Download DISTANCE EDUCATION M.Sc. (Physics) DEGREE EXAMINATION

DE–878
11
DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, DECEMBER 2010.
CLASSICAL AND STATISTICAL MECHANICS
(2008 onwards)
Time : Three hours
Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
1. (a)
State D’Alemberts principle in words and represent mathematically.
(5)
(b)
Explain Hamilton’s variational principle.
(c)
Derive Lagranges equations from variational principle. Deduce it to
conservative system.
(10)
2. (a)
(5)
List the properties of Generalized coordinates.
(5)
(b)
Explain the Principle of least action.
(5)
(c)
Derive the conditions necessary for the transformation to be canonical.
(10)
3. (a)
Derive
equations
(10)
of
motion
from
Poisson
brackets.
(b)
Explain Hamilton’s principal function.
(c)
Using the method of action-angle variables, determine the frequency of a
simple pendulum of length L.
(5)
4. (a)
(5)
Explain Principal axes of Inertia in a rigid body. (5)
(b)
Calculate Kinetic energy of a rigid body.
(5)
(c)
Establish the relationship between angular momentum and kinetic
energy of a rigid body. (10)
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5. (a)
Discuss the steady precession motion of a top.
(5)
(b)
Summarise the applications of small oscillations. (5)
(c)
Determine the normal modes of vibration of linear triatomic molecule.
(10)
6. (a)
Use Lagrange’s equations to show that the motion of simple pendulum is
simple harmonic. (10)
(b)
State the mertis of Hamilton’s canonical equations of motion.
(5)
(c)
Use Hamilton Jacobi equation to study the motion of a simple pendulum.
(5)
7. (a)
Calculate the volume of a point particle in Phase space.
(5)
(b)
Compare and contrast the different types of ensembles.
(10)
(c)
Discuss
the
conservation
of
density
in
Phase
space.
(5)
8. (a)
Explain statistical equilibrium.
(5)
(b)
State Maxwell’s Distribution law.
(5)
(c)
Calculate mean root mean square and most probable velocity of
molecules. (10)
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DE–879
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DISTANCE EDUCATION
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DE–878
M.Sc. (Physics) DEGREE EXAMINATION, DECEMBER 2010.
MATHEMATICAL PHYSICS
(2008 Onwards)
Time : Three hours
Maximum : 100 marks
Answer any FIVE questions.
Each question carry 20 marks.
1. (a)
(b)
(c)
Explain Eigen values and Eigen vectors of a matrix.
(5)
Show that the vectors (1,1,1) (2, 1, 3) (1, 0, 2) are linearly dependent.
(5)
 5 0

Find the eigen values and eigen vectors of the matrix  0 3

 3 0

(10)
Show that  m, n    n, m .
(5)
(b)
1 
n
Prove that H 2n 0   1 22n   .
 2 n
(5)
(c)
Find
2. (a)
1  x 
2
3. (a)
the
solution
of
d y
dy
 2x
 ky  0 .
2
dx
dx
Legendre’s
2
(5)
 
2
n  1 .
(b)
Show that n n 
(c)
Obtain the series solution of Bessel differential equation.
(10)
4. (a)
Find the Fourier transform of
(5)
1
.
x
(5)
(b)
State and prove convolution theorem for Fourier transform.
(5)
(c)
Using Fourier transforms, solve
ux , 0   f x  ,
(10)
equation
(10)
Find the value of J 1 and J  3  .
2
differential
3 
0 .

3 

 2u 1  2u
with the initial conditions

x 2 c 2 t 2
u
x , 0  0 and the interval extends from   to   .
t
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5. (a)
Find the residue of
theorem.
(b)
z2
z 2  a2
at z  ia by writing Cauchy’s residue
(5)
Find the integral
zdz
 9  z z  1
2
where ‘C’ is the circle z  2 (described
C
in the +ve sense).
(c)
6. (a)
(5)
State and prove Taylor’s series.
(10)
Obtain the solution of one dimensional wave equation by the method of
separation
of
variables.
(5)
(b)
Derive the two dimensional wave equation for a vibrating rectangular
membrane.
(5)
(c)
Derive two dimensional Laplace’s equation for the steady state
temperature distribution in a thin rectangular plate bounded by the lines
x 0,
x  l , y  0 , the edges x  0 ,
x  l , y  0 are kept at
temperature zero.
