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The particle in a 1-D box is sometimes used as a model for electrons in a...

The particle in a 1-D box is sometimes used as a model for electrons in a conjugated pi-bond system (alternating double and single bonds).

a. The molecule has four pi electrons. Assume that two are in the state corresponding to n=1 and that two are in the state corresponding to n=2. Find the frequency and wavelength of the light absorbed if an electron makes a transition from n=2 to n=3.

b. Calculate the probability that a particle in a 1-D hard box will be found within one standard deviation of its mean position for the n=2 state. Comment on the comparison with the fact that with a Gaussian distribution the probability would be 0.683.

c. Calculate the probability that a particle in a 1-D hard box will be found within one standard deviation of it mean position for the n=3 state.

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