Question

An electron of mass m is confined to a 3-dimensional boxthat has y dimension twice that of x or y so that it has size L x 2L x L (Lx = L, Ly = 2L and Lz = L).

a) Derive an expression for the energy of each of the following bound states: (nx, ny, nz) = (1,1,1) and (2,1,1). (You do not need to use the S.E. to solve for the energy expression; use your formula sheet).Plug in the values of (nx, ny, nz) in each expression so that your expressions are in terms of L, m, and constants.E(1,1,1)= ? E(2,1,1) = ?

b) What wavelength photon would be emitted if the electron transitions from (2,1,1) to the ground state?

c) Complete the sentence: the probability distribution function...(choose one):1.oscillates in time, with a frequencythat depends on the size of the box.2.oscillates in time, with frequency that is independent of box size,3.varies with time, but the variation is not a simple oscillation.4.does not vary with time.

Answer #1

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An electron (mass m) is contained in a rectangular
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