Potential Energy in Molecules

  • Thread starter getty102
  • Start date
  • #1
38
0

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?

Homework Equations





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?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,836
251
hi getty102! :smile:
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?
 
  • #3
38
0
F(req) = -[U0'[(ro/req)13-(r0/req)9][((-13r013)/req14)+(9r09)/req10] ?
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,836
251
(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 :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)
 
  • #5
38
0
When F(r) = 0, stable equilibrium?
 
  • #6
tiny-tim
Science Advisor
Homework Helper
25,836
251
When F(r) = 0, stable equilibrium?

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

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

Related Threads on Potential Energy in Molecules

  • Last Post
Replies
2
Views
17K
  • Last Post
Replies
1
Views
2K
Replies
0
Views
978
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
4
Views
53K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
14
Views
2K
  • Last Post
Replies
19
Views
2K
  • Last Post
Replies
1
Views
853
  • Last Post
Replies
1
Views
913
Top