3.

The nuclei 5 B11 and 6 C] l are said to be a pair of mirror nuclei because they have the same number of nucleons, and the number of protons in one equals the number of neutrons in the other. If nuclear forces are charge independent, their total binding energies should differ only in that the Coulomb energy is higher in 6C11 . The atomic mass of 5 B11 is 11.009305u, and the atomic mass of 6 Cl 1 is 1 1.01 1432u. (3) Evaluate the difference in their total binding energies. (b) Assuming both nuclei to be uniformly charged spheres of the same radius r', and using the expression for the Coulomb energy given by 3 Zze2 V = _ 5 41t60r' Find the value of 1" that leads to a difference in Coulomb energy that agrees with the difference in binding energy. (0) Compare this charge distribution radius with the radial dependence of the 6 C] 2 charge density for the similar nucleus shown in the Figure below. 0.10 0.04 p (r) (proton charges per F3) 0.02 ND The charge densities of a number of nuclei. Use the half-value radius parameter a, surface thickness 2b and interior charge density p(0), shown for 6C