The allowed energy levels (En) for a particle of mass m in a one-dimensional box of length a are given by: En = n2h2/(8ma2) , n = 1, 2, 3, ... The carbocyanine dye 1 has 10 electrons in the conjugated π-system (highlighted in bold). The energy levels (“orbital energies”) of the π-electrons can be estimated by treating the πsystem as a one-dimensional box of length 1.40 nm. Each level can then be occupied by up to 2 electrons. 1 Calculate the energy difference between 5th and 6th energy levels (i.e., the gap between the highest occupied and lowest unoccupied orbitals). Convert this energy to a wavelength, λ. The actual absorption wavelength is 575 nm. Comment on why the result of your calculation is different from this. h = 6.626 × 10–34 J s, me = 9.109 × 10–31 kg, c = 2.997 × 108 m s–1