Please help with the following question regarding molecules:

Let's consider a toy example of a diatomic molecule as a rigid, massless rod with two point masses m1 and m2 located at either end. The system is free to rotate about its center of mass. (a) Write down the Hamiltonian of the system in terms of the angular momentum operators, assuming a xed center of mass. (b) Compute the energy levels of the system that correspond to different angular momentum states. (C) Compute the degeneracy of each excited state. (d) Suppose that transitions may take place between any state with angular momentum quantum number E and the state )9 1, since the photon can carry away one unit of angular momentum in units of B (so let us forbid, for example, transitions between E and E 2). To clarify, as the system transitions from the higher energy level to the lower energy level it emits a photon in the process with energy equal to the difference in energy levels (by energy conservation). Derive a formula for all of the possible wavelengths of emitted photons that could come from the ensemble of rotational transitions. (e) Let's use this system to approximate molecular CO (carbon monoxide). You can approximate the CO atoms as being separated by around 0.12 nm. In this case, what is the (approximate) wavelength of the longestwavelength photon that can arise from a rotational transition in CO? (Is this wavelength in the radio band, the IR, optical, UV?)