Problems and Solutions on Thermodynamics and Statistical Mechanics

Stdimtical Physics 267

Fig. 2.20.

Solution:
The density of states is

47rV ( 2m)3/2

h3

D(E) =

(a) If T = 0, the total number of electrons is

2

3

EF

N = l D(E)dE = -D(EF)EF.

(c) At low temperatures 1.1 >> kT,

= /,'D(E)dE + 7r2 -(kT)'D'(p) + -(kT)4D"'(p) 7T4 +...

6 3 60

Fy 87~V(2rn)~/' 3h3 p3/2 [1+ f (?,"I ,