i) The fundamental vibrational frequency of a molecule occurs at . Determine the position of Raman line if the molecule is excited with a laser of wavelength
.
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Determine the collisional width for laser operating at a gas pressure of
and gas temperature of
. Obtain the ratio of spontaneous and stimulated emission if the wavelength is
.
a) Determine the shift in energy caused by relativistic correction to kinetic energy for and
levels of hydrogen atom. Using appropriate selection rules, show which transitions are allowed.
The spacing between of
molecule in Raman spectrum is
. Calculate the bond length of the molecule.
The anti-symmetric spin function for a two electron system is given as:$
Prove that is an eigenfunction of
.
The rotational constant for the excited electronic state of a particular molecule is 20% smaller as compared to the rotational constant of its ground electronic state. Determine the values for the first 15 lines of the R-branch. Discuss the variation of the separation between successive transition lines of this branch.
Using molecular orbital method, construct all pssible trial wavefunctions (including spin) for a diatomic molecule. Of these functions, which trial function is expected to have the minimum energy? Give justification for your answer.
Using Thomas-Fermi method, derive an expression for the total kinetic energy of N electrons in a cubic box of side L, and hence obtain the expression for pressure.