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# PS3 - Chem 442 Homework Set#3 DUE Friday November 7 2008 1...

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Problem Set #3 - 1 - Chem 442 Homework Set #3 DUE: Friday, November 7, 2008 1) a) McQ&S, 3-26 b) Assume there is an electron in this box where a =5.00Å. Calculate the frequency of a photon emitted if the electron makes a transition from the first excited state to the ground state. 2) McQ&S, C-4 3) a) McQ&S, 4-6 b) In problem 4-6 you were given a state for the particle in a box. For a box of length, a=1, plot that state, ψ (x). On the same graph plot the lowest eigenstate for the 1-D particle in a box, ψ 1 (x). c) For a box of length, a=1, consider a new state, ψ Q (x) = Ax(1-x). Determine A so that the state is normalized. d) Determine <E> for ψ Q (x) in part c. e) Which state, ψ Q (x) or ψ (x) from problem 4-6, has an energy closest to the lowest eigenenergy, E 1 , for the 1-D particle in a box? f) Add ψ Q (x) to your plot in part b). Do you have an idea why the energy of one of these states is closer in energy to E 1 ? 4) a) We know that ,<x> = L/2 for all n for a particle in a 1-D box. For the n=1, n=2, n=3 states, find the most probable location(s) of the particle. b) Explain why the average position is not necessarily a likely position

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PS3 - Chem 442 Homework Set#3 DUE Friday November 7 2008 1...

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