The Lennard-Jones Potential A commonly used potential energy function for the interaction of two molecules (see Fig. 18.8) is the Lennard-Jones 6-12 potential


Where, is the distance between the centers of the molecules and U0 and Ro arc positive constants? The corresponding force F(r) is given in Eq. (13.26). (a) Graph U (r) and F(r) versus r,
(b) Let r1 be the value of r at which U(r) = 0, and let r2 be the value of r at which F(r) = 0. Show the locations of rl and r2 on your graphs of U(r) and F(r).
Which of these values represents the equilibrium separation between the molecules?
(c) Find the values of r1 and r2 in terms of R0 and find the ratio r1/r2.
(d) If the molecules are located a distance r2 apart [as calculated in part (c)],
how much work must be done to pull them apart so that, r→00?

12 U(r) = U.