Chemistry 252
Homework 2.
Due Wed. February 4
1.
The vibrations of a diatomic molecule are well modeled by harmonic oscillator.
As you know the energy states of a harmonic oscillator are given by
E
n
=
h
ω
n
+
1
2
.
From spectroscopy we know that
h
ω
=
214.5 cm
1
for I
2
molecule.
By using appropriate Boltzmann factors calculate the ratio of the
numbers of molecules in the 1
st
excited vibrational state (n=1) to that in the
ground vibrational state (n=0) in iodine gas at room temperature (T = 300 K).
An
energy unit conversion table behind the front cover of the book may help.
2.
Solve the same problem for hydrogen gas.
h
ω
=
4401cm
1
for H
2
.
3.
Rotational energy states of a linear molecule are:
E
J
=
BJ J
+
1
(
)
, where
J =
0,1,2… is the angular momentum.
It is
important
that there are total of 2
J
+1
states for every
J,
e.g.
there are 3 states of
J
=1.
What is the number of hydrogen
molecules that are in
J
=1,
J
=2, and
J
=3 states compared to that of
J
=0 at 300 K.
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 Spring '09
 Atom, Mole, j=1, N1 EQ

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