Physical Chemistry Third Edition

23.8 Other Types of Spectroscopy 993

EXAMPLE23.15

The ground-state vibrational frequency for nitrogen is 2359 cm−^1. The spacing between the

lines in the rightmost set of lines corresponds to 2150 cm−^1 , and the line for the transition

fromv0tov0 is at 15.58 eV. Find the ionization energy from the minimum of the

ground-state potential curve to the minimum in the ion curve.

Solution

The ionization energy from thev0 vibrational state to thev0 vibrational state differs

from the desired quantity by the difference of the zero-point vibrational energies, given by

∆Ezero−point

hνmolecule

2

−

hνion

2



hc

2

( ̃νmolecule− ̃νion)



(6. 6261 × 10 −^34 J s)(2. 9979 × 1010 cm s−^1 )

2

(209 cm−^1 )

 2. 08 × 10 −^21 J 0 .0130 eV

∆Ee−e∆E 0 − 0 + 0 .013 eV 15 .58 eV+ 0 .013 eV 15 .59 eV

Exercise 23.12

Explain why the spacing between the lines in the leftmost set in Figure 23.20 is greater than

2359 cm−^1 , the vibrational spacing of the ground level, whereas the spacing between the lines

in the other two sets is smaller than 2359 cm−^1.

Photoacoustic Spectroscopy

Photoacoustic spectroscopy is a type of absorption spectroscopy in which absorption

of energy is detected by the generation of sound waves. A beam of monochromatic

radiation is directed on the sample though a “chopper,” which is usually a rotating

disk with several notches cut in the edge so that the beam is alternately passed and

interrupted (chopped).

Photoacoustic spectroscopy was
originatedbyAlexander Graham Bell,
1847–1922,the inventor of the
telephone.

If the radiation is absorbed by the sample, it will heat the surface of the sample and

the air next to it during the time that the beam is passed by the chopper. During the

time that the beam is interrupted, the sample and the air will cool off. The air will thus

alternately expand and contract with the frequency of the chopper, producing a sound

wave that can be detected by a microphone. If the radiation is not absorbed, no sound

wave is generated. The frequency of the chopper must be slow enough so that the air

has time to cool off during the period of beam interruption, but fast enough to make

a detectable sound wave. A chopper frequency of around 50 hertz is common. The

intensity of the sound wave can be measured electronically as the wavelength of the

light is varied, giving an absorption spectrum. The principal advantage of the method

is that an opaque sample can be used.

Circular Dichroism and Optical Rotatory Dispersion

Circular dichroism and optical rotatory spectroscopy involve study of optically active

substances. Plane-polarized light is described in Section 14.3 and in Appendix F as an