Physical Chemistry , 1st ed.

At lower frequencies than visible light, there are infrared (“lower than red,” ab-
breviated IR) radiation, microwaves, and radio waves.
A convenience in spectroscopy is that most of the individual types of tran-
sitions (rotational, vibrational, electronic, and so on) occur in characteristic re-
gions of the electromagnetic spectrum. Most pure rotational transitions occur
by absorbing or emitting microwave radiation. Most pure vibrational transi-
tions occur by absorbing or emitting infrared radiation. Similarly, electronic
transitions occur in the presence of visible and ultraviolet light. There are ex-
ceptions, of course: transitions of electrons among the forbitals (that is, in
rare-earth atoms) can occur in the infrared region, and rotational transitions
can be observed superimposed on a vibrational spectrum, also in the infrared
region. But it is still convenient to refer to a type of spectroscopy by the region
of the electromagnetic spectrum being probed.

Example 14.1

Assuming that the general regions of the various atomic or molecular tran-

sitions above are followed, put pure electronic, rotational, and vibrational

transitions in order of increasing energy.

Solution

Assuming that electronic transitions occur in the visible or UV portion of the

spectrum, the rotational in the microwave region, and the vibrational in the

IR, then rotational transitions are lowest in energy, vibrational transitions are

higher in energy, and electronic transitions are the highest of the three.

Another convenience for spectroscopists (but perhaps not for students!) is
the fact that each type of spectroscopy uses its own units to indicate the en-
ergy changes measured by a spectrum. All units are related to energy, but one
may have to apply cor Ehto convert into energy units. Often, tran-
sitions in the microwave region are stated in units of frequency (MHz or GHz),
whereas changes in electronic energies are typically expressed in units of nm
or Å. In both cases, the numerical value and unit collectively refer to the pho-
ton that is absorbed or emitted in the course of the transition. Vibrational
spectroscopy, in the infrared region, uses units of micrometers, or microns,to
indicate the wavelength of the photon involved in the transition. (Microns are
typically denoted instead of the SI-approved m. Although the micron is not
an SI-approved unit (micrometer is preferred), it is often found in scientific
literature. Therefore, you should be familiar with it.) Commonly, the wavenum-
berunit is used. It is defined as the number of waves of light per centimeter,
so it has the unit cm^1 .* It equals the reciprocal of the wavelength (in centi-
meters) of the light involved. Therefore,

wavenumber  ̃ 

1

 (14.6)

It is easy to show that the wavenumber of any photon is proportional to its fre-
quency, so wavenumber is sometimes referred to as “frequency.” Be careful to
distinguish between  ̃, having units of cm^1 , and  (no tilde above the letter),
which represents frequency and has units of s^1.

14.3 The Electromagnetic Spectrum 465

*The SI-approved unit for wavenumbers is m^1 ,but cm^1 is used almost exclusively.