2.17 A very simple model of a polyene is the free electron molecular orbital (FEMO) model. Regard a chain of N conjugated carbon atoms, bond length Rcc, as forming a box of length L = (N 1)Rcc. Find an expression for the allowed energies. Suppose that the electrons enter the states in pairs so that the lowest N states are occupied. Estimate the wavelength of the lowest energy transition, taking Rcc = 140 pm and N = 22. Repeat the calculation of the wavelength if the length of the chain is taken to be (N+ 1)Rcc (an assumption that allows for electrons to spill over the ends slightly). %3D