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11. The FermiDirac occupation probability is given by
Pe
EkT
FD
=+
11
/
/
∆
c
h
, and the
Boltzmann occupation probability is given by
B
=
−∆
/
. Let
f
be the fractional
difference. Then
f
PP
P
e
e
e
=
−
=
−
−
+
−
BF
D
B
∆
∆
∆
/
/
/
.
1
1
Using a common denominator and a little algebra yields
f
e
e
=
+
−
−
∆
∆
/
/
.
1
The solution for
e
–
∆
E
/
kT
is
e
f
f
−
=
−
∆
/
.
1
We take the natural logarithm of both sides and solve for
T
. The result is
T
E
k
f
f
=
−
F
H
G
I
K
J
∆
ln
.
1
(a) Letting
f
equal 0.01, we evaluate the expression for
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 Spring '08
 Any
 Physics

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