P7D.5 When -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 11C atoms and one O atom. In the ground state of retinal, each level up to n=6 is occupied by two electrons. Assuming an average internuclear distance of 140pm, 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. (c) Using your results, choose among the words in parentheses to generate a rule for the prediction of frequency shifts in the absorption spectra of linear polyenes: The absorption spectrum of a linear polyene shifts to (higher/lower) frequency as the number of conjugated atoms (increases/decreases). 1-Carotene