ADVANCED TOPICS IN LASER SPECTROSCOPY I���� PHYS 286

Fall 2002

Homework #3

Dr. P. Misra

1.                  (a)������� In the pure rotational Raman spectrum of homonuclear diatomic molecule a 5:3 intensity alternation is observed.� Assuming that the portion of the wave function exclusive of nuclear spin and rotation is totally symmetric, explain the observed intensity alternation with the aid of a well-labeled energy level diagram.

(b)������� For a certain diatomic molecule, the fundamental vibration-rotation band in the ground electronic state occurs at 4 μm in the infrared.� The raman spectrum for the same molecule was excited by using the radiation from a certain source; where the filter between the source and the sample transmits the monochromatic wavelength 4000 �.� Calculate (to the nearest �) the wavelength of the Raman band that one would observe corresponding to the infrared fundamental.

2.                  In a portion of the solar spectrum, a group of four lines were identified to be due to absorption by the (1-0) band of ¹⁴N₂ in the Earth�s atmosphere.� The wavenumbers of these lines (in cm^-1) were:� 2395.96, 2403.57, 2411.13, and 2418.65.� Identify the S-branch transitions (ΔJ = +2) responsible for these four lines on a clearly labeled energy-level diagram.� (Remember that N₂ is a homonuclear diatomic molecule and has no electric dipole transitions corresponding to ΔJ = 0; but it does have electric quadrupole allowed transitions corresponding to ΔJ = +2).

3.                  A portion of the Raman spectrum of ¹⁴N₂ corresponding to the Stokes branch is excited using the 4358.3 � line of mercury.

The wavenumbers (in cm^-1) of the Raman lines with serial numbers are: 22,908.92, 22,900.96, 22,893.01, 22,885.06, 22,877.11, 22,869.16, 22,861.22, and 22,853.28, respectively.� Determine the J assignments for the eight Raman lines.