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University : Kolhan University
Course : B.Sc Hons.
Part 3 Question Paper
Paper V Physics
Exam Year : 2011
- Answer any four of the following questions :
(a) Distinguih 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 expre ss 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 byconstructing two Brillouin zones for a square lattice.
- State Hamilton's principle and deduce Lagrange's equation of motion from it. Obtain Lagrange's equation of motion of a silnple pendulum.
- 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/r^2 ]
- State and prove Liouveille's theorem and outline its consequences in statistical mechanics consequences in statistical mechanics.
- 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.
- Deduce the distribution law for Bose-Einstei statistics. Apply is statistics to derive Planck's law for blackbody radiation.
- Obtain an expression for specific heat capacity of a solid on the basis of Debye model. How does it differ from Eistei model?
- 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.
- 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.