Chapter4_2

Chapter4_2 - = = α D h h h with 137 1 2 ≈ = c Ke h and c...

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PHY3063 R. D. Field Department of Physics Chapter4_2.doc University of Florida Bohr’s Model of the Hydrogen Atom (1) 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 =
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Unformatted text preview: = = α D h h h , with 137 1 2 ≈ = c Ke h and c m e e h D = . Also, c n r n m n r m n v e n e n 1 2 = = = h h . Total Energy: 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 − = − = + = . r v electron charge = -e proton charge = +e F Quantum Number n r Ke v m e 2 2 2 2 1 = Bohr’s Postulate!...
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