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Potential Energy in Molecules

  1. Mar 30, 2012 #1
    1. The problem statement, all variables and given/known data

    One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is U(r)=U0[(r0/r)13-(r0/r)9] where r0=0.85nm and U0=6.2eV. What is the distance between the atoms when the molecule is in stable equilibrium?

    2. Relevant equations



    3. The attempt at a solution

    I set U(r)=0 b/k it's stable equilibrium and solved for r which gave me r0 which is incorrect. Any ideas?
     
  2. jcsd
  3. Mar 30, 2012 #2

    tiny-tim

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    hi getty102! :smile:
    the zero of potential energy is arbitrary

    in this case, it has been deliberately set to 0 at r = ro

    what is the connection between potential energy and force?
     
  4. Mar 30, 2012 #3
    F(req) = -[U0'[(ro/req)13-(r0/req)9][((-13r013)/req14)+(9r09)/req10] ?
     
  5. Mar 31, 2012 #4

    tiny-tim

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    (just got up :zzz:)
    yes, except Uo is a constant, and your Uo' should just be Uo :wink:

    and now what is the connection between force and equilibrium? :smile:

    (btw, we don't usually write "eq" until the last line of the proof, it's too confusing)
     
  6. Mar 31, 2012 #5
    When F(r) = 0, stable equilibrium?
     
  7. Mar 31, 2012 #6

    tiny-tim

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    well, equilibrium of some sort (whether it's stable is another question) :smile:

    so you're looking for U' = 0, and for U'' … … ? :wink:
     
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