The particle in a box problem is often used as a model for the pi electrons in conjugated molecules. Assume that the four pi electrons of 1,3-butadiene move along a straight line of 578 pm (2 C=C bond lengths of 135 pm, one C-C bond length of 154 pm, plus an additional C-C bond length at the 2 terminal C atoms). The energy level diagram indicates that 2 electrons reside in the E₁ energy level and 2 are in the E₂ level.

(a) Why are only two electrons placed in E₁?

(b) What is the energy of an electron in E₂?

(c) At what energy (in Joules) is the E₃ level?

(d) What energy is required to promote an electron from E₂ to E₃ (in Joules)?

(e) If this energy is supplied by a photon, what is the wavelength of the photon? How does this compare to the experimentally observed wavelength of 217 nm?