The potential energy shared by two atoms in a diatomic molecule, depicted in Figure 5.17,...

The potential energy shared by two atoms in a diatomic molecule, depicted in Figure 5.17, is often approximated by the fairly simple function U(x) — (a/x2) -(b/x6), where constants a and b depend on the atoms involved. In Section 5.7, it is said that near its minimum value, it can be approximated by an even simpler function—it should "look like" a parabola.

(a) In terms of a and b, find the minimum potential energy U(x0) and the separation ,x0 at which it occurs.

(b) The parabolic approximation Up(x) = U(x0) + ½ K(X – x0)2 has the same minimum value at .v0 and the same first derivative there (i.e., 0). Its second derivative is K, the spring constant of this Hooke's law potential energy. In terms of a and b, what is the spring constant of U(x)