(10)
7. (a)
Show that the velocity of a fluid at any point is a contra variant tensor of
rank one. (5)
(b)
Write the rules to construct a character table.
(c)
State and prove the orthogonality theorem.
8. (a)
What is Schwartz inequality in a vector space?
(5)
(10)
(5)
(b)
What are reducible and irreducible representations of a group?
(5)
(c)
Derive the moment of inertia of a tensor.
(10)
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DE–880
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DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, DECEMBER 2010.
INTEGRATED AND DIGITAL ELECTRONICS
(2008 onwards)
Time : Three hours
Maximum : 100 marks
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Answer any FIVE questions.
Each question carries 20 marks.
1. (a)
Explain the need for biasing a transistor.
(5)
(b)
Calculate the gain of a CE transistor amplifier whose hybrid parameters
are hie 1100  hfe  50 hoe  25 s , RL  5k , hre  2.510 4 .
(5)
(c)
Describe the working of transformer coupled power amplifier with neat
diagram and obtain the efficiency expression.
(10)
2. (a)
Explain how the power efficiency of push pull amplifier is calculated?
(7)
(b)
Write briefly about the circuit arrangement and working of class B push
pull amplifier.
(8)
(c)
Mention the advantages of JFET over BJT.
3. (a)
(5)
Mention the unique feature of Boolean algebra. Discuss the fundamental
laws. (5)
(b)
Explain the operation of a ‘‘Four Bit Binary Counter’’.
(5)
(c)
Explain the operation of a NOT and XOR gate. Give its truth table.
(10)
4. (a)
Prove that Boolean identies.
(i)
AC  ABC  AC
(ii)
A  AB  A  B .
(5)
(b)
Explain arithmetic group instructions and jump instructions in 8085
microprocessor with examples.
(10)
(c)
Write a note on band pass filter.
5. (a)
(b)
(c)
(5)
What are the different characteristics of an ideal operational amplifier?
(5)
Explain how an Op-Amp can be used as
(i)
Differentiator
(ii)
Integrator.
(8)
Define the term ‘Slew rate’. Discuss how it affects the a.c. operation of
Op-Amp. (7)
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6. (a)
Define the figure of merit of differential amplifier.(4)
(b)
Describe, will suitable example how analog computation is done by OpAmp. (6)
(c)
Explain the function of emitter-coupled differential amplifier with
necessary circuit. (10)
7. (a)
What is an interrupt?
(3)
(b)
Discuss in detail the types of interrupts available in 8080 A and 8085
microprocessor.
(10)
(c)
Draw block diagram of 8085 microprocessor to show the internal
architecture.
(7)
8. (a)
What is Hall effect? Explain.
(5)
(b)
Explain the advantages of solar cell.
(3)
(c)
Explain the various steps involved to fabricate monolithic circuit and also
solar cell. (12)
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DE–881
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DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, DECEMBER 2010.
ELECTROMAGNETIC THEORY
(2008 onwards)
Time : Three hours
Maximum : 100 marks
Answer any FIVE questions.
Each questions carries 20 marks.
1. (a)
Explain poynting theorem.
(5)
(b)
Derive Fresnel's Law for phase velocity.
(7)
(c)
Prove that the electro magnetic waves travel with the speed of light in
free space. (8)
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2. (a)
Show that the tangential component of electric field intensity E is
continuous across the interface.
(6)
(b)
Obtain the boundary condition for magnetic field intensity vector ‘H’.
(6)
(c)
With a neat diagram, discuss Brewster's law and degree of polarisation.
(8)
3. (a)
Write the characteristics of normal dispersion.
(2)
(b)
Derive Lorentz dispersion equation.
(9)
(c)
Prove that in the case of gases the maximum and minimum values of
refractive index occur at the positions where the absorption co-efficient
reaches half its maximum value.
(9)
4. Write a short note on the following :
(a)
Klystron.
(4)
(b)
Gunn diodes.
(6)
(c)
Discuss in detail theory of rectangular cavity resonator showing that
lowest modes are possible in TE mode.
(10)
5. (a)
Briefly discuss the conditions for existence of a plasma.
(7)
(b)
Discuss the motion of a charged particle in
(i)
A uniform magnetic field.
