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Bonding in Solid State Physics

  1. Nov 17, 2013 #1
    1. The problem statement

    The potential energy between two ions is
    u(r) = -α/r2 + β/r8


    (i) The intermolecular distance ro for which the potential energy is minimum
    (ii) The inter-atomic distance for which the potential energy is zero is

    R= (2)-1/6ro

    2. Relevant equations

    du/dr=o at equilibrium distance, ro

    3. The attempt at a solution

    i) du/dr= 2α/r3 - 8β/r9 = 0 at equilibrium distance ro

    we end up with

    ro = (4β/α)1/6

    ii) -α/r2 + β/r8 = 0

    which give us

    R-6 = α/β

    We can express the ratio α/β interms of ro so that

    R-6 = 4ro-6

    and finally

    R = (4)-1/6ro

    My question now is why does my answer have a 4 instead of a 2 in it?
    Last edited: Nov 17, 2013
  2. jcsd
  3. Nov 17, 2013 #2


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    Homework Helper

    Your result is correct, and it can be written also as R=2-1/3 r0.

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