Chapter 8, Problem 74P

(III) The potential energy of the two atoms in a diatomic (two-atom) molecule can be written

$U\left(r\right)=-\frac{a}{r^6}+\frac{b}{r^{12}},$

where r is the distance between the two atoms and a and b are positive constants. (a) At what values of r is U(r) a minimum? A maximum? (b) At what values of r is U(r) = 0? (c) Plot U(r) as a function of r from r = 0 to r at a value large enough for all the features in (a) and (b) to show. (d) Describe the motion of one atom with respect to the second atom when E < 0, and when E > 0. (e) Let F be the force one atom exerts on the other. For what values of r is F > 0, F < 0, F = 0? (f) Determine F as a function of r.