32. (a) At T = 300 K
3kT 3(8.62 × 10-5 eV/K)(300 K)
f = = =5.5 × 10-3 .
2EF 2(7.0eV)
(b) At T = 1000 K,
3kT 3(8.62 × 10-5 eV/K)(1000 K)
f = = =1.8 × 10-2 .
2EF 2(7.0eV)
(c) Many calculators and most math software packages (here we use MAPLE) have built-in numerical
integration routines. Setting up ratios of integrals of Eq. 42-7 and canceling common factors, we
obtain
"
"
F
E/(e(E-E )/kT +1) dE
F
frac = E "
"
F
E/(e(E-E )/kT +1) dE
0
where k =8.62×10-5 eV/K. We use the Fermi energy value for copper (EF =7.0 eV) and evaluate
this for T = 300 K and T = 1000 K; we find frac =0.00385 and frac =0.0129, respectively.

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