F-Center: An Electron Trapped in an Infinite Cubic Well

Question:
(a) An F-center can be modelled as an electron trapped in a cubic three-dimensional infinite square well. Calculate the wavelength of the electromagnetic radiation emitted when an electron makes a transition from the third energy level, E3, to the lowest energy level, E1, in such a well. Take the sides of the cubic box to be of length L = 3.2 × 10−10 m and the electron mass to be me = 9.11 × 10−31 kg.

(b) Specify the degrees of degeneracy of the E1 and E3 energy levels, explaining your reasoning. (You may ignore any effects due to the spin of the electron).

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