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Lennard-Jones Potential: Derive an expression for equilibrium constant

  1. Aug 15, 2014 #1
    Edit: well this is frustrating, not sure why the itex things aren't working..

    Edit2: I've attached a picture of the question at the bottom as well.

    1. The problem statement, all variables and given/known data
    The cohesive energy of a solid noble gas may be written as

    (See picture below)

    Derive an expression for the equilibrium separation r0 of the atoms.


    3. The attempt at a solution

    At Ecohesive, r=r0 and dE/dr0 = 0

    So first I rearranged the main equation into something nicer to differentiate:

    E = 6.065Br[itex]^{-12}_{0}[/itex] - 7.225Ar[itex]^{-6}_{0}[/itex]

    Then differentiated:

    dE/dr0 = -72.78[itex]\frac{B}{r^{13}_{0}}[/itex] + 43.35[itex]\frac{A}{r^{7}_{0}}[/itex] = 0

    43.35[itex]\frac{A}{r^{7}_{0}}[/itex] = 72.78[itex]\frac{B}{r^{13}_{0}}[/itex]

    r[itex]^{6}_{0}[/itex] = [itex]\frac{72.78}{43.35}[/itex][itex]\frac{B}{A}[/itex]

    So r0 = ([itex]\frac{72.78}{43.35}[/itex][itex]\frac{B}{A}[/itex])[itex]\frac{1}{6}[/itex]

    But this looks pretty horrible, is it any good?

    Cheers.

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    vfe5wm.png
     
    Last edited: Aug 15, 2014
  2. jcsd
  3. Aug 15, 2014 #2
    Finally found a similar question in the depths of the internet and looks like it is right, so all is good here.
     
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