[UPSC CSE 2005] Molecular Physics (Q267, 30+30M)

Obtain an expression for the vibration-rotation energy levels of a diatomic molecule in a given electronic state. The wave numbers of the vibrational transitions occuring in HF, HCl and HI molecules are 4141 \cdot 3 \text{ cm}^{-1}, 2988 \cdot 9 \text{ cm}^{-1} and 2309 \cdot 5 \text{ cm}^{-1} respectively. Compare the force constants of these three molecules.