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Isn't Born-Landé equation double the electrostatic energy?

  1. Aug 31, 2015 #1

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    I'm confused as to how the Born-Landé equation can be extrapolated to find the electrostatic potential for an ionic lattice without halving it, as each interaction is otherwise counted twice.

    As I understand it, and according to Wikipedia, the electric potential energy in a charge configuration can be found by this equation:
    9464d36ae5844070bd99178f3858f25a.png
    This is half the sum of the products of the charge of each ion in the lattice with the electric potential at its location provided by each other ion - the Born-Landé equation, however, does not include this factor of 1/2.
    I accept that
    gRi8SXa.png
    is the correct sum of the energy stored in the interactions of any one ion, but the final equation multiplies this by the Avogadro constant:

    e4e1219b20a6dffdd490de8fe82c9f08.png

    I would have thought that this would have counted every interaction twice, by following this equation for the energy stored in a charge configuration:

    Chapter2604.gif
     
    Last edited: Aug 31, 2015
  2. jcsd
  3. Sep 5, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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