Buckminsterfullerine is a molecule of 60 carbon atoms arranged like the stitching on a soccer-ball. It may be approximated as a conducting spherical shell of radius R=3.5 Å. A nearby electron would be attracted, according to Prob. 3.9, so it is not surprising that the ion C60− exists. (Imagine that the electron—on average—smears itself out uniformly over the surface.) But how about a second electron? At large distances it would be repelled by the ion, obviously, but at a certain distance r (from the center), the net force is zero, and closer than this it would be attracted. So an electron with enough energy to get in that close should bind.
(a) Find r, in Å. [You'll have to do it numerically.]
(b) How much energy (in electron volts) would it take to push an electron in (from infinity) to the point r?
[Incidentally, the C60−− ion has been observed.]