# Lennard-Jones potential - equilibrium [closed]

If I have Lennard-Jones potential, how can I calculate equilibrium? $$U(r)=\epsilon \left ( \left (\frac{r_m}{r} \right )^{12}-2 \left (\frac{r_m}{r}\right )^6 \right ) \$$

-

## closed as too localized by dmckee♦May 6 '13 at 2:10

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

-Is this a HW question by chance? We don't usually solve HW questions here. If you want a hint, I would sketch a plot of the potential. Particular points should jump out as candidates for an equilibrium positions - if recall your calculus class there is a way to find said points... –  DJBunk Jul 11 '12 at 21:25
Equilbrium of what? Two atoms? Temperature? Zero temperature? Many atoms? fluid? gas? This is not a question as it stands. –  Ron Maimon Jul 12 '12 at 1:45
$\vec F = -{d U \over dr } = 0$ –  Santosh Linkha Jul 12 '12 at 2:59

## 1 Answer

A hint: The derivative of a potential energy such as $U$ is, with suitable sign, a force. At equilibrium what should the force be?

-