Chapter5_7 - PHY4604 R. D. Field Bohrs Model of the One...

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PHY4604 R. D. Field Department of Physics Chapter5_7.doc University of Florida Bohr’s Model of the One Electron Atom Assume that the nucleus with charge +Ze is at rest and the electron travels in a circular orbit around the proton ( i.e. assume M nucleus >> m e ). The force on the electron is r v m a m r KZe F e e 2 2 2 = = = and 2 2 2 r KZe r v m e = . Hence, we must replace e 2 by Ze 2 in all the formulas. Thus, 0 2 r Z n r n = , c Z n v n α 1 = , and 0 2 2 E n Z E n = . Correction for a Finite Nuclear Mass: Let the nucleus have mass M and speed V and the electron mass m e and speed v e . Then the center-of-mass is at the point x determined by m e (r-x) = Mx and hence M m r m x e e + = and M m Mr x r e + = The total angular momentum is ω µ 2 2 2 2 ) ( r r M m M m Mx x r m L e e e = + = + = ,
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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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