Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.

•• (a) Following the suggestions in Problem 1, find the potential energy that an electron would have at the center of a nucleus. (b) Repeat for . (c) Compare your answers with the minimum kinetic energy, which is of order 100 MeV.

Problem 1

•• Supposing that nuclei could contain electrons, estimate the potential energy of one such electron at the center of a nucleus of 27Al. Compare your answer with the minimum kinetic energy (16.10) of an electron in a nucleus. [Hint: The required potential energy is −eV(0), where V(r) is given by Eq. (16.49) below. The radius R is given by (16.3), and the total charge acting on the electron is Q = (Z + 1)e.]