Physical Chemistry Third Edition

998 23 Optical Spectroscopy and Photochemistry

ADDITIONAL PROBLEMS

23.53a.Would H 2 have a microwave spectrum?

b.Would H 2 have an infrared spectrum?

c.Would H 2 have a rotational Raman spectrum?

d.Would H 2 have a vibrational Raman spectrum?

e.Describe all of the spectra that would occur, including

band centers and splittings in reciprocal centimeters

for optical spectra. For Raman spectra, specify the

Raman shifts.

23.54The nitronium ion, NO+ 2 , has a single Raman band with a
Raman shift of 1400 cm−^1. Strong IR bands are found at
540 cm−^1 and at 2360 cm−^1 , but not at 1400 cm−^1.
What is the shape of NO+ 2? A weak IR band is found at
3735 cm−^1. What is it due to?

23.55At room temperature, the most highly populated
rotational level of HF corresponds toJ2. Neglect
the corrections to the energy levels and use the
harmonic-oscillator, rigid-rotor approximation.
a.Sketch the room-temperature microwave spectrum of
HF as a function of reciprocal wavelength. Specify the
reciprocal wavelength of each of the first four spectral
lines and indicate the approximate relative intensities
of the lines.

b.Sketch the fundamental IR band of HF at room

temperature as a function of reciprocal wavelength.

Specify the reciprocal wavelength of the band center

and the splitting between adjacent lines of the two

branches. For each branch tell what transitions

produce the lines.

c.At what reciprocal wavelength would you look for the

center of the first overtone band of HF?

d.Sketch the Stokes branch of the rotational Raman

spectrum of HF as a function of Raman shift in

reciprocal wavelengths. Specify the Raman shift of

each of the first four lines.

23.56a.Would sulfur hexafluoride, SF 6 , have a microwave
spectrum?
b.Would sulfur hexafluoride have a rotational Raman
spectrum?
c.How many vibrational normal modes would sulfur
hexafluoride have?

d.Orient the sulfur hexafluoride molecule so that the

fluorine atoms are on the coordinate axes. Consider a

normal vibrational mode in which all fluorine atoms

move perpendicular to thexzplane, with the fluorine

atoms in thexzplane moving in one direction, whereas

those on theyaxis move in the opposite direction.

Would this normal mode be seen in the infrared

spectrum? Would it be seen in the Raman spectrum?

e.Consider the symmetric stretch normal mode, in

which all fluorine atoms move away from the sulfur

atom simultaneously. Would this normal mode be seen

in the infrared spectrum? Would it be seen in the

Raman spectrum?

23.57For each of the following molecules, tell whether the

specified motion will give rise to a Raman line or

band, an emission/absorption line or band, both, or

neither:

a.The symmetric stretch of CO 2.

b.The asymmetric stretch of CO 2.

c.The rotation of CH 4.

d.The vibration of N 2.

e.The rotation of N 2.

23.58Carbon dioxide exhibits a strong infrared absorption band

at 667.2 cm−^1. This band has aQbranch. There is

another strong infrared band at 2349.3 cm−^1.

a.Identify the normal mode involved with each of these

bands. Explain your answer. Would you expect to find

aQbranch in the band at 2349.3 cm−^1?

b.How many additional strong infrared bands would

you expect to find? If any, where would you expect to

find them?

c.What would you expect to find in the vibrational

Raman spectrum of CO 2?

23.59Consider the two substances, N 2 and CO. Assume all

nuclei are the most common isotopes.

a.Describe the microwave spectra of the two substances

at room temperature, including reciprocal wavelength

values.

b.Describe the fundamental band in the infrared spectra

of the two substances, including the band center and