Problems and Solutions on Thermodynamics and Statistical Mechanics

260 Problems d Solutiotu on Thermodynamic8 6' Statistical Mechanics

The number of electrons in the continuum (weak-degeneracy approxima-
tion) is

where

From (1) and (2), we get

Substitute (3) in (2), we get

Nf - kT N Ed

p = kTln- - -1n - - -.

N, 2 N, 2

2089

(a) For a system of electrons, assumed non-interacting, show that the

probability of finding an electron in a state with energy A above the chem-

ical potential p is the same as the probability of finding an electron absent

from a state with energy A below p at any given temperature T.

(b) Suppose that the density of states D(E) is given by

U(& - "p , E>%,

O<E<Eg,

&<O,