The particle in a box problem is a very simple model for electrons in conjugated

Question

The particle in a box problem is a very simple model for electrons in conjugated systems. Consider lycopene, which is responsible for the color of some fall leaves: Assuming that the color of lycopene is due to transition between an electron in the highest occupied energy state and the lowest unoccupied energy state, find the energy of this transition and calculate the color of lycopene. You can assume that each energy level can contain two electrons. The size of the "box" is generally assumed to contain 1 more bond than the conjugated pi system. A resonance stabilized CC bond is ~ 0.140 nm. How much of an effect on the color does this assumption of a slightly larger "box" have?

Explanation / Answer

lycopene is found in tomato a red coloured compound

transition energy = 30CC bond

= 30 x 0.140nm

= 4.2nm

The spectrum of lycopene is obtained, Because of the bent geometry of the cis compound, a peak at 360 nm will appear where none appears in the spectrum of the all trans isomer. Additionally, a hypochromatic effect (decrease in intensity) is observed upon isomerization. This is because the isomerization is reversible and an equilibrium trans-cis mix eventually forms. Finally, a slight hypsochromatic shift (blue shift to shorter wavelengths) is also observed

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