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.
The Hamiltonian of a multi-electron atom with (N) electrons and a nucleus of charge (+Ze) is expressed as the sum of kinetic and potential energies of all particles. It can be written as [ \hat{H} = \sum_{i=1}^{N} \left[ ____ ______ _____ __________ __________ ______ _______ ___ ______ ____ ___.
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The spacing between of
molecule in Raman spectrum is
. Calculate the bond length of the molecule.
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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and gas temperature of
. Obtain the ratio of spontaneous and stimulated emission if the wavelength is
.
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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.