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 +Zeis at rest and the electron travels in a circular orbit around the proton (i.e.assume Mnucleus>> me). The force on the electron is rvmamrKZeFee222===and 222rKZervme=. Hence, we must replace e2by Ze2in all the formulas. Thus, 02rZnrn=, cZnvnα1=, and 022EnZEn=. Correction for a Finite Nuclear Mass: Let the nucleus have mass Mand speed Vand the electron mass meand speed ve. Then the center-of-massis at the point xdetermined by me(r-x) = Mxand hence Mmrmxee+=and MmMrxre+=−The total angular momentumis ωµωωω2222)(rrMmMmMxxrmLeee=+=+−
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