When β-carotene (1) is oxidized in vivo, it breaks in half and forms two molecules of retinal (vitamin A), which is a precursor to the pigment in the retina responsible for vision. The conjugated system of retinal consists of 11 carbon atoms and one oxygen atom. In the ground state of retinal, each level up to n = 6 is occupied by two electrons. Assuming an average internuclear distance of 140 pm, calculate:
a) The separation in energy between the ground state and the first excited state in which one electron occupies the state with n = 7, and
b) The frequency of the radiation required to produce a transition between these two states.