Physical Chemistry Third Edition

23.8 Other Types of Spectroscopy 991

corresponds to∆J−2, and theSbranch corresponds to∆J+2. These branches

consist of sets of lines with the same spacings as the lines in the rotational Raman

spectrum.

PROBLEMS

Section 23.7: Raman Spectroscopy

23.44a.From data in Table A.22 of Appendix A, find the
Raman shift for the band center of the Stokes
vibrational fundamental band of diatomic oxygen.
If the incident light has wavelength 253.7 nm, find
the wavelength of this band center.
b.Find the splitting in cm−^1 between the band center
(theQbranch) and the first line of theSbranch.
c.Find the splitting in cm−^1 between adjacent lines in
theSbranch. How does this compare to the splittings
between the lines of theObranch?

23.45The rotational Raman spectrum of H 2 has lines at
Raman shifts of 354 cm−^1 , 586 cm−^1 , 814 cm−^1 ,
and 1034 cm−^1. At room temperature, the line of
greatest intensity is at 586 cm−^1. Explain the relative
intensities and calculate the internuclear distance for H 2.

23.46From the frequency in Figure 22.6, find the Raman shift
in reciprocal wavelength for the band center of the
symmetric stretch of carbon dioxide. If the incident light
has wavelength 253.7 nm, find the wavelength of this
band center.

23.47Which of the following substances will have a rotational
Raman spectrum?

a.CCl 4

b.BF 3

c.CO 2

23.48Which of the following substances will have a rotational

Raman spectrum?

a.SF 6

b.PCl 5

c.NH 3

23.49Which of the substances in Problem 23.25 will have a

rotational Raman spectrum?

23.50Using computer software such as CAChe or Spartan,

find the normal modes of vibration of the following

molecules, using both semiempirical and ab initio

methods. Compare the calculated frequencies with the

experimental frequencies.^26 Decide which modes will

lead to an infrared band and which will lead to a Raman

band.

a.Acetylene (ethyne) C 2 H 2

b.CS 2

c.OF 2

23.8 Other Types of Spectroscopy

There are a number of types of spectroscopy in addition to those that we have discussed

so far.

Photoelectron Spectroscopy

In this technique ultraviolet radiation is absorbed by a molecule, causing ejection of

an electron:

M+photon→M++e− (23.8-1)

(^26) G. Herzberg,Molecular Spectra and Molecular Structure, Vol. II, Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand Reinhold,
New York, 1945.