(6)
(ii)
A simultaneous electric and magnetic field. (7)
Derive Maxwell's first equation divd   .
(5)
(b)
Discuss the significance of poynting vector.
(3)
(c)
Discuss the theory of propagation of electromagnetic waves in isotropic
6. (a)
dielectrics medium.
(12)
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7. (a)
Derive Fresnel's formula for an electromagnetic wave incident on the
interface with E vector perpendicular to the plane of incidence.
(b)
(8)
On the basis of electromagnetic theory, explain total internal reflection.
(8)
(c)
8. (a)
Write a note on space plasma.
(4)
Explain anomalous dispersion.
(2)
(b)
Derive and discuss Thomson's scattering formula for differential and
total scattering cross-sections.
(14)
(c)
Explain the following :
(i)
The clear sky appears to be blue.
(2)
(ii)
The rising or setting sun appears to be red. (2)
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DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION,
DECEMBER 2010.
Fourth Semester
NUMERICAL METHODS AND PROGRAMMING
(2008 onwards)
Time : Three hours
Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
1. (a)
Give the character set permitted in C.
(5)
(b)
Describe the structure of a C program.
(5)
(c)
Write a C program to find the average of three real numbers.
(10)
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2. (a)
What is a function in C? Give its syntax and write an example.
(5)
(b)
What are arrays? How will you enter data into an array?
(5)
(c)
Write a C program by using array to find the average mark obtained by a
class of 20 students in a test.
(10)
3. (a)
List the operators in C and review their priorities.
(5)
(b)
Distinguish the principle of a while and do-while statement with the help
of a program segment. (10)
(c)
What is the use of structure in C? Explain how structure elements are
stored in the memory. (5)
4. (a)
(b)
To store 10 floating point numbers what would you prefer; an array or a
structure?
Justify
your
answer.
(5)
Explain the following declaration
(i)
(c)
5. (a)
int i = 5;
(ii)
int  j;
(5)
Describe the file open and file close functions in C.
(10)
Mention the different types of error. Give examples for each type.
(5)
(b)
Obtain an interactive formula for Newton-Raphson's method.
(5)
(c)
Using the Bisection method solve the equation
x 3  9x  1  0
6. (a)
(10)
Find the root of xe x  2  0 which lies between 0 and 1 using the method
of false position.
(5)
(b)
Explain the procedure of forward substitution to solve a system of
simultaneous equations.
(5)
(c)
By Gauss-Jordan method, solve the following equations.
(10)
2x  3 y  z  1
x  4 y  5z  25
3x  4 y  z  2
7. (a)
Explain the principle of Least squares in curve fitting.
(5)
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(b)
Use the method of least square to fit a straight line to the following data.
(10)
x : 0 5 10 15 20
y : 7 11 16 20 26
(c)
8. (a)
Intrepret Trapezoidal rule geometrically.
(5)
Obtain the Simpson's one third rule formula for evaluating the integral I.
(5)
(b)
Compare Trapezoidal rule with Simpson's rule.
(5)
(c)
Solve (dy / dx )  x  y ; y (1)  0 numerically upto
x  1.2 with h  0.1 .
(10)
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DE–883
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DISTANCE EDUCATION
M.Sc.(Physics) DEGREE EXAMINATION, DECEMBER 2010.
SPECTROSCOPY
(2008 onwards)
Time : Three hours
Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
1. (a)
Explain Molecular orbital theory.
(8)
(b)
Explain the method of Heitler-London theory to obtain the energy values
for
the
hydrogen
molecule.
(6)
(c)
Describe SP 2 hybridization.
2. (a)
(6)
Discuss rotational spectra of a diatomic molecule, treated as a non rigid
rotator.
(5)
(b)
Discuss the rotational spectra of symmetric top molecules. Interpret the
result to obtain the bond lengths of polyatomic molecules. (10)
(c)
What is stark effect? Explain.
(5)
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3. (a)
Explain how a diatomic molecule is behaving as rotating – vibrator.
(7)
(b)
Give the theory of Vibrational Raman Spectra.
(7)
(c)
Write a short note on Frank-Condon principle.
(6)
4. (a)
Explain Hyper Raman effect using classical treatment.
(8)
(b)
Give
(c)
Write a note on two photon absorption.
