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51. The Fermi-Dirac distribution function for the free electrons in a metal cannot be

approximated by the Maxwell-Boltzmann function at STP for energies in the neighborhood of kT.

Verify this by using the method of Exercise 49 to show that A>1 in copper if

f()Aexp(/kT). As calculated in Sec. 9.9 N/V=8.48x10
28

electrons/m
3
for copper. Note that

Eq.(9.55) must be used unchanged here.

sol

Here, the original factor of 8 must be retained, with the result that

A



 



1 N 3 3/2
h (2mekT)

2V
1 26

2 (8.4810 m3)(6.6310

3.50103,






34 3

Js) [2(9.1110






31 23 3/2

)(1.3810 J/K )(293 K)]

Which is much greater than one, and so the Fermi-Dirac distribution cannot be approximated

by a Maxwell-Boltzmann distribution.











Inha University Department of Physics

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