Though the particle in a box (infinite potential well) seems like avery unrealis

Question

Though the particle in a box (infinite potential well) seems like avery unrealistic potential, it can actually be used to explain abit about how humans see. The important light absorbing molecule inhuman eyes is called retinal. Retinal consists of a chain of carbonatoms, roughly long. Anelectron in this long chain molecule behaves very much like aparticle in a box. Find the wavelength of the photon that mustbe absorbed by an electron to move it from the state of a box to the state. Assume that thebox has length and that the electron has mass .Express your answer in terms of , , Planck's constant (divided by ) , the speed of light , and .

Explanation / Answer

E = E(n+1) - E(n) = (((h_bar)^2 pi^2)/(2mL^2)) * ((n+1)^2 - n^2)

f = E/((h_bar) 2 pi)

lamda = c/f = (2 (h_bar) c pi)/E = (2 (h_bar) c pi)/((((h_bar)^2 pi^2)/(2mL^2)) * ((n+1)^2 - n^2))

==> lamda = (4 c m L^2)/(pi (h_bar) (2n+1))

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