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The wave nature of electrons affects the electron's energy levels. Electrons form standing waves and each energy level has to have a whole number of wavelengths for the standing wave to exist. So, the wave property of electrons dictates how there are fixed energy levels for each electron.
I think Dr. Lavelle used the example of constructive and destructive interference in light waves to illustrate the idea of diffraction so that he could show us that because electrons passing through a crystal show diffraction they have wave-like properties. So if you were asked to explain how electrons show wave properties it would be useful to know!
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