Physics - Modern Physics Question with Solution | TestHub

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by$E=\frac{3}{5}\frac{Z\left(Z-1\right)e^2}{4\pi {\epsilon }_{0}R}$The measured masses of the neutron,${}_1{}^{1}H, {}_8{}^{15}O$are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u respectively. Given that the radii of both the${}_7{}^{15}N and {}_8{}^{15}O$nuclei are same, 1u = 931.5 Me V/$c^2$(c is the speed of light) and$\frac{e^2}{\left(4\pi {ϵ}_0\right)}=1.44 MeV fm.$Assuming that the difference between the binding energies of${}_7{}^{15}N and {}_8{}^{15}O$is purely due to the electrostatic energy, the radius of either of the nuclei is$\left(1 fm={10}^{-15}m\right)$