HW3_chapter 18:
183:
Q.
Show that
1/2
2
2
( , )
B
trans
mk T
q
a T
a
h
in one dimension and that
2
2
2
( , )
B
trans
mk T
q
a T
a
h
in two dimensions. Use these results to show that
trans
has a contribution of
/2
B
kT
to its
total value for each dimension.
A.
Remember that
2
1/2
0
4
n
e
dn
. Then, for one dimension,
2 2
2
1/2
/8
2
0
2
( , )
h n
ma
B
trans
mk T
q
a T
e
dn
a
h
And for two dimensions,
2 2
2
2
/8
2
2
0
2
( , )
h n
ma
B
trans
mk T
q
a T
e
dn
a
h
Now
2
ln
trans
trans
B
V
q
T
The partition function is proportional to
n
T
, where
n
is the dimension, so
ln
2
trans
V
q
n
TT
and
2
22
B
trans
B
nk T
n
T
.
185:
Q.
Using the data in Table 18.1, evaluate the fraction of lithium atoms in the first excited state at
300K, 1000K, and 2000K.
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View Full DocumentA.
We can use the second line of Equation 18.10 to calculate the fraction of lithium atoms in the
first excited state, with
g
e1
= 2,
g
e2
= 2,
g
e3
= 4, and
g
e4
= 2:
2
234
2
2
2
2
4
2
...
e
e
e
e
e
f
e
e
e
Using the data in Table 8.6, we find that the numerator of this fraction is
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 Fall '08
 Bersuker
 Physical chemistry, Atom, pH, Max, qtrans

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