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Electrostatic Potential Energy of an ion

  1. Mar 17, 2013 #1
    Working from Krane's Modern Physics 11.5

    Calculate the first 3 contributions to the electrostatic potential energy of an ion in the CsCl lattice.

    I believe the formula I'm supposed to use is
    [tex]
    U_{c}\,=\,-\alpha\frac{e^{2}}{4\pi\epsilon_{0}R}
    [/tex]

    Just from looking in the chapter I can see this is a bcc type lattice with an [itex]\alpha[/itex] of 1.7627, but I'm not sure how they're getting the answer in the back of the book which is;
    [tex]
    U_{c}\,=\,-\frac{e^{2}}{4\pi\epsilon_{0}R}\left(8-\frac{6}{2/\sqrt{3}} + \frac{24}{\sqrt{11/3}}\right)
    [/tex]
    There's an example in the book showing the same procedure for an fcc lattice (NaCl) and that converging term is,
    [tex]
    6-\frac{12}{\sqrt{2}}+\frac{8}{\sqrt{3}}-\ldots
    [/tex]
    but it doesn't derive it, so I'm not really sure how they get it.

    Just looking for a few pointers, thanks.
     
  2. jcsd
  3. Mar 17, 2013 #2
    Figured it out.
     
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