[UPSC CSE 2004] Molecular Physics (Q268, 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 4141.3\text{ cm}^{-1}, 2988.9\text{ cm}^{-1} and 2309.5\text{ cm}^{-1} respectively. Compare the force constants of these three molecules.