05_02_02 - classical mechanics and electrodynamics....

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Georg.Hoffstaetter@Cornell.edu 20 02/02/2005 The Rutherford-Bohr Atom The Balmer lines of Hydrogen ) ( 2 2 1 4 1 n H n cR - = π ϖ Visible range: 430-750 THz 700-400 nm 1.8 –3.1 eV photons Rutherfords scattering experiment (1909) lead to the insight that an atom has a positively charged core in a negatively charged surrounding. Bohrs posutlates (1913): 1) Electrons orbit around the core with Z protons according to classical mechanics but do not radiate. 2) Electrons can change their orbit only by radiating a photon with the energy h Q . 3) Observation of Balmer lines then leads to the conclusion that only certain radii are possible: r Ze r Ze r Ze r mv mv E F 0 2 0 2 2 0 2 2 8 4 2 2 1 4 πε - = - = = = ) ( )] ( ) ( [ 1 1 8 0 2 i f r r Ze i f photon r E r E E - = = - - = ! Hydrogen for 1 , ) ( 2 2 0 0 2 1 1 8 , 2 0 = - = = Z n a r n j a Ze n j n Balmer lines: j=2, lines for j=1,4,5 were found with Bohr’s prediction. λ
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Georg.Hoffstaetter@Cornell.edu 21 Leads to the correct Rhydberg constant and ionization energy : Leads to the He + spectrum with Correspondence principle For large quantum numbers, the predictions of quantum theory must agree with the predictions of
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Unformatted text preview: classical mechanics and electrodynamics. Dropping to the next lower energy level for quantum number N: Classical radiation of a charge which oscillates with frequency Q : 2 3 2 3 2 2 2 2 2 2 2 ) ( ] [ 4 1 4 ) 1 ( 1 2 8 1 ) 1 ( 1 8 , 1 N r a a Ze N a Ze N N N a Ze N N a Ze N N = =-=----3 4 4 1 1 2 ) ( 3 2 2 2 2 r a ma Ze r Ze mr r mv mr = = = m a a Z m Ze m Ze N N N 10 1 4 4 2 2 10 529 . , 1 1 / lim 2 2 2 2 , 1- = = = =-) ( 2 ) ( 2 2 2 3 2 4 2 1 4 1 2 1 2 1 ) 4 ( 2 , 2 n H n m e Z n R cZ-=-= 2 2 , 1 6 . 13 2 Z eV R cZ E H ion = = = ! ! 2 = Z 02/02/2005...
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05_02_02 - classical mechanics and electrodynamics....

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