EXAMPLE:  Calculate the wavelength of the retinal, using the "particle in a box" model:

(1) Look at the structural formula of the retinal imine (A).

(2) Count the alternant carbon, carbon (and carbon, nitrogen) bonds, there are twelve bonds (B).

(3) Assume that (a) all conjugated bonds are about the same length (true for benzene) and (b) that the lengths is about 140 pm.

(4) Use high-school geometry and trigonometry to calculate approximate length of twelve conjugated bonds zig-zagged by 120 degree (C).

(5) Find the length of the "box" (the 1-D potential well).

(6) Keeping in mind that there twelve C, N centers and twelve (p)π-electrons electrons, arrange them in the lowest levels of the box -- these are occupied orbitals -- and calculate the total electronic energy.

(7) Assume that the molecules absorbed light and one of the electrons in the highest orbital (HOMO = Highest Occupied Molecular Orbital) "jumped" to the lowest unoccupied orbital (LUMO = Lowest Unoccupied Molecular Orbital) ; calculate the energy difference between (7) and (6), the so-called HOMO-LUMO energy difference, ΔE (LUMO-HOMO).

(8) Equate the ΔE(LUMO-HOMO) to the energy of one photon of light and calculate the wavelength of this light.  What is the color of this light?