Physical Chemistry Third Edition

966 23 Optical Spectroscopy and Photochemistry

fundamental band. Those spectral lines for which the value ofJin the upper state

is larger than the value ofJin the lower state constitute theRbranchof the band,

and the spectral lines for which the value ofJin the upper state is smaller than

that in the lower state constitute thePbranch. If lines occurred for which the val-

ues ofJin both states were the same, they would constitute theQbranch. The rota-

tional selection rules are well obeyed, and they forbid theQbranch, which is not

observed. The location that theQbranch would have if it were present is theband

center. The vibrational selection rules are less well obeyed than are the rotational

selection rules, and forbidden vibrational transitions are frequently observed. A spec-

tral band corresponding to∆v±2 is called afirst overtone, one corresponding to

∆v±3 is called asecond overtone, and so on. Bands for which the lower value ofv

is larger than zero are calledhot bands. Hot bands are generally not seen in absorption

spectra near room temperature because of the small population of excited vibrational

states.

If we neglect thexe,α, andDterms in the energy level expression of Eq. (22.2-45)

the reciprocal wavelength of a line of theRbranch of the fundamental band is given by

̃νR

1

λR

(E1,J+ 1 −E0,J)/hc ̃νe+ 2 ̃Be(J+1) (J0, 1, 2,...) (23.3-10)

whereJis the value of the rotational quantum number in the lower (v0) state. In this

approximation theRbranch consists of a set of equally spaced lines with spacing 2 ̃Be.

v 50

P branch R branch

J 55

J 54

J 53

J 52

J 51

J 50

v 51

J 55

J 54

J 53

J 52

J 51

J 50

Figure 23.8 Allowed Transitions Leading to a Vibration–Rotation Spectral Band of

a Diatomic Substance.In theRbranch, the value ofJin the upper level is greater than

that in the lower level, and in thePbranch, the opposite is the case. There is noQbranch,

which would correspond to the same value ofJin the upper and lower energy levels.