(5)
What do you mean by the term chemical shift?
(5)
5. (a)
the
theory
of
photo
acoustic
Raman
(7)
(b)
What is ESR? Give its principle.
(c)
What are the applications of Mossbaure spectroscopy?
(5)
6. (a)
Scattering.
(10)
Discuss the role of quadrupole hyperfine interaction in rotational spectra
of polyatomic molecules.
(7)
(b)
Give the theory of mutual exclusion principle.
(c)
Explain the role of IR spectroscopy in the study of molecular structure.
(7)
7. (a)
(6)
Distinguish IR spectroscopy from FTIR.
(8)
(b)
Write a note on Predissociation.
(6)
(c)
Discuss
8. (a)
(b)
the
special
features
of
inverse
(6)
Give the theory of NQR.
Raman
effect.
(10)
Write notes on Dipole-Dipole interaction and spin lattice interaction.
(10)
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DE–884
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DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, DECEMBER 2010.
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DE–878
QUANTUM MECHANICS
(2008 Onwards)
Time : Three hours
Maximum : 100 marks
Answer any FIVE questions.
All questions carry equal marks.
1. (a)
(i)
State the uncertainity principle.
(2)
(ii)
Discuss the Various applications of it.
(8)
(b)
What are the fundamental postulates of Quantum mechanics?
(5)
(c)
Briefly explain the quantum mechanical tunneling.
(5)
2. (a)
Explain Eigen functions and Eigen vectors.
(5)
(b)
Obtain an expression for the energy of the three dimensional harmonic
oscillator. (10)
(c)
What do you mean by a rigid rotator? Explain.
3. (a)
(b)
Solve the Schrodinger equation for a hydrogen atom in spherical
coordinates.
(10)
Write notes on :
(i)
Zero point energy
(3)
(ii)
Bound states
(5)
(iii) Parity.
4. (a)
(b)
5. (a)
(b)
6. (a)
(5)
(2)
Explain the various operators available in quantum mechanics.
(10)
(i)
What is W.K.B approximation?
(4)
(ii)
Discuss the validity conditions of this approximation.
Discuss the first order time independent perturbation theory.
(10)
Explain quadratic Stark effect
State and explain Fermi’s Golden rule.
12
(10)
(5)
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(6)
(b)
7. (a)
Discuss
the
time
dependent
Explain the Semi classical theory of radiation.
perturbation
(15)
(12)
(b)
Write a note on selection rules.
(3)
(c)
Obtain the optical theorem.
(5)
8. (a)
(b)
(c)
theory.
Explain the angular momentum of a system of particles.
(8)
Prove that :
(i)
J X , J Y ihJ z
(2)
(ii)
J  , J  2hJ z .
(2)
Discuss the Born approximation for the diffusion scattering.
(8)
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DE–885
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DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, DECEMBER 2010.
SOLID STATE PHYSICS
(2008 Onwards)
Time : Three hours
Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
1. (a)
Explain the difference between ferromagnetic order and antiferro
magnetic order. (6)
(b)
Explain the difference
ferromagnetism.
(c)
What is meant by mononuclear system? Give the Quantum theory of
diamagnetism
of
mononuclear
system.
(8)
2. (a)
(b)
diamagnetism,
paramagnetism
What are the thermoelectric effects of intrinsic semiconductor?
(6)
Explain the following :
(i)
between
(6)
(6)
Semimetals
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and
(ii)
Super lattices
(iii) Band gap.
(c)
Discuss the role of impurity states in determining the electrical conductivity of
a doped semiconductor.
(8)
3. (a)
State and prove Bloch theorem. Discuss its importance in the band
theory.
(6)
(b)
Explain the concept of effective mass.
(c)
Discuss the formation of allowed and forbidden energy bands on the basis of
the Kronig-Penney model.
(8)
4. (a)
(6)
What is meant by the free electron gas model of metals?
(6)
(b)
The atomic radius of sodium is 1.86 Å. Calculate the Fermi energy of sodium at
absolute zero.
(6)
(c)
Define electrical conductivity and summarize the general characteristics of
electronic conduction in metals.
(8)
5. (a)
Write a note on thermal properties of phonons.
(b)
Explain anharmonic crystal interactions.
(c)
Enlist the salient features of Einstein’s heat capacity.
