The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by E=3/5 (Z(Z-1) e²)/(4 π ε₀ R) The measured masses of the neutron, ₁¹ H, ₇¹⁵