H 2 x . (4)
4. (a) Find the Laplace transform of
1 e .
t
(5)
t
(b) State and prove Cauchy’s Residue theorem for a complex function.
(7)
(c) Find the Fourier transform of
1 x 2
if x 1
f x . (8)
0
if x 1
5. (a) Evaluate the integral
2
sin2 d
0
5 4 cos
. (8)
(b) Apply calculus of residues to show that
3 DE–8979
WK 5
sin x
0
x
dx .
2
(7)
(c) State and explain convolution theorem. (5)
6. (a) Solve the two dimensional heat flow equation. (8)
(b) Determine the two dimensional wave equation for a rectangular
membrane. (8)
(c) What is heat flow equation? Express it in Cartesian co-ordinates.
(4)
7. (a) Explain subgroups and cosets. (4)
(b) Establish that the Kronecker delta is a mixed tensor of order two.
(6)
(c) Explain reducible and irreducible representations. Obtain the character
table for C2v point group. (10)
8. (a) State and prove that great orthogonality theorem for irreducible
representations of a group. (10)
(b) What are isomorphism and Homomorphism? (4)
pq
(c) Show that if Ars is a tensor than
pq qp
Ars Asr is a symmetric tensor and
pq qp
Ars Asr is a antisymmetric tensor. (6)
————————
DE–8981 13
DISTANCE EDUCATION
M.Sc. DEGREE EXAMINATION, MAY 2010.
Physics
INTEGRATED AND DIGITAL ELECTRONICS
(2008 onwards)
Time : Three hours Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
4 DE–8979
WK 5
1. (a) Define h-parameter. Describe how the h-parameters of transistor can be
found from its characteristics.
(5)
(b) Describe with neat diagram, the working of Class
‘A’ power amplifier and also find the efficiency of the amplifier.
(10)
(c) What is distortion? Explain the different types of distortion.
(5)
2. (a) Construct a common source amplifier and discuss its characteristics of
FET. (10)
(b) Write briefly on temperature drift of input offset voltage and current.
(5)
(c) Write notes on transistor biasing. (5)
3. (a) Write and explain the Boolean expression for OR, AND and NOT
circuits. (5)
(b) Discuss the operation of a JK master slave flip flop with necessary
circuit. (7)
(c) Define a register. What is a shift register? Explain the operation of a
serial in serial out shift register.
(8)
4. (a) Write a note on architecture of 8086 microprocessor.
(5)
(b) Discuss about ‘‘counters’’. (5)
(c) Write notes on ‘‘Flip-flop’’. (10)
5. (a) Draw the circuit diagram of an inverting amplifier and explain its
operation. Derive an expression for its voltage gain. (7)
(b) Explain how an OP-AMP can be used as
(i) integrator
(ii) adder. (8)
(c) Define : CMRR and slew rate. (5)
6. (a) If a differential amplifier has CMRR of 10000 and a differential voltage
gain of 200, how much output voltage is obtained for a common mode
input voltage of 10 mv? (5)
(b) Write a note on active filters. (10)
(c) Explain the working of OP-AMP as comparator. (5)
5 DE–8979
WK 5
7. (a) List the uses of flag register in 8085. (4)
(b) With a neat diagram explain the various registers and flags available in
8085 microprocessor. (10)
(c) Explain arithmetic group instructions and jump instructions in 8085
microprocessor with examples.
(6)
8. (a) What is a solar cells? Mention the different types of solar cells. and its
uses. (6)
(b) Explain the working of photovoltatic detector. (6)
(c) Explain the method of fabricating monolithic IC’S assuming you already
have a substrate. (8)
——————
DE–8982 14
DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2010.
ELECTROMAGNETIC THEORY
(2008 onwards)
Time : Three hours Maximum : 100 marks
Answer any FIVE questions.
Each questions carries 20 marks.
1. (a) Derive differential form of Maxmell’s equations. (8)
(b) Derive integral from of Maxmell’s equations and also explain their
physical significance. (8)
(c) Explain pointing vector. (4)
2. (a) Prove that the normal component of electric displacement is not
continuous at the interface. (6)
(b) Define Snell’s law. (3)
(c) Derive Fresnel’s equations for non conducting media when E vector in
parallel to the plane of incidence.
