Answer: The Lennard-Jones Potential. A commonly used

Chapter 18, Problem 18.69

(choose chapter or problem)

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: U1r2 = U0 c aR0 r b 12 - 2a R0 r b 6 d where r is the distance between the centers of the molecules and U0 and R0 are positive constants. The corresponding force F1r2 is given in Eq. (14.26). (a) Graph U1r2 and F1r2 versus r. (b) Let r1 be the value of r at which U1r2 = 0, and let r2 be the value of r at which F1r2 = 0. Show the locations of r1 and r2 on your graphs of U1r2 and F1r2. 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 S q?