JEE (Advanced) 2016 Paper-2 Question 1

Question 1

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by
$$E = \frac{3}{5}\frac{Z(Z - 1)e^2}{4 \pi ε_0 R}$$
The measured masses of the neutron, $$^1_1H, ^{15}_7N$$ and $$^{15}_8O$$ are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u,respectively. Given that the radii of both the $$^{15}_7N$$ and $$^{15}_8O$$ nuclei are same, $$1 u = 931.5 MeV/c^2$$ (c is the speed oflight) and $$\frac{e^2}{(4 \pi ε_0)} = 1.44 MeV fm$$. Assumingthat the difference between the binding energies of $$^{15}_7 N$$ and $$^{15}_8 O$$ is purely due to the electrostatic energy, the radius of either of the nuclei is$$(1 fm = 10^{-15}m)$$

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