Chapter4_9 - 137 1 2 = c Ke h and c m e e h D = . Energy...

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PHY4604 R. D. Field Department of Physics Chapter4_9.doc University of Florida r Ke v m e 2 2 2 2 1 = Bohr’s Model of the Hydrogen Atom Circular Motion: Assume that the proton is at rest and the electron travels in a circular orbit around the proton ( i.e. assume M p >> m e ). The force on the electron is r v m a m r Ke F e e 2 2 2 = = = and 2 2 2 r Ke r v m e = . The orbital angular momentum is given by L = m e vr , and hence v = L/(m e r) and 2 2 Ke m L r e = but h n L = , where n = 1, 2, 3,… . Thus, the allowed values for the radius are 2 2 2 Ke m n r e n h = or 0 2 r n r n = , where nm Ke c c m Ke m r e e e 0529 . 0 2 2 2 0 = = = α D h h h , Is called the Bohr radius with
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Unformatted text preview: 137 1 2 = c Ke h and c m e e h D = . Energy Levels: The energy of the electron is the sum of the kinetic energy plus the potential energy as follows: r Ke r Ke v m U KE E e 2 2 2 2 1 2 1 = = + = . The allowed energies of the electron are ) ( 2 1 2 1 2 1 2 2 2 2 2 2 c m n r n Ke r Ke E e n n = = = . Thus, 2 1 E n E n = with eV c m E e 6 . 13 ) ( 2 1 2 2 = . r v electron charge = -e proton charge = +e F Ground State Energy! Bohrs Postulate!...
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This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.

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