11. The Fermi-Dirac occupation probability is given by PeEkTFD=+11//∆ch, and the Boltzmann occupation probability is given by B=−∆/. Let fbe the fractional difference. Then fPPPeee=−=−−+−BFDB∆∆∆///.11Using a common denominator and a little algebra yields fee=+−−∆∆//.1The solution for e– ∆E/kTis eff−=−∆/.1We take the natural logarithm of both sides and solve for T. The result is TEkff=−FHGIKJ∆ln.1(a) Letting fequal 0.01, we evaluate the expression for
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