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PHY322S Atomic Physics . Atom as a quantum object Atom is a QUANTUM object. Enter . Bohr quantizes angular momentum mva 0 = giving a 0 = 2 me 2 = 0.53 × 10−10 m Energy is −13.6 eV. Binding energy. Is atom big or small? How strong is electromagnetic interaction? Is motion non-relativistic? We must interpret a 0 . 10
PHY322S Atomic Physics . Atomic size from uncertainty principle Assume electron confined to atomic box <strong>of</strong> size a. Uncertainty principle says momentum p ∼ /a, so non-relativistic kinetic energy is p 2 /2m. Add Coulomb energy to get total E ∼ 2 2ma − e 2 2 (4πɛ 0 )a Choose a to get a 0 that minimizes E, ie set dE/da = 0 a 0 = 4πɛ 0 2 e 2 m ( = 4πɛ0 c )( ) e 2 mc = α −1 λ e where fine structure constant α = (1/4πɛ 0 )(e 2 /c) ∼ 1/137 and electron Compton wavelength λ e = /mc ∼ 3.85 × 10 −13 m Atomic size a 0 = (137)(3.85 × 10 −13 ) ≃ 0.53 × 10 −10 m. 11
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