The HCl molecule shows its first and second overtone transitions at and
, respectively. Assuming anharmonic oscillator model, determine the anharmonicity constant, the equilibrium vibrational frequency, zero point energy, and the force constant of this molecule.
The vibrational energy levels of a diatomic molecule like HCl can be described using the anharmonic oscillator model, which corrects the harmonic oscillator approximation by accounting for bond anharmonicity. The energy levels are given by [ E_v = h\nu_e \left(v + \frac{1}{2}\right) - h\nu_e x_e \left(v + \frac{1}{2}\right)^2 ] where (v = 0, 1, 2, \dots) is the vibrational quantum number, (\nu_e) is ______ ______ ______ _________ ___ _____ __________ ____ _________ _____ _____ _____.
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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 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.
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The anti-symmetric spin function for a two electron system is given as:$
Prove that is an eigenfunction of
.
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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
.