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30. The probability that a state with energy
E
is occupied at temperature
T
is given by
PE
e
EE k
T
F
()
/
=
+
−
1
1
where
k
is the Boltzmann constant and
23
4
2
2/3
28
3 2/3
19
31
0.121
0.121(6.626 10
J s)
(1.70 10 m )
3.855 10
J
9.11 10
kg
F
e
h
En
m
−
−−
−
×⋅
==
×
=
×
×
is the Fermi energy. Now,
19
19
20
4.00 10
J 3.855 10
J
1.45 10
J
F
EE
−
−=
×
−
×
=
×
and
20
23
1.45 10
J
5.2536
(1.38 10
J / K)(200K)
F
kT
−
−
−
×
×
,
so
3
5.2536
1
( )
5.20 10 .
1
e
−
×
+
Next, for the density of states associated with the conduction electrons of a metal, Eq. 41
5 gives
(
)
3/2
31
3/2
1/2
19
33
4
3
56
3/2
3
3
19
46
3
8 2
8 2 (9.109 10
kg)
( )
4.00 10
J
(6.626 10
J s)
1.062 10 kg
/ J s
4.00 10
J
6.717 10
/ m J
m
NE
E
h
ππ
−
−
−
−
×
×
=×
⋅
×
⋅
where we have used 1 kg =1 J·s
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This note was uploaded on 05/19/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Energy

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