IGNOU MPH 16 SOLVED ASSIGNMENT

Ques 1.

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. 

Ques 2.

The anti-symmetric spin function for a two electron system is given as:
$
Prove that  is an eigenfunction of .

Ques 3.

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. 

Ques 4.

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. 

Ques 5.

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. 

Ques 6.

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. 

Ques 7.

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. 

Ques 8.

 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 .

Ques 9.

The spacing between  of  molecule in Raman spectrum is . Calculate the bond length of the molecule.

Ques 10.

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 .

Ques 11.

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.

Ques 12.

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. 

Ques 13.

The anti-symmetric spin function for a two electron system is given as:
$
Prove that  is an eigenfunction of .

Ques 14.

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. 

Ques 15.

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. 

Ques 16.

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. 

Ques 17.

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. 

Ques 18.

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. 

Ques 19.

 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 .

Ques 20.

The spacing between  of  molecule in Raman spectrum is . Calculate the bond length of the molecule.

Ques 21.

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 .

Ques 22.

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.

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