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PH503: Year 2015

Problem Set-IX

Instructor: Subhradip Ghosh

1. Two unlike atoms, each one in a 3Pstate, form a molecule. Write down the spectroscopicterms for the molecular states.

2. Draw Molecular Orbital energy diagrams for HCl and CO molecules.

3. A beam of hydrogen molecules travel in the z direction with a kinetic energy of 1 eV.The molecules are in excited state, from which they decay and dissociate to two hydrogenatoms.When one of the dissociation atoms has its final velocity perpendicular to the z di-rection its kinetic energy is always 0.8 eV. Calculate the energy released in the dissociativereaction.

4. Make a rough estimate of the energy contributions due to electronic, vibration and rota-tional contributions to the total energy of a diatomic molecule, in terms of fundamentalphysical constants like nuclear mass, electronic mass, electronic charge etc.

5. Consider a diatomic molecule with nuclei with masses m1 and m2,in a central force fielddescribed by the potential

V (r) = 2V0

1

1

22

where = r/a, a some characteristic length parameter.

(a)Show that for smallB ,B = l(l+1)h2

2a2V0, is the reduced mass in centre of mass frame, the

Schrodinger equation reduces to that of a simple harmonic motion with frequency

=

2V0

a2 (1 + B2)3

1/2

(b) Assuming h2/2 >> a2V0, find the rotational, vibrational and rotational-vibrationalenergy levels for small oscilations.