ENG045_HW1

ENG045_HW1 - DATE: DUE: ENG45, homework set #1. September...

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DATE: September 30, 2011 DUE: October 7, 2011 ENG45, homework set #1. 1. The Bohr Atom. This is the most primitive model for why the atom is stable and for how atomic energies are quantized. It is built on a planetary type motion of an electron cir- cularly orbiting a (Hydrogen) nucleus. Based on realizations from the photoelectric effect and special relativity, where photon energy E ph = and photon momentum is p = h/λ [ h is Planck’s constant, ν is the frequency (in Hz) and λ is the wave- length. The speed of light is c = νλ ], the electron momentum is associated with a wave length, and the quantization of orbits is accomplished. The results are: r n = r B n 2 , r B = ¯ h 2 4 πε 0 m e e 2 (1) v n = v B 1 n , v B = ¯ h m e r B (2) E n = - E B 1 n 2 , E B = 1 2 e 2 4 πε 0 r B (3) where n = 1 , 2 , ··· is the (primary) quantum number, ¯ h = h/ 2 π , ε 0 is the vacuum permittivity, m e is the mass of the electron 1 , and e is the proton charge. The three cal- culated constants are the Bohr radius
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ENG045_HW1 - DATE: DUE: ENG45, homework set #1. September...

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