The particle on a ring is a useful model for the motion of electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. We may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. Assume that in the ground state of the molecule quantized each level is occupied by two electrons. (A) Calculate the energy and angular momentum of an electron in the highest occupied level.
(B) Calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.