CHEM106: Assignment 11
Microwave, IR, and Raman Spectra
1. Which of the following molecules are microwave active? Indicate the reason for your
choice.
A. F2; not active
B. NO; active
C. CH3I; active
D. CO2; not active
According to the gross selection rule, the molecule must possess a permanent
dipole moment for a rotational transition in the microwave spectroscopy.
2. Which of the following vibrational modes of the carbon dioxide molecule CO2 will be
IR active? Which will be Raman active?
To be IR active, there must be a change in dipole moment as the molecule
undergoes vibrational motion. So the v2 and v3 modes of vibration are IR active.
To be Raman active, there must be a change in polarizability as the molecule
undergoes vibrational motion. So the v1 mode of vibration is Raman active.
3. The spacing between the lines in the microwave spectrum of H19F is 41.9 cm-1.
Calculate the bond length of the H19F molecule.
h
Spacing in the microwave spectrum equals to 2B (in Hz), where B 
. We also
8 2 I
know that the moment of inertia I  r 2 , where  is the reduced mass,
mm
1  19
19
 1 2 
amu 
amu  1.661  10 27 kg / amu  1.5779  10 27 kg .
m1  m2 1  19
20
At first, we need to express the line spacing in unit of Hz:
~
2 B  2 B  C = 41.9 cm -1  3.0  1010 cm/s = 1.257 x 1012 Hz .
Next, we need to figure out the moment of inertia I:
I=
h
8p 2 B
Finally, r 
=
6.626 ´10-34 J × s
=1.337´10-47 kg × m2 .
2
11 -1
8× 3.14159 × 6.285´10 s
I


1.337  1047 kg  m 2
 9.2  1011 m  0.92 Å.
1.5779  1027 kg
4. The fundamental vibrational frequency of H127I is 2309.5 cm-1. Calculate the force
constant for the stretching vibration of the H127I molecule.
The vibrational frequency  is related to the force constant k by the relationship
1 k

, where  is the reduced mass,
2 

m1m2
1  127
127

amu 
amu  1.661  10 27 kg / amu  1.648  10 27 kg .
m1  m2 1  127
128
We also know that   c /   c ~  3.0  1010 cm / s  2309.5cm 1  6.92  1013 s 1 .
Therefore,
k  4 2  2  4 2  1.648  1027 kg  (6.92  1013 s 1 ) 2  312.3 kg  s 2  312.3N / m .
5. Determine the number of normal mode vibrations in the following molecules.
A. HCl; For a linear molecule, the number of normal modes of vibration is
3N – 5 = 6 – 5 = 1.
B. C6H6; For a nonlinear molecule, the number of normal modes of vibration is
3N – 6 = 36 – 6 = 30.
C. CHCl3; For a nonlinear molecule, the number of normal modes of vibration is
3N – 6 = 15 – 6 = 9.
D. CO2; For a linear molecule, the number of normal modes of vibration is
3N – 5 = 9 – 5 = 4.