Beta-carotenes are highly conjugated polyenes found in many vegetables. They can be oxidized and used to synthesize pigments that play important roles in the chemistry of mammalian vision. The parent compound, ß-carotene, has a maximum absorption of light that occurs at 480 nm. If this transition corresponds to an n = 11 to n = 12 transition of an electron in a particle-in-a-box system, what is the approximate length of the molecular ‘box'?