- #1
Nacho Verdugo
- 15
- 0
Homework Statement
I need to calculate the work donde by the Lennard-Jones Law, considering:
F(r)=F0 [2(σ/r)13-(σ/r)7]
when approximating two atoms from infinity to the equilibrium position between both atoms
Homework Equations
First thing I don't know how to calculate is the equilibrium position (x0) between two arbitrary atoms
The Attempt at a Solution
I just integrated this force, considering
WAB=∫F⋅dr ; r=A to r=B
As I don't know the x0, I just integrate from A to B, to later analyze the result. Assuming A=-∞ and B=x0
W= ∫ F0 [2(σ/r)13-(σ/r)7] dr ; r=A to r=B
= integrating...
= 2F0σ13 ( r-12 /-12) - F0σ7 (r-6/-6) ; still need to evaluate
Considering that A=-∞, I finally obtain:
W= F0σ7/6 (1/x06)-F0σ13/6(1/x012)
Is it right until here?