Particle in a Box - Quantum Mechanics

Consider the conjugated molecule 1,3,5-hexatriene as a one-dimensional particle in a box model for its π electrons. The box length can be approximated as L = 5 × 1.40 Å = 7.00 Å (5 C-C bonds × bond length). (a) Calculate the energy levels for n = 1 through n = 4. (b) Six π electrons fill the levels according to the Pauli exclusion principle. Determine the HOMO-LUMO gap. (c) What wavelength of light would excite an electron from HOMO to LUMO? (d) How does this compare with the experimental absorption maximum (~258 nm)?