Using the particle in the 1-D box model, estimate the first 4energy levels of the π-network in hexatriene, C6H8(H2C=CH–CH=CH–CH=CH2). To calculate the box length, assume that themolecule is linear and use the values 135 and 154 pm for the C=Cand C–C bonds, respectively. Only 2 out of the 6 ‘π-electrons’ ofthe 6 C-atoms can occupy each energy level (Pauli exclusionprinciple). Ignore the rest of the electrons (forming the core andthe ??-bonding network). Sketch and label an energy level diagramshowing the occupied levels and the first unoccupied one. What isthe wavelength of the photon required to induce the HOMO-LUMOtransition? Derive the expression for the photon’s wavelengthsymbolically! How does your numeric result compare with theexperimental value of 240 nm?
