a) The oscillation of the atoms around their equilibrium positions in the molecule HI can be modeled as harmonic oscillator of mass m = m _H (the iodine atom is almost stationary) and the force k = 313.8N/m. Evaluate the separation of the energy levels and predict the wavelength of the light needed to induce the transition between the neighboring levels.

b) What is the relative probability of finding the HI molecule with its bond length 10 percents greater than its equilibrium value (equilibrium bond length of 161 pm) when it is in (a) the v = 0 state, (b) v = 4 state. Use the information from the problem above.