Unformatted text preview: and quantized in a particular way. de Broglie came up with an explanation for why the angular momentum might be quantized in this way. de Broglie realized that if you use the wavelength associated with the electron, and only allow for standing waves to exist in any orbit (in other words, the circumference of the orbit has to be an integral number of wavelengths), then you arrive at the same relationship for the angular momentum that Bohr got. The derivation works like this, starting from the idea that the circumference of the circular orbit must be an integral number of wavelengths: Taking the wavelength to be the de Broglie wavelength, this becomes: The momentum, p, is simply mv as long as we're talking about nonrelativistic speeds, so this becomes: Rearranging this a little, and recognizing that the angular momentum for a point mass is simply L = mvr, gives the Bohr relationship:...
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 Fall '10
 DavidJudd
 Physics, Atom, Energy, Fundamental physics concepts

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