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Lennard-Jones Potential

  1. Jul 28, 2013 #1
    1. The problem statement, all variables and given/known data
    The Lennard-Jones equation shown below gives the potential energy of two atoms when they are separated by a distance r.
    U(r)=4 U_0 \left[\left(\frac{r_0}{r}\right)^{12}-\left(\frac{r_0}{r}\right)^6\right]

    a)What is the distance between atoms at the condition of stable equilibrium? (Enter r sub 0 or U sub 0 by typing r_0 or U_0). If you choose to give an approximate answer, be sure to give your answer to at least 4 digits after the decimal.

    b)What is the minimum work needed to completely dissociate the molecule by separating the atoms from each other if they are initially at equilibrium? (Enter r sub 0 or U sub 0 by typing r_0 or U_0)
    2. Relevant equations

    3. The attempt at a solution
    Honestly this looks like Ancient Greek to me. I have no shadow of inking of an idea on how to even start on this problem. If someone could help me that would be awesome!
  2. jcsd
  3. Jul 28, 2013 #2
    What is the condition of stable equilibrium?
  4. Jul 28, 2013 #3
    Where there are no forces acting on an object.
  5. Jul 28, 2013 #4
    You mean the net force is zero.

    If the force is zero, what can be said about the potential energy? How are they related?
  6. Jul 28, 2013 #5
    If the force is 0 then the potential energy is zero?
  7. Jul 28, 2013 #6
    Why would that happen?

    Again, what is the relation between force and potential energy?
  8. Jul 28, 2013 #7
    I don't know.
  9. Jul 28, 2013 #8
    What is the definition of "potential energy"?

    Given potential energy, can you determine the force?
  10. Jul 28, 2013 #9
    Potential energy is the energy of an object or a system due to the position of the body or the arrangement of the particles of the system.

    No you can't determine the force from the potential energy.
  11. Jul 28, 2013 #10
    Wait a minute : U(\vec{r}) = - \int_{\vec{r}_{ref}}^{\vec{r}}\vec{F}\cdot d\vec{r}
  12. Jul 28, 2013 #11
    You need a review on potential energy and force. You seem to remember something, which is good, but you do not seem to have a solid understanding of the relationship between force and potential energy.
  13. Jul 28, 2013 #12
    Wait, F(x) = -\frac{dU}{dx}
  14. Jul 28, 2013 #13
    You might want to look at my questions in #4 again.
  15. Jul 28, 2013 #14
    If the force is 0 then the potential energy is 0.
  16. Jul 28, 2013 #15
    Does this follow from #12?
  17. Jul 28, 2013 #16
    I figured it out, the answer to the first part is r_0*2^(1/6) and the second part is u_0. Thanks for your help!
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