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.
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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 spacing between of
molecule in Raman spectrum is
. Calculate the bond length of the molecule.
Write the laser rate equation for a two level system and hence prove that the steady state population inversion cannot be achieved in a two level system.
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.
The anti-symmetric spin function for a two electron system is given as:$
Prove that is an eigenfunction of
.
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.
Write the Hamiltonian of a multi-electron atom. Obtain an expression for the effective potential experienced by an electron of this atom under the central field approximation.