A very common interaction between neutral molecules is described by the Lennard-

Question

A very common interaction between neutral molecules is
described by the Lennard-Jones (LJ) potential energy function?
The LJ potential energy is given by U(R) = -A/R6 +B/R12, where
R is the separation between the two molecules.
(a) Sketch the potential energy as a function of R
(b) What is the associated force?
(c) For what value of R is the potential energy a minimum?
(d) For what value of R is the force zero?
(e) If the molecules are separated by the distance R you foundin
part (d), how much work is required to separate them by twicethat
distance?

Explanation / Answer

This one isnt really complicated... . (a) sketch... I cant do that for you here. Just plug insome values for r, calc U, and sketch U vs r . (b)   Force = - dU /dr           sojust take the derivative of the given function. . (c)    potential energy is minimum when forceis zero. So just set your expression from (b) equal to zero andsolve for r. . (d) same thing as part (c)... they just want you to seethat. . (e)   find the potential energy at the value of rfrom part (c), then find the potential energy at twice that value.The work done is the difference in potential energy.

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