DEGREE EXAMINATIONS 2008
Level 2 (PRINCIPAL COURSE)
Friday 16th May 2008, 09:30 – 11:30
STATISTICAL MECHANICS AND SOLID STATE PHYSICS
Candidates should attempt to answer FOUR questions,
TWO from section A and TWO from section B of the paper.
Tables of physical and mathematical data may be obtained from the
SECTION A: STATISTICAL MECHANICS (Answer TWO questions)
1. (a) Explain the meaning of microstate and macrostate. As an example, give one
macrostate of the “tossing a coin three times” system, and write down all
corresponding microstates. 
(b) Explain why the expression
Ω = N!
gives the number of microstates for a given macrostate with niparticles in the
non-degenerate energy level Ei. 
(c) Which macrostate will be observed in a real system? 
(d) Starting with the above expression for Ω, derive the expression
for the number of particles in the energy level Ei. 
(e) For the following assume β=1
kBT. Show that the normalization constant is
where ZSP is the single particle partition function, and N the number of parti-
(f) Hence, show that the internal energy is given by
where T is the temperature, and kBis the Boltzmann constant.