Physical Chemistry Third Edition

968 23 Optical Spectroscopy and Photochemistry

% Transmittance

3059.32

3056.97

3045.06

3042.73

3030.09

2998.042981.002963.292961.072944.902942.722925.902923.722906.242865.102843.622821.562798.942775.782752.04

3027.78

3014.41

3012.12

2995.78

2978.75

2904.11 2863.02

2841.582819.562796.97

2773.82

2750.13

2727.78

2725.92

2703.01

2701.08

2677.73

2675.94

2651.96

2650.22

v/cm
^1

~

Figure 23.9 The Fundamental Band of the Vibration–Rotation Spectrum of HCl.The resolution of the spectrum is sufficient to show
the lines for H^35 Cl and H^37 Cl. The^35 Cl is the more abundant isotope of chlorine, and produces the more intense lines. From N. L. Alpert,
W. E. Keiser, and H. A. Szymanski,IRTheory andPractice of InfraredSpectroscopy, 2nd ed., Plenum Press, New York, 1970.

As in most molecules, theDterm is small and its effect is negligible. Theνexeterm

does not affect this spectrum because all lines in this spectrum correspond to the same

vibrational transition, fromv0tov1.

With the full energy level expression of Eq. (22.2-45), the reciprocal wavelength of

the band center of the fundamental band is

̃νBC

1

λBC

 ̃νe− ̃νexe[(3/2)^2 −(1/2)^2 ]

 ̃νe− 2 ̃νexe (center of the fundamental band) (23.3-12)

The reciprocal wavelength of the band center of the first overtone band is

̃νBC

1

λBC

 2 ̃νe− 6 ̃νexe (center of the first overtone band) (23.3-13)

If the overtone band can be observed it is possible to evaluate the anharmonicity

parameter ̃vexefrom it.

EXAMPLE23.7

Find the reciprocal wavelength for the band centers of the fundamental and the first overtone

of the CO molecule, including the ̃νexecorrection.

Solution

For the fundamental, the reciprocal wavelength of the band center is

̃νBC

1

λBC

 2169 .81 cm−^1 −2(13.29 cm−^1 ) 2167 .22 cm−^1

For the first overtone,

̃νBC

1

λBC

2(2169.81 cm−^1 )−6(13.29 cm−^1 ) 4259 .86 cm−^1