PHAS0099 - Molecular Physics
Academic year 2021/22
Problem sheet 2
Coursework deadline is Friday 11th March. The penalty for late submission is 10% of the total mark obtained
per each day of delay.
1) Chemical bonding in HF [6 marks]
Draw a molecular orbital correlation diagram for the valence electrons of the HF molecule. Indicate the
atomic orbitals that you use and indicate for each molecular orbital if it is of bonding, anti-bonding, or
non-bonding type. [6]
2) Vibrational modes. [8 marks]
(a) Consider the following two isomers of C6O.
How many translational, rotational and vibrational degrees of freedom do Molecules 1 and 2 have? [4]
(b) Explain why N2 does not absorb IR radiation while CO2 does. [4]
3) Potential energy curve. [6 marks]
The figure below shows potential energy curves for the electronic ground state of two homo-nuclear diatomic
molecules A and B which both have the same reduced mass.
Explain which molecule has:
(i) the lower dissociation energy; [2]
(ii) the larger zero point vibrational energy; [2]
(iii) the larger rotational constant; [2]
4) Water [8 marks]
(a) Consider the rotation of the H2O molecule about the principal axis that passes through the oxygen atom
and lies in the H-O-H plane. What would be the spacing between lines in the resulting microwave spectrum
if this rotation is selectively excited? The H-O-H bond angle is 104.5 degrees and the bond length is 95.7
pm. [5]
(b) The wavenumbers of the three normal modes of a H2O molecule are 1595, 3652, and 3756 cm
−1. Deter-
mine the ground-state vibrational energy of the molecule within the harmonic oscillator approximation. [3]
5) Diatomic molecule in the harmonic oscillator and rigid rotor approximation. [12 marks]
The molecular bond of 14N2 in the harmonic oscillator approximation has a spring constant of k=2295 Jm
−2.
In the rigid rotor approximation, the rotational constant for 14N2 is Be = 2.010 cm
−1, where Be =~/(4picI)
and I the moment of inertia.
(a) Calculate the equilibrium bond lengths for the 14N2 molecule. [3]
(b) Neglecting rotations, estimate the relative number of 14N2 molecules in excited vibrational states, with
respect to those in the ground state at T =298 K. [4]
(c) Using the rigid rotor model, estimate what is the most probable value of the rotational quantum number
J for 14N2 molecules at T =298 K. [5]

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