272 Problems 8 Solutiom on Thermodynam’cs d Statistical Mechanica
Solution:
(a) When T = 0 K, the Fermi distribution is
The density of quantum states is
N 47r
V
Therefore, - = sodF ,,(2m)3/2&de, giving
h2 213
&F=-(”) 2m 87rV ,i.e.,(b) As nX/2 = a and p = h/X, the quantum levels of the valence
electrons in the cube of copper are given by
where nl, n2, n3 = 0,1,2,... (not simultaneously 0). The 1st excited state
of the Fermi gas is such that an electron is excited from the Fermi surface
to the nearest higher energy state. That is
Hence- 6.0 x J.
h2
8ma2
A&=--A&
Ic(c) - = 4.4 x IO-’K 1K.