Physical Chemistry , 1st ed.

energy differencebetween the incoming light and the outgoing light. Thus, if the

incoming light is in the visible part of the spectrum, the outgoing light is also in

the visible part of the spectrum. It’s the changesin the energy of the photons that

equal the vibrational energy differences (rather than the absolute energies of the

photons). Figure 14.39 shows two scales on the abscissa of the spectrum, an ab-

solute frequency of the light (which shows that the spectrum is being measured

in the visible portion of the electromagnetic spectrum), and a difference in fre-

quency of light (which shows magnitudes that are consistent with vibrations of

molecules). A value of 0 is at the frequency of the incoming, excitation light—

in this case, the 632.8-nm wavelength of the red light of a He-Ne laser. There is

a very large peak at that position because of the relatively intense Rayleigh scat-

tering of the incoming light. Some photons appear at lower frequencies, with the

energy shifts corresponding to the vibrational frequencies of C 2 F 4. Thus, this

Raman spectrum is giving us a vibrational spectrum of the sample.

Another difference between Raman spectroscopy and regular absorption

spectroscopy is that occasionally an outgoing photon increasesits energy by in-

teracting with a molecule that is energetically excited. In this circumstance, the

photon increases its frequency and we see a spectrum on the higher-energy

side of the excitation light. Because the same energy levels of the molecule are

involved, we see the same—but reflected—vibrational spectrum we see on the

lower-energy side of the excitation line, only less intense (because there are

typically fewer molecules in the excited energy states). This is also shown in

Figure 14.39. The lines of the spectrum on the lower-energy side are called the

Stokes lines,and the lines of the spectrum on the higher-energy side are called

the anti-Stokes lines(after George Gabriel Stokes, an Irish mathematician who

discovered fluorescence in 1852).

512 CHAPTER 14 Rotational and Vibrational Spectroscopy

 2000

 (cm^1 )

1872 cm

^1

1340 cm

^1

394 cm

^1

551 cm

^1

Excitation line

Stokes lines 778 cm Anti-Stokes lines

^1

508 cm

^1

 (cm^1 )

 2000

13,800 17,800

 1500

14,300

 1000

14,800

 500

15,300

0

15,800

 500

16,300

 1000

16,800

 1500

17,300

Figure 14.39 A Raman spectrum of tetrafluoroethylene, CF 2 CF 2. The difference between the

frequency of the emitted photon and the excitation photon equals an energy of vibration of

the molecule. The Stokes lines and anti-Stokes lines are modified mirror images of each other,

reflected through the excitation frequency. Anti-Stokes lines are always lower in intensity than the

corresponding Stokes line.