Chem 120B
Problem Set 2
Due: February 4, 2011
1. Problems 178 and 1743 in McQuarrie & Simon’s
Physical Chemistry
textbook.
For problem 178, note that the two spin states of a proton in a magnetic field have energies
±
planckover2pi1
γB
z
/
2
.
Calculate the field strength
B
z
for which the number of protons aligned with the field is twice that of
protons aligned against the field,
N
w
= 2
N
o
, at
T
= 300
K
.
2. Consider a particle of mass
m
in a uniform gravitational field. Its potential energy is
E
(
h
) =
mgh
,
where
h
is the height above sea level and
g
is the earth’s gravitational constant,
g
= 9
.
8
m/s
2
.
(i) According to the Boltzmann distribution, what is the probability
p
(
h
)
of finding the particle at
height
h
, relative to the probability
p
(0)
of finding it at sea level (
h
= 0
), at temperature
T
?
[In truth,
p
(
h
)
is a probability
density
, since
h
is a continuous variable. A more proper way to word
this question would be in terms of the probability
p
(
h
)Δ
h
of finding the particle in a small range of
height between
h
and
h
+Δ
h
. But since
(
p
(
h
)Δ
h
)
/
(
p
(0)Δ
h
) =
p
(
h
)
/p
(0)
, the answer would be the
same.]
(ii) Now imagine that there are
N
such masses, all identical and noninteracting. On average, how
many of these objects reside at height
h
, relative to the number at sea level? Express your answer in
terms of relative densities,
ρ
(
h
)
/ρ
(0)
, where
ρ
(
h
)
denotes the average number of particles per unit
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 Spring '09
 JAMESAMES
 Physical chemistry, Atom, Proton, pH, Excited state, excited states

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