Thermodynamics, Statistical Physics, and Quantum Mechanics

188 SOLUTIONS

Disregarding the 1 in the denominator of(S.4.74.16) andexpanding the

square rootwithrespect to the small parameter for

we obtain, from(S.4.74.16),

where we set We then findthat theconcentrations are

andso

Alternatively, we can take anapproach similar to the one in(d). Using the
formula for thechemicalpotential of anideal gas (seeProblem4.39)gives

We can immediatelywrite

to obtain thesameresult in(S.4.74.18) and (S.4.74.19).

f) For the electrons are highly relativistic, and we canwrite
in (S.4.74.16). Then