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Physics (Paper- V)
2011
GROUP-A
Answer any four of the following questions:
(a) Distinguish Lagrangian, Hamiltonian and. Newtonian formulations from each
other, explaining the advantages and disadvantages of each.
(b) What is coriolis force? Discuss the effects of this force in
some natural phenomena.
(c) Prove the formula S=k In w, where S is the entropy of the system, w is the
number of microstates accessible and k is the Boltzmann constant.
(d) Explain partition function and express helmholtz free
energy in terms of it.
(e) What do Bose-Eistein and Fermi-Direc distributions lead
to classical distribution?
(f) What is reciprocal lattice? Show that f.c.c lattice is the
reciprocal of b.c.c lattice.
(g) Discuss the concept of effective mass of an electron in a. crystal. How is the
negative effective mass of an electron accounted for?
(h) What are Brillouin zones? Illustrate your answer by constructing two Brillouin
zones for a square lattice.
GROUP-B.
2. State Hamilton's principle and deduce Lagrange's equation
Of motion from it. Obtain Lagrange's equation of motion of a
simple pendulum.
3. State the three laws of planetary motion determined by Kepler. Use Hamilton's
equation to find the differential equation for planetary motion and prove that the area!
velocity is constant.
[Assume force 𝑓(𝑟) = −
𝑘
𝑟2
]
4. State and prove Liouveille's theorem and outline its consequences in statistical
mechanics consequences in statistical mechanics.
5. What is meant by grand canonical ensemble?
find the probability in the ensemble of finding the system in
given state. Discuss the thermodynamic behaviour of an
deal gas in a grand canonical ensemble.
6. Deduce the distribution law for Bose-Einstei statistics. Apply
is statistics to derive Planck's law for blackbody radiation.
7. Obtain an expression for specific heat capacity of a solid on the basis of Debye
model. How does it differ from Eistei model?
8. Discuss, with theory, kronig-Penney model for the motion of an electron in a
periodic potential and hence explain the occurrence of energy gap in a solid.
9. Write notes on any two of the following:
(a) Madelung constant (b) Gibbs’ parado
(c) Hall effect (d) Bragg's law and its characteristic features.
2009
GROUP-A
Answer any four the following question:
a) Explain the statement "Generalised coordinates need not have the dimension of length and
similarly components of generalised force do not necessarily have the dimensions of force,
but their product necessarily has the dimensions of work".
b) What do you understand by Coriolis force? Explain the action of Coriolis force on a body
falling freely under gravity.
c) What is statistical weight and how is it related to entropy?
.
d) Explain what you understand by Gibbs paradox.
e) Explain partition function and expres Helmholtz free energy in terms of it.
f) With reference to crystals, state what you understand by the following terms : primitive
cell, Unit cell; Packing factor; Single crystal; Coordination number.
g ) Give the concept of effective*mass of electrons in a crystal.
h) Prove that the persistent current in a superconductor is not consistent with Meissner effect.
GROUP-B
Answer only four questions :
2) State Hamilton's principle and deduce La grange's equation motion from it. Obtain
Lagrange's equation of motion of a compond pendulum.
3) Discuss the theory of Rutherford scattering and derive anexpression for scattering angle
and differential cross-section in terms of energy and impact parameter of the incoming
particle.
4) State and prove Liouville's theorem. How is it analogous to equation of continuity of an
incompressible fluid?
5) Derive Gibbs canonical distribution and apply it to a perfect is to obtain its equation of
state.
6) Derive Bose—Einstein distribution law and apply it to obtain planck's black-body
radiation formula.
7) State Bragg's law and explain its role in the diffraction of X-rays by crystals.-Obtain the
law in-terms of the reciprocal lattice. .
2008
1. Answer any four of the following questions :
a. If u and v are two constants of motion of any given tholonomic dynamical system, show
that the Poisson bracket [u, v] is also a constant of motion.
b. Find the deviation of a freely falling body due to coriolis force, in the northens
hemisphere.
c. Define Micro-canonical, Canonical and grand canonical ensemble , with reference to
the condition of energy , volume , Temperature, number of particas…. Etc.
d. Give , in brief , a comparative Study of the postulates of Maxwell- Boltzmann, Bose
Einstien and Fermi-Dirac Statistics.
e. Claculate the Fermi energy at ok of metallic silver containing one free electron per
atom . Density of Silver is 10.5 gm cm-3 and At. Wt is 108.
f. Explain meissner effect in superconductivity.
g. Give the assumptions in Einstein’s Model of specific heat .whtydebye Modified
Einstein’s Theory? Give the assumptions mode in Debye’s Model of Specific Heat.
h. Show that specing `d` between two Consecutive Planners in the set (h, k, l) in a simple
cubic lattice of side `a` is
𝑑ℎ𝑘𝑙 =
𝑎
√ℎ2 + 𝑘 2 + 𝑙2
Group – B
Answer any four of the following questions :
2. Explain the need of conical transformation and define Conical transformation.
Inteoducing generating function and Hamilton’s extended principle, obtain
canonical transformation and hence derive Hamilton’s
Canonical transformation relations of four different kids.
3. Explain the Eulerian Angles. Derive the transformation relation for the components
of a vector in the fixed inertial freame and the body frame Obtained by three
Eulerian Rotations. Using these transformation equations derive
Eular’sGeomatrical equations.
4. Derive Maxwell-Boltzmann Ditribution law for molecules of a gas Evaluate the
constants appering in the expression. Use the law to find the average speed of
molecules of the gas.
5. Find the partition function of a monatomic perfect gas using the canonical
ensemble . Hence find expression for:
(a) Helmholtz free energy (b) Entropy (c) Internal Energy
6. Derive Fermi-Direc Distribution law . Find an expression for the total energy and
the pressure of a strongly degenerate Fermi gas at absolute zero.
7. Write the expression for binding energy in an ionic crystal and the madelung
content. Derive an approximate value of the madelungconstant inNaCl crystal.
Find the value of the binding energy at equilibrium.
8. Discuss the vibration of a diatomic linear chain and discuss the optical branch and
acoustical branch. Explain, With the necessary mathematical expression, why the
branches are so called.
9. State the drawbacks of free electron theory. Discuss with theory the Kronig –
penney model for the motion of the valence electron in periodic potential and hence
explain the formation of energy bands.