How Do You Calculate the Spring Constant in Van der Waals Potential?

[Fr3shFr0st]

Homework Statement

The van der Waals potential between two inert atoms is often characterized by the expression:

http://bama.ua.edu/~stjones/253hw_files/image025.gif

Sketch the function. Expand the potential around the minimum in the form U = U(ro) + ½ k(r-ro)2. Evaluate k in terms of s and e.

Homework Equations

Above

The Attempt at a Solution

I got the sketch down fine. I am just unclear about the second part. Nothing in my physics textbook helps. What i have done so far is take the original equation and substitute it in
U = U(ro) + ½ k(r-ro)2. Doing that i got:

U = 4e[(σ/ro)^12-(σ/ro)^6] + ½ k(r-ro)2

From there i solved for k and got:

k={U-[4e[(σ/ro)^12-(σ/ro)^6]]/(r-ro)^2}*2

Im not sure if I am the right path but from here i don't know how to get k in terms of s and e. Any help is greatly appreciated!

 

[Redbelly98]

Are you familiar with Taylor Series expansions (from when you took calculus)? That's the key to solving this one.