The electronic structure of p-carotene

For reasons that will become clear in Sections 9.9 and 10.4, we assume that only one electron per carbon atom is allowed to move freely within the box and that, in the lowest energy state (called the ground state) of the molecule, each level is occupied by two electrons. Therefore, the levels up to n = 11 are occupied. From eqn 9.10 it follows that the separation in energy between the ground state and the state in which one electron is promoted from the = 11 level to the n = 12 level is 

We can relate this energy difference to the properties of the light that can bring about the transition. From the Bohr frequency condition (eqn 9.1), this energy separation corresponds to a frequency of 

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