Agas containing hydroxide (oh ) molecules has been an absorption line at wave number 1/λ = 3500 cm-1. this means that when photons with that wave number hit the molecule, they can be ab- sorbed due to a transition between two successive energy levels of the molecule whose energy difference, ae, equals the energy of the photon. the two energy levels correspond to different vibrational states of the molecule. you may assume that the molecular vibrations can be described by the oscillating motion of the h+ ion (i. e. a proton) around its equilbrium distance from the o2- ion, which can be considered fixed (since its mass is uh larger than that of the proton) (a) calculate the energy of photons absorbed in this line hint: use the speed of light to obtain the frequency of the light, then use planck's equation giving the energy of a photon in terms of its frequency and planck's constant (b) deduce the angular frequency w of the effective harmonic oscillator potential in which the proton moves hint: use the equation obtained in the lectures for the energy difference between two successive energy levels of a sho and equate it to the photon's energy. solve for the harmonic oscillator quency (c) what pairs of vibrational states can be involved in the absorption of the photon?