Raman Scattering: When electromagnetic radiation is incident on a molecule, the
ID: 2077963 • Letter: R
Question
Raman Scattering: When electromagnetic radiation is incident on a molecule, the vibrational modes of the bonds can modulate the polarizability, which results in scattered light that has a different frequency from the incoming light. This inelastic scattering process (omega_ in not equal to omega_ out) is called Raman scattering, after C. V. Raman, one of the discoverers of the effect [Nature, 121 501- 502 (1928), http://dx.doi.org/10.1038/121501c0]. Here we will discuss the classical treatment of Raman scattering, although a proper treatment requires quantum mechanics. Suppose that a molecule is modelled by two atoms which have equal and opposite charges. We saw in class that incoming electromagnetic radiation with frequency and polarized along the x-axis can create a time-dependent dipole moment of the form p = alpha cos (omega t) x cap. Suppose that the "polarizability" alpha = epsilon_0x actually depends on the separation between the two molecules. Show that that if the molecule oscillates at its natural frequency omega_0, the polarizability can be written as alpha almost equal to alpha_0 + alpha_1 delta Q, where alpha_0 is the polarizability at the equilibrium bond length Q_0, delta Q identical to Q - Q_0 is the deviation of the length of the bond from equilibrium, and alpha_1 = partial alpha/partial Q |+Q = Q_0. Assume that omega >> omega_0, that is, the incoming radiation frequency is much larger than the vibrational frequency of the molecule. Show that if delta Q(t) = delta Q_0 COS(Omega _t + phi), the magnitude of the polarization, using the approximation in (a), is p(w, t) = alpha_0 E_0 cos (wt) + (alpha_1 delta Q_0 E_0/2) {cos[(w - w_0) t + phi] + cos [(w + w_0) t + phi]}. The result in part (b) indicates that an oscillating dipole will be created at three frequencies: omega_ r = omega and omega_ r = omega plus minus omega_0. The oscillation of the dipole will lead to re-radiation of light in those three frequencies. Elastic (or Rayleigh) scattering is obviously given by the first term, which is at the same phase as the incoming radiation, while radiation at omega_ r = omega plus minus omega_0 is known as Raman scattering, which is in general phase shifted. Radiation at omega_ r = omega - omega_0, yielding longer wavelength scattered light, is known as Stokes scattering, while omega_ r = omega + omega_0 is known as anti-Stokes scattering. Raman scattering is permitted only under certain symmetry conditions that govern alpha_1. For example show that if alpha(delta Q) is symmetric (i.e., alpha(delta Q) = alpha(-delta Q)), then Raman scattering is forbidden.Explanation / Answer
Please put your question in a straight forward way the link you given is for what . What do you actually want to know about Raman scattering . So please put your question in a simple and straight forward way. So that it is also helpful for you in getting a good answer. Thankyu.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.