The color of dyes results from the preferential absorptionof certain wavelengths of

Chapter 28, Problem 74

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The color of dyes results from the preferential absorptionof certain wavelengths of light. Certain dye moleculesconsist of symmetric pairs of rings joined at the center by achain of carbon atoms, as shown in Figure P28.74. Electronsof the bonds along the chain of carbon atoms are sharedamong the atoms in the chain, but are repelled by the nitrogencontainingrings at the end of the chain. These electrons arethus free to move along the chain but not beyond its ends.They look very much like a particle in a one-dimensional box.For the molecule shown, the effective length of the "box"is 0.85 nm. Assuming that the electrons start in the lowestenergy state, what are the three longest wavelengths thismolecule will absorb?

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