# Rutherfords gold foil experiment shows that the

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Rutherford’s gold foil experiment shows that the electrons move outside the positively charged nucleus. This creates a big puzzle for classical physics. I Maxwell’s equations predict that moving charges continually radiate energy. I Consequences: I Atomic spectra should be continuous (like a rainbow). I Atoms shouldn’t be stable: electrons should spiral down into the nucleus, collapsing the atom. Solution: quantum mechanical Bohr atom

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The Bohr atom Hydrogenic atom: one electron circling a nucleus of atomic number Z Examples: H, He + , Li 2+ , etc. Assumption: circular electron orbit Key fact: The electron has a wavelength given by λ = h / p .
Wavelength mismatched to orbit: Destructive interference = no wave/particle

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Wavelength matched to orbit: = 2 π r = n λ n = 1 , 2 , 3 , . . .
Quantization conditions and quantum numbers I The equation 2 π r = n λ is a quantization condition . It constrains a physical observable to certain values. I n is called a quantum number .

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The energy of an orbiting electron I For a nucleus of charge Ze separated from an electron of charge - e by a distance r , | F | = Ze 2 4 π 0 r 2 I From the theory of circular motion, the force required to create a circular orbit of radius r is | F | = m e v 2 r I Equating the two expressions and solving for v 2 , we get v 2 = Ze 2 4 π 0 m e r (1)
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• Fall '06
• Marc
• Electron, de Broglie, quantization condition, Ze, circular electron orbit

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