The molecule 1,3,5-hexatriene exhibits an electronic transition in the uv with the absorption maximum occurring at gamma = 268 nm. in this problem, we will approximate pi-electrons as being non-interacting particles in a box, with the box formed by the conjugated network of pi-bonds.

a. taking the c-c single bond length to be r_c-c = 154 pm (picometers) and the c = c double bond length to be r_c = c = 135 pm, calculate the approximate box length. to keep things simple, we will ignore the true geometry of the molecule to pretend that all of the bonds collectively form a straight line.

b. assuming that the transition observed in the experiment involves an electron moving from the highest-energy occupied state to the lowest-energy unoccupied state, identify the quantum numbers involved in the transition. in doing so, remember from general chemistry that the pauli exclusion principle requires that each energy level only contains up to two electrons. note that you should only consider the pi-electrons in this analysis.