Physical Chemistry , 1st ed.

Pure rotational spectra usually occur in the microwave region of the elec-

tromagnetic spectrum, so the phrases “rotational spectra” and “microwave

spectra” are sometimes used synonymously. The lines in rotational spectra are

also expressed using several typical units, as the above examples showed. In the

microwave region, it is typical (for historical, habitual, and practical reasons)

to express transitions in units of frequency. In the microwave region, frequen-

cies are in the megahertz (MHz) or gigahertz (GHz) range. It is not unusual

to see rotational spectra displayed using frequency units. Figure 14.10 shows a

pure rotational spectrum in terms of frequency.

Rotations frequently occur along with vibrations (which is why we use

the phrase “pure rotational spectra” to differentiate those from rotational-

vibrational spectra), so it is also customary to express the rotational transitions

in a common unit of vibrational transitions, the wavenumber (in cm^1 ).

Figure 14.11 shows a rotational spectrum in terms of wavenumber. There is a

potential problem when a rotational spectrum is displayed in terms of wave-

length, because wavelength is not directly proportional to energy and the con-

sistent spacing of rotational levels is not obvious. Figure 14.12 shows the same

spectrum as Figure 14.11 but in terms of wavelength units. The equal spacing

isn’t obvious, despite the fact that each spectrum illustrates the same informa-

tion. (This will be discussed further in our treatment of vibrational spectra,

later in this chapter.)

476 CHAPTER 14 Rotational and Vibrational Spectroscopy

0.10

0.00

12000

Frequency (MHz)

14000

Intensity

12500 13000 13500

0.08

0.06

0.04

0.02

Figure 14.10 A pure rotational spectrum of sarin (a nerve gas), in units of frequency. Studies

like this are useful in the development of detectors for nerve gas.

Wavenumber (cm^1 )

Relative intensity

Frequency (s^1 )

Relative intensity

Figure 14.12 The same spectrum as Figure

14.11, but in frequency units. The spacing be-

tween lines is now not equal.

Figure 14.11 A simulated rotational spec-

trum, plotted in wavenumber units. Since wave-

numbers are proportional to energy, the absorp-

tions are evenly spaced.