A. Find the energy levels for a particle in a 3-D box. Explain, providing examples, why states lose their degeneration when the box is no longer cubic and becomes a rectangular box. Evaluate the cases in which a = b #c and a + b c. B-A crude treatment for the n electrons of a conjugated molecule considers these electrons to be particles moving in a box, where the length of the box is slightly longer than the length of the conjugated chain. The Pauli exclusion principle allows no more than two electrons to occupy each level (these two have opposite spins). For butadiene, CH2 = CHCH = CH2, consider the box length as 7.0 and use this model to estimate the length of the absorbed light when an n electron is excited from the highest occupied level to the lowest unoccupied level. DISCUSS THE RESULT OBTAINED, COMPARING IT WITH THE EXPERIMENTAL VALUE (217 nm). C- In some zeolites, the adsorption of ethylene leads to a red shift in the transition. Use the mechanical-quantum model of the particle in the box to predict what happens to the length of the C = C bond of ethylene when adsorbed to the zeolite, AE = (2n +1) 8mL where AE is the energy difference between states n and n + 1.