Chapter 10, Problem 10.50E

The electronic spectrum of the molecule butadiene, ${\text{CH}}_{\text{2}}\text{=CH}-{\text{CH=CH}}_{\text{2}}$, can be approximated using the one dimensional particle-in-a-box if one assumes that the conjugated double bonds span the entire four-carbon chain. If the electron absorbing a photon having wavelength $2170\stackrel{\circ }{\alpha }$ is going from the level $n=2$ to the level $n=3$, what is the approximate length of the ${\text{C}}_{\text{4}}{\text{H}}_{\text{6}}$ molecule? (The experimental value is about $4.8\stackrel{\circ }{\alpha }$.)