Reflected nucleis are couple of nucleis that have the same mass atomic (A) but n

Question

Reflected nucleis are couple of nucleis that have the same mass atomic (A) but number of protons and neutrons are exchanged between them for example N[nytrogen](Z=7 ; N=8) O[oxygen](Z=8;N=7) . Supposed that number of protons are uniformly distrubute in the volume of the nucleus. Show that the additional(supplemental) electrostatic energy created by replacement (substitution) of neutrons with protons is proportional with ~(6 Z e^2)/(5 r) where Z is number of protons , e is the charge of electron and r is radius of nucleus.
Note : Start from taking account voltage difference.

Explanation / Answer

from the electrostatic equipotential spherical nucleus the magnitue of potential is given by the equation

V = 3/5(Z^2e^2/4r)

so for the above reflected the nucleus the difference in potential

V = 3/5[K(Z^2-(Z+1)^2)e^2/r]

   = modulus3ke^2(2Z+1)/5r

   = 6Ke^2z/5r

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