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 anti-symmetric spin function for a two electron system is given as:$
Prove that is an eigenfunction of
.
The spacing between of
molecule in Raman spectrum is
. Calculate the bond length of the molecule.
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
.
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.
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
.
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.
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.