or equal to about J4 or 5. (How does this compare with the spectrum in
Figure 14.35?)
c.Given that the band head occurs at around J33, we are 28 or so quantum
rotational levels away. Since the spectrum in Figure 14.35 seems to diminish in
intensity rather quickly, it is doubtful that the band head will be observed for
this molecule at this temperature. Chances of observing it would be better if
the temperature were increased. With the inclusion of the centrifugal distor-
tion, however, the band head would be expected to occur at slightly lower J,but
still not low enough to be observed at normal temperatures.14.18 Raman Spectroscopy
When light is passed through a transparent sample, most of the light is trans-
mitted through the sample. A tiny amount of light (about 1 photon in 10^4 ) is
scattered from the sample at some angle and comes off at some angle. This
light has the same frequency as the incoming light, and the extent to which
light is scattered is inversely proportional to the fourth power of its wave-
length.* This phenomenon is called Rayleigh scattering.Rayleigh scattering can
be thought of as elasticcollisions between molecules and photons.
An even smaller amount of light (about 1 photon in 10^7 ) is scattered but
changes frequency: these can be thought of as inelastic collisions between mol-
ecules and photons. This phenomenon is called Raman scattering,after the
Indian physicist Chandrasekhara Raman, who is credited with discovering the
effect in 1928. Raman scattering is interesting because the energy changes of
the outgoing photons correspond to changes in quantized energy levels of the
molecules in the sample:
E(photon) E(energy levels) (14.43)Thus, Raman scattering forms the basis for a type of spectroscopy, called
Raman spectroscopy.Today, Raman spectroscopy is performed using lasers as
the incoming light source because the laser light is intense (providing a better
chance to observe photons that have shifted frequency) and monochromatic
(making it easier to find shifted-frequency photons).†
Raman spectroscopy is used to study many different types of spectral
transitions, but for our purposes we focus on the use of Raman scattering to
study the vibrational energy transitions of molecules. Incoming photons will
interact with molecules and, in a small number of cases, lose some of their
energy to the vibrations of the molecules. The outgoing photons, scattered
in all directions, will lose a small amount of energy equal to the difference in
the vibrational energy levels of the molecule. From quantum mechanics, the
energy difference between the incoming and outgoing photon equals the
energy difference in the quantized vibrational energy levels:
E(photon) hi (14.44)where iis the classical frequency of the ith vibration of the molecule.
An example of a Raman spectrum of tetrafluoroethylene, C 2 F 4 , is shown in
Figure 14.39. There are some differences between a Raman spectrum and an
absorption vibrational spectrum. First, a Raman spectrum is a plot of the
14.18 Raman Spectroscopy 511*Rayleigh scattering is reponsible for the blue color of the sky. Blue light scatters more
than other wavelengths because of its shorter wavelength.
†Raman and his colleagues used sunlight and, later, mercury lamps as light sources.