2. Consider the harmonic oscillator as a model of vibration in a diatomic molecule A B, where the transition between states = 0 and = 1 can be observed via infrared spectroscopy. (a) Show that the photon energy corresponding to the energy difference between the = 0 and = 1 energy levels is 4E = ~ s k (1) where k is the force constant and is the reduced mass. (b) Given the vibrational frequency of H35Cl, 8.661013 Hz, calculate the vibrational frequency of H37Cl where the force constant is the same for the two isotopologues. (c) Sketch the relative energy levels of the first three vibrational states of H35Cl and H37Cl. 1