The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given byE=35Z(Z−1)e24πε0RThe measured masses of the neutron, 11H,157N and 158O are 1.008665 u,1.007825 u,15.000109 u and 15.003065 u respectively. Given that the radii of both the 157N and 158O nuclei are same, 1u=931.5MeV/c2 (c is the speed of light) and e2/(4πε0)=1.44MeVfm. Assuming that the difference between the binding energies of 157N and 158O is purely due to the electrostatic energy, the radius of either of the nuclei is (1fm=10−15m)

The electrostatic energy of Z protons uniformly distributed throughout

1.	The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given byE=35Z(Z−1)e24πε0RThe measured masses of the neutron, 11H,157N and 158O are 1.008665 u,1.007825 u,15.000109 u and 15.003065 u respectively. Given that the radii of both the 157N and 158O nuclei are same, 1u=931.5MeV/c2 (c is the speed of light) and e2/(4πε0)=1.44MeVfm. Assuming that the difference between the binding energies of 157N and 158O is purely due to the electrostatic energy, the radius of either of the nuclei is (1fm=10−15m)
Answer» The electrostatic energy of $Z$ protons uniformly distributed throughout a spherical nucleus of radius $R$ is given by $E = \frac{3}{5} \frac{Z (Z - 1) e^{2}}{4 π ε_{0} R}$ The measured masses of the neutron, $_{1}^{1} H,_{7}^{15} N$ and $_{8}^{15} O$ 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, $1 u = 931.5 M e V / c^{2}$ ( $c$ is the speed of light) and $e^{2} / (4 π ε_{0}) = 1.44 M e V f m$ . 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 $(1 f m = 10^{- 15} m)$

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