Chemistry 21b
Problem set # 4
Out: 26 January 2011
Due: 02 February 2011
Problems are worth: 1a=15, 1b=10; 2a=10, 2b=15; 3a=10, 3b=5, 3c=5, 3d=5; 4ae=5 points each
(for 25 points total).
1. A problem about simple symmetric tops.
(a.) Prove the moment of inertia formulae for a symmetric top of form A
3
B can be written as:
I
b
= 2
m
A
(1

cosθ
)
R
2
I
⊥
=
m
A
(1

cosθ
)
R
2
+
m
A
m
B
m
(1 + 2
cosθ
)
R
2
where
R
is the AB bond length and
θ
the ABA bond angle.
(b.) Treat AsCl
3
as a rigid rotor with transitions as follows:
75
As
35
Cl
3
has its J=4
→
5 transition
at 21,472 MHz and
75
As
37
Cl
3
has its J=5
→
6 transition at 24,536 MHz. Fom these data
calculate the geometry of the molecule, that is,
R
AsCl
and
θ
ClAsCl
.
2. Consider the molecule thioformaldehyde, H
2
CS.
a) Using the asymmetric rotor energy level formulae given in Lecture #10 (Table 10.1 on p. 82),
calculate the ±rst few (
J
=0, 1 and 2) rotational energy levels of the molecule. The rotational
constants are A= 291291.641 MHz, B=17699.628 MHz, and C= 16651.83 MHz. Draw an
energy level diagram. This molecule is a nearsymmetric top. Which one (oblate or prolate)?
b) The total permanent dipole moment of thioformaldehyde is 1.649 Debye.
What are the
projections of this dipole moment along the
a
,
b
, and
c
inertial axes? Using these results,
and the selection rules also noted in Lecture #10, indicate in the energy level diagram which
transitions are electric dipole allowed. Do the transitions lie in the centimeter, millimeter,
submillimeter or far–infrared part of the spectrum?
3. a) From the following wave numbers of the
P
and
R
branches of the 1–0 infrared vibrational
band of
1
H
127
I in the X
1
Σ
+
state, obtain values for the rotational constants
B
0
,
B
1
and
B
e
(in
cm
−
1
), the band center ˜
ν
0
(in cm
−
1
), the vibration–rotation interaction constant
α
e
(in cm
−
1
).
v
= 0
→
1 Rovibrational Transitions for
1
H
127
I
Transition
Frequency (cm
−
1
)
Transition
Frequency (cm
−
1
)
R(0)
2242.087
P(1)
2216.723
R(1)
2254.257
P(2)
2203.541
R(2)
2266.071
P(3)
2190.025
R(3)
2277.510
P(4)
2176.168
b) What value results for the internuclear distance
R
e
(in
˚
A)? How does the value for
R
e
compare
with the value
R
e
=1.607775
˚
A for
2
H
127
I? How should it compare? Why?