University of Delhi 2011 B.Sc Physics Statistical - Question Paper
1229
This question paper contains 4 printed pages.] Your Roll No............
B.Sc. (Hons.) / III A
PHYSICS - PAPER - XIX (Statistical Physics)
Time : 3 Hours Maximum Marks : 38
(Write your Roll No. on the top immediately on receipt of this question paper.) -
Attempt five questions in all.
Question No. 1 is compulsory.
Answer one question from each unit.
(Symbols have their usual meanings.)
1. Attempt any five: 5 * 2
(a) Under .what conditions do the Bose-Einstein and Fermi Dirac distribution approach Maxwell Boltzmann distribution ? Represent graphically.
' (b) What is the difference between a degenerate gas and a degenerate energy level ?
(c) Give the units of Einsteins A & B coefficients.
(d) Determine the wavelength corresponding to the maximum emissivity of a black body at ,a temperature equal to 300 K. Take b = 2898 jim K.
(e) Discuss the variation of *the chemical . potential of a Fermi gas with temperature
graphically.
(f) Show that electron gas in a white Dwarf Star is strongly degenerate and rel'ativistic in nature.
(g) Show that absolute zerois unattainable on the basis of. the third Law of Thermodynamic.
UNIT-I
Derive Sackur Tetrode equation for the entropy
of an ideal monoatomic gas. How does it resolve
the Gibbs Paradox ?
(a) State and derive the law of equipartition of energy. Discuss its relevance and, limitations with respect to the specific heat of a diatomic gas.
(b) Three distinguishable particles have to be accommodated in four available states. Find the number of ways in which this can be done if the particles obey Maxwell Boltzmann Statistics.
UNIT-II
(a) Show that for an adiabatic expansion of a black body radiation
TV1 = constant.
(b) Deduce Weins law for energy distribution in Black Body radiation.
Define Sahas ionisation formula and discuss one of its important applications.
UNIT-III
(a) Explain Bose-Einstein condensation. How does it differ from ordinary condensation ? Derive an expression for the critical temperature at which this phenomenon sets in.
(b) Show that the molar specific heat of a strongly degenerate Bose gas is given as
Represent it graphically..
Derive the vibrational partition function for a diatomic. molecule. Derive the expression for vibrational specific heat and show that it reduces to the classical value at high temperatures.
8. Derive Richardson Dishman equation for thermionic emission of electrons from a metal surface. How can it be used to calculate the work function of the metal ? 7
9. (a) Plot and explain the variation of the
distribution function for a Fermi gas at T = 0 K and T > 0 K. Obtain therein the expression for Fermi energy and pressure for a completely degenerate Fermi gas. 5
(b) Calculate the temperature at which there is 1% probability that a state with an energy
0.5 eV above the Fermi energy will be ' occupied by an electron. 2
1229 4 1,600
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