(8)
6. (a)
(6)
(6)
Obtain the various vibrational modes of a linear monoatomic lattice.
(6)
(b)
What is Hydrogen bond? Explain the properties of hydrogen bonded solids.
(6)
(c)
Explain the inelastic scattering by phonons.
7. (a)
(8)
What are Brillouin zones? Discuss the construction of the first three
Brillouin zones for a square lattice.
(6)
(b)
Discuss E wald construction and derive bragg’s diffraction condition interms of
reciprocal lattice vector.
(6)
(c)
What is meant by crystal analysis? Mention its importance.
(8)
8. (a)
Write a note on fundamental types of lattices with examples.
(6)
(b)
Show that the face centered tetragonal structure is geometrically equivalent to
a body centered tetragonal structure.
(6)
(c)
Draw a plan view of sodium chloride structure. In how many ways can this
structure be interpreted?
(8)
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DE–886
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DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, DECEMBER 2010.
NUCLEAR AND PARTICLE PHYSICS
(2008 Onwards)
Time : Three hours
Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
1. (a)
State and explain Gammow’s theory of  -decay. (10)
(b)
Derive Geiger-Nuttal law from the above theory. (6)
(c)
Write a note on internal conversion.
2. (a)
(4)
Explain the salient features of a single particle nuclear shell model.
(8)
(b)
How does the shell model predict magic numbers?(8)
(c)
Explain why nuclei cannot have permanent electric dipole moment.
(4)
3. (a)
Give the theory of n-p scattering at low incident energies.
(10)
(b)
What information on the nature of nuclear force can be obtained n-p
scattering studies?
(6)
(c)
What are tensor forces?
4. (a)
(4)
Give an account of the phenomenon of nuclear fusion. What are the
conditions necessary for achiving fusion reactions in laboratory? (10)
(b)
Discuss the interaction of neutrons in bulk matter.
(5)
(c)
Discuss the source of energy in sun and stars.
(5)
Explain classification of elementary particle.
(10)
5. (a)
(b)
What are strange particle? What strangeness they possess?
(5)
(c)
What are weak interactions? Describe the experiment performed to
confirm that parity is not conserved in weak interaction. (5)
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6. (a)
Write a note on deuteron.
(5)
(b)
What is the spin-orbit force in a nucleus?
(5)
(c)
Write a brief notes on SU(2) and SU(3) symmetry groups.
(10)
7. (a)
Write a note on the liquid drop model of the nucleus. How does this
model account for the phenomenon of nuclear fission.
(10)
(b)
Discuss the role of a moderator in a nuclear reactor.
(6)
(c)
Describe Yukawa’s meson theory of nuclear forces.
(4)
8. (a)
Explain
the
criticality
condition
in
nuclear
(8)
(b)
What are controlled thermonuclear reactions?
(6)
(c)
Write a note on Baryons and Quarks.
(6)
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DISTANCE EDUCATION
M.Sc. (Physics) DEGREE EXAMINATION, DECEMBER 2010.
MATERIALS SCIENCE
(2008 onwards)
Time : Three hours
1. (a)
(b)
2. (a)
(b)
3. (a)
(b)
Maximum : 100 marks
Answer any FIVE questions.
Each question carries 20 marks.
Explain the various methods of corrosion.
(8)
Write down the elastic, inelastic behaviour of materials.
(12)
What is an optical resonator? Explain its purpose in lasers.
(10)
Discuss about the semiconductor lasers.
(10)
Explain in detail about electro optical effect?
(10)
What is Faraday’s effect with an example.
(10)
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reactors.
4. (a)
(b)
5. (a)
(b)
6. (a)
(b)
7. (a)
(b)
8. (a)
(b)
Explain any one method to measure the thickness of the thin films in
detail.
(10)
Discuss
the
theory
of
LB
films
and
(10)
its
applications.
Give
its
(12)
applications.
What are copper ion conductors and its applications?
(12)
Explain the electrochromic display systems.
(8)
Give a note on polymers.
(8)
Discuss
about
the
gas
lasers.
Explain the second harmonic generation in KDP crystal with necessary
theory.
(12)
Write about the deposition processes.
(8)
Write a brief theory of fuel cells.
(10)
Discuss about the solid state battery.
(10)
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