(11)
6 DE–8979
WK 5
3. (a) Explain normal and anomalous dispersion. (4)
(b) Derive Lorentz-Lorentz formula. (12)
(c) On the basis of rayleigh scattering explain, why red light in used for
danger signals. (4)
4. (a) What is meant by ware guide? (3)
(b) Write a short note on magnetron. (7)
(c) Discuss the propagation of electromagnetic waves through rectangular
wave guide. (10)
5. (a) Write a short note on the occurrence of plasma. (7)
(b) Write four criterion for the existence of a plasma.
(6)
(c) Briefly discuss about plasma works. (7)
6. Write short notes on :
(a) Poynting theorem. (6)
(b) Polarisation of electromagnetic waves. (6)
(c) Discuss the theory of propagation of electromagnetic waves in an
anisotropic non-conducting medium.
(8)
7. (a) Define reflection and transmission coefficients. (4)
(b) Derive and discuss the reflection and transmission coefficients at the
interface between two
non-conductivity media. (8)
(c) Write short note on magnetic confinement. (8)
8. Briefly discuss the following :
7 DE–8979
WK 5
(a) Polarisation of scattered light. (6)
(b) Coherence and incoherence of scattered light. (6)
(c) Gunn diodes. (8)
———————
DE–8983 15
DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2010.
NUMERICAL METHODS AND PROGRAMMING
(2008 onwards)
Time : Three hours Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
1. (a) Give rules for declaring variables in C. (5)
(b) Explain all the expressions available in C with an example.
(10)
(c) Differentiate the while statement and do-while statement with examples.
(5)
2. (a) How pointers are declared and used in C? (5)
(b) Explain the method of handling the data files with detailed examples.
(10)
(c) Define unions in C. (5)
3. (a) Explain switch-case statement. Write a C program to illustrate this
statement. (10)
(b) Distinguish between unconditional and conditional branching statement.
(5)
(c) Give examples for formatted input and output. (5)
8 DE–8979
WK 5
4. (a) Write a C program to find the factorial of a number using recursion
function. (8)
(b) Explain the character input and output and string input and output
statements in C. (7)
(c) Derive the general formula for secant method. (5)
5. (a) What is a C-function? List out its advantages. (5)
(b) Write a note on Newton Raphson method. (5)
(c) By successive approximation method find the real root for the equation
x 3 x 2 100 0 . (10)
6. (a) Explain Gauss Seidal method. (5)
(b) Explain the principle of least square fitting. (5)
(c) Solve the equation x 3 4 x 9 0 using bisection method.
(10)
7. (a) Using Euler’s method, solve the following equation
dy
2 y 0 ; y 0 1 , take h 0.1 and obtain y 0.2 .
dx
(6)
(b) Discuss the Simpson’s rule for integration. (5)
(c) From the given table, find the value of the function X 9 .
(9)
X: 5 7 11 13 17
Y : 150 392 1452 2366 5202
Using Lagrange’s method.
8. (a) Discuss any five library functions with examples. (5)
(b) Discuss the advantages and disadvantages of any two iterative methods.
(5)
dy
(c) Prove that the solution for the equation y, y 0 1 yields
dx
m
1
ym 1 h h2 , using second order Runge-Kutta method. (10)
2
9 DE–8979
WK 5
——————————
DE–8984 21
DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2010.
SPECTROSCOPY
(2008 onwards)
Time : Three hours Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
1. (a) Discuss valance bond theory. (6)
(b) Give Heitler-London theory for the hydrogen molecule and discuss the
exchange degeneracy. (8)
(c) Describe ammonia in terms sp 3 hybrid orbtials. (6)
2. (a) Find the eigen values and eigen functions of a rigid rotator. How are
these results used to explain roational spectrum of diatomic molecule.
(10)
(b) The rotational spectrum of CO shows a series of lines placed 3.84235 cm -1
apart. Calculate the moment of inertia and the bond length of C O bond.
(5)
(c) Why in general strong bands in infrared corresponds to weak bands in
Raman and vice versa? (5)
3. (a) Discuss the main features of the vibrational Raman spectra of diatomic
molecules. (6)
(b) Describe frank condon principle in emission and absorption.
