The Raman Effect

Light of frequency $\nu$ is incident on a target. If the emergent light is analysed through a spectrometer it is found that theere are components at two new frequencies $\nu-\Delta \nu$ and $\nu+\Delta \nu$ known as the Stokes and anti-Stokes lines respectively. This phenomenon was discovered by Sir. C.V. Raman and it is known as the Raman Effect.

As an example, we consider light of frequency $\nu=6.0 \times 10^{14} Hz$ incident on benzene which is aliquid. It is found that there are three different pairs of Stokes and anti-Stokes lines in the spectrum. It is possible to associate each of these new pair of lines with different oscillations of the benzene molecule. The vibrations of a complex system like benzene can be decomposed into different normal modes, each of which behaves like a simple harmonic oscillator with its own natural frequency. There is a separate Raman line associated with eah of these different modes. A closer look at these spectral lines shows them to have a finite width, the shape being a Lorentzian corresponding to the resonance of a damped harmonic oscillators. Figure 4.2 shows the Raman line corresponding to the bending mode of benzene.

Figure 4.2:

Problem For the Raman line shown in Figure 4.2

a.

What is the natural frequency and the corresponding $\omega_0$?

b.

What is the FWHM?

c.

What is the value of the quality factor $Q$?