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PHYS 271: Problem Set 6
Due Tuesday, Apr. 14, 2009 at the start of class.
1. Imagine we have a chunk of metal whose density of states is given by
g
(
E
)=
10
23
×
E
(
E
0
)
2
where
E
is in eV, and
E
0
=
10 eV.
(a) If our chunk of metal is at zero temperature (in degrees Kelvin), and has 10
23
electrons in it, Fnd the
±ermi energy
E
F
of the metal. Do not worry about spin (i.e. assume that each energy level can have at
most one electron in it).
(b) Suppose now that we are at some nonzero temperature
T
. Also assume that the ±ermi energy is the
same as what you found in part (a). Let
p
be the probability that an energy level with
E
=
1
.
01
E
F
is
occupied. What must
T
be to have
p
=
0
.
01? Give your answer in degrees Kelvin.
(c) Suppose we are at the same temerpature
T
as part (b). How many electrons do we expect to Fnd in
energy levels with energies between
E
=
E
F
and
E
=
E
F
+
10

2
k
B
T
? Note that you DO NOT need to
do any integrals here! Use the same value of
E
F
as you found in part (a).
2. An aluminum atom has in its outermost shell 2 electrons in the
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This note was uploaded on 01/10/2011 for the course PHYS 271 taught by Professor Aashishclark during the Winter '10 term at McGill.
 Winter '10
 AashishClark
 Quantum Physics

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