(7)
(c) Write a note on predissociation spectra. (7)
4. (a) Describe the photo acoustic Raman Scattering. (6)
(b) Give the classical treatment of Hyper Raman effect.
(6)
(c) What is meant by multiphoton absorption? Explain.
(8)
5. (a) Explain the term Nuclear magnetic resonance. (5)
(b) What is diamagnetic shielding? (5)
10 DE–8979
WK 5
(c) Describe the experimental arrangement for studying Mossbaure spectra.
(10)
6. (a) What is stark effect? Give its importance in microwave spectroscopy.
(7)
(b) Discuss the rotational spectra of symmetric top molecules.
(7)
(c) Justify that Raman spectroscopy is a major tool for the study of
molecular structure. (6)
7. (a) Describe the vibrational spectra of polyatomic molecules.
(7)
(b) What is inverse Raman effect? Will it be used to study the inorganics
liquids. (8)
(c) Explain the term chemical shift. (5)
8. (a) Derive the block equations for Nuclear resonance. (8)
(b) Write notes on Dipole-Dipole interaction and spin lattice interaction.
(6)
(c) Give the theory of NQR. (6)
——————
DE–8985 22
DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2010.
QUANTUM MECHANICS
(2008 onwards)
Time : Three hours Maximum : 100 marks
Answer any FIVE questions.
All questions carry equal marks.
1. (a) Outline the postulates of quantum mechanics. (5)
(b) Explain why electrons do not exist in nucleus. (5)
(c) Drive time independent Schrödinger wave equation.
(10)
11 DE–8979
WK 5
2. (a) Calculate the transmission coefficient of electrons of energy E through
one dimensional rectangular potential barrier. (12)
(b) Obtain solution for Schrödinger wave equation for rigid rotator with fixed
plane (8)
3. (a) Obtain wave equation for three dimensional harmonic oscillator.
(8)
(b) Obtain ground state wave function for hydrogen atom using Schrödinger
equation. Calculate the most probable distance of electron from nucleus.
(12)
4. (a) What is meant by hermitian operator? Show that hermitian operators
have real Eigen values. (10)
(b) Write a note on Schwartz inequality. (10)
5. (a) Outline the perturbation theory for non degenerate levels and apply it to
explain first order stark effect in hydrogen atom. (15)
(b) Write a short notes on Fermi’s golden rule. (5)
6. (a) Discuss semi classical theory of radiation and determine the condition for
allowed transition. (14)
(b) Explain Raman scattering. (6)
7. (a) Write a note on Born approximation. (7)
(b)
Show that : J 2 , J z hJ . (7)
(c) Express the expectation value of an operator in terms of matrix elements.
(6)
8. (a) Discuss the properties and evaluation of CG coefficients for j 1
2
system. (12)
(b) Write a note on particle wave analysis. (8)
——————
DE–8986 23
DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2010.
SOLID STATE PHYSICS
(2008 onwards)
Time : Three hours Maximum: 100 marks
12 DE–8979
WK 5
Answer any FIVE questions.
Each questions carries 20 marks.
1. (a) Derive the equipoints of the following space groups :
(i) P3m1
(ii) P31m
(iii) P4bm. (6)
(b) Show that the fcc centred tetragonal structure is geometrically
equivalent to a body centred tetragonal structure. Why are the face-
centred and body centred cubic structures district?(6)
(c) Describe the crystal structures of CsCl. Explain clearly how this
structure differs from that of diamond.
(8)
2. (a) Discuss E wald construction and derive Bragg’s diffraction condition
interms of reciprocal lattice vector.
(6)
(b) How are Brillouin zones constructed? (6)
(c) Mention the importance of crystal analysis. (8)
3. (a) Obtain the various vibrational modes of a linear monoatomic lattice.
(6)
(b) What do you understand by the normal modes of vibration?
(6)
(c) Explain the inelastic scattering by phonous. (8)
4. (a) Explain the Thermal Conductivity of metals. (8)
(b) What are called Anharmonic crystal interactions and explain.
(6)
(c) Write short notes on heat capacity of a metal. (6)
5. (a) What is meant by the free electron gas model of metals?
