# Potential Energy in Molecules

1. Mar 30, 2012

### getty102

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. Mar 30, 2012

### tiny-tim

hi getty102!
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?

3. Mar 30, 2012

### getty102

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

4. Mar 31, 2012

### tiny-tim

(just got up :zzz:)
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)

5. Mar 31, 2012

### getty102

When F(r) = 0, stable equilibrium?

6. Mar 31, 2012

### tiny-tim

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

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