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particle in a box calculations

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calculate the first optical transition for 1,3,5,7 octatetraene using particle in a 1-D approximation?

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It is possible to treat electrons in conjugated pi systems as particles in one-dimensional boxes. This is not the best approximation, but it's really not too bad for how simple it is.
Here is how to approach the problem:
First, determine the dimensions of the "box" and then find its energy levels. With the energy levels, you can find the transition energies between levels, and then find the frequency of the photon with just enough energy to bump an electron from a higher to lower level. You are looking for the first optical transition, which means that you are looking for a transition from the ground state of the molecule to the lowest excited state. (The keyword "optical" is a strong hint that the photon should be in the visible spectrum.)
But first things ...

Solution Summary

The expert calculates the first optical transition for 1, 3, 5, 7 octatetraene using particle in a 1-D approximation.