(6)
(b) Show that the fermi surface for the free electron is Spherical. Give its
importance. (6)
(c) Define the electrical conductivity and summarize the general
characteristics of electronic conduction in metal.
(8)
6. (a) What is the concept of effective mass? (6)
13 DE–8979
WK 5
(b) Discuss what information does one obtain about the effective mass of
electron moving in a periodic potential.
(6)
(c) Discuss the Kronig-Penny model for the energy band structure of solids.
(8)
7. (a) What is an extrinsic Semiconductor? (6)
(b) What are impurity states and what role do they play in determining the
electrical conductivity of a doped Semiconductor? (6)
(c) Discuss qualitatively BC impurity electrical conductivity.
(8)
8. (a) Explain antiferromagnetism and describe the temperature – variation of
its susceptibility. (8)
(b) Calculate the critical NeCl Temperature of antiferromagnetism.
(4)
(c) Explain the difference between :
(i) Diamagnetism and Paramagnetism.
(ii) Paramagnetism and Ferromagnetism. (8)
–––––––––––––––
DE–8987 24
DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2010.
NUCLEAR AND PARTICLE PHYSICS
(2008 onwards)
Time : Three hours Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
1. (a) Give Fermi’s theory of decay. (10)
(b) How far Fermi’s theory has been verified experimentally?
(6)
(c) Write a note on nuclear isomerism. (4)
14 DE–8979
WK 5
2. (a) Explain salient features of collective model of nucleus.
(8)
(b) How does the collective model help to understand the phenomenon of
nuclear forces? (8)
(c) Identify the differences between nuclear shell model and liquid drop model.
(4)
3. (a) What are the general characteristics of nuclear forces?
(5)
(b) Give brief account of the Meson theory of nuclear forces.
(10)
(c) Write a note on the charge independence of nuclear forces.
(5)
4. (a) Explain the compound nuclear model of nuclear reactions.
(10)
(b) Explain briefly the stripping and pickup reactions.
(5)
(c) What are the sources of stellar energy? (5)
5. (a) Give the theory of low energy n p scattering and deduce an expression
for the scattering cross sections in terms of the scattering length and the
effective range. (16)
(b) What are the selection rules for the decay? (4)
6. (a) What are the fundamental interactions? (5)
(b) Write a note on SU 2 and SU 3 symmetry groups.
(10)
(c) Explain CPT theorem. (5)
7. (a) Give an account of the phenomena of nuclear fission and discuss the
Bohr-Wheeler theory to explain its mechanism. (10)
(b) Calculate the fission threshold energy and discuss its significance.
(6)
(c) Explain the phenomenon of internal conversion. (4)
8. (a) What are magic numbers? Give atleast five evidences in support of them.
(6)
(b) How the existence of magic number can be explained with shell model of
the nucleus? (10)
(c) What are thermonuclear reactions? (4)
——————————
15 DE–8979
WK 5
DE–8988 25
DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, MAY 2010.
MATERIALS SCIENCE
(2008 onwards)
Time : Three hours Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks
1. (a) Explain addition and condensation polymerization.
(12)
(b) Enlist various methods of corrosion. How is it controlled in actual
practice? (8)
2. (a) What is fatigue? Explain. (10)
(b) What is mean by population inversion? Enumerate the methods to
obtain it. (10)
3. (a) Explain the working and applications of He-Ne laser.
(12)
(b) Write a short note on compound semiconductor laser.
(8)
4. (a) What is an optical resonator? Explain its purpose in lasers.
(8)
(b) Explain the working of an Electro-optic modulator using Kerr effect.
(12)
5. (a) Explain Faraday’s effect with an example. (8)
(b) Explain the second harmonic generation in KDP crystal with necessary
theory. (12)
6. (a) Discuss in detail the sputtering methods and mention their advantages.
(12)
(b) Explain the principle and working of penning gauge.
(8)
16 DE–8979
WK 5
7. (a) Explain any one method to measure the thickness of the thin films in
detail. (10)
(b) Write a note on fuel cell. (10)
8. (a) What are silver ion conductors explain its applications?
(8)
(b) Write an essay on LB films and its applications. (12)
————————
17 DE–8979