# Potential Energy in Molecules

## Homework Statement

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?

## 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?

tiny-tim
Homework Helper
hi getty102! U(r)=U0[(r0/r)13-(r0/r)9]

I set U(r)=0 b/k it's stable equilibrium and solved for r which gave me r0 which is incorrect. Any ideas?

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?

F(req) = -[U0'[(ro/req)13-(r0/req)9][((-13r013)/req14)+(9r09)/req10] ?

tiny-tim
Homework Helper
(just got up :zzz:)
F(req) = -[U0'[(ro/req)13-(r0/req)9][((-13r013)/req14)+(9r09)/req10] ?

yes, except Uo is a constant, and your Uo' should just be Uo and now what is the connection between force and equilibrium? (btw, we don't usually write "eq" until the last line of the proof, it's too confusing)

When F(r) = 0, stable equilibrium?

tiny-tim
well, equilibrium of some sort (whether it's stable is another question) so you're looking for U' = 0, and for U'' … … ? 