JEE Advanced 2016 Paper 2 Physics Q1

Physics · Nuclei & Radioactivity

Problem

The electrostatic energy of

Z

protons uniformly distributed throughout a spherical nucleus of radius

R

is given by

E=\dfrac{3}{5}\dfrac{Z(Z-1)e^2}{4\pi\varepsilon_0R}.

The measured masses of the neutron,

{}^{1}_{1}\mathrm H

{}^{15}_{7}\mathrm N

and

{}^{15}_{8}\mathrm O

are

1.008665

1.007825

15.000109

u and

15.003065

u, respectively. Given that the radii of both the

{}^{15}_{7}\mathrm N

and

{}^{15}_{8}\mathrm O

nuclei are same,

1

=931.5\,\mathrm{MeV}/c^2

(

c

is the speed of light) and

e^2/(4\pi\varepsilon_0)=1.44\,\mathrm{MeV\,fm}

. Assuming that the difference between the binding energies of

{}^{15}_{7}\mathrm N

and

{}^{15}_{8}\mathrm O

is purely due to the electrostatic energy, the radius of either of the nuclei is

(1\,\mathrm{fm}=10^{-15}\,\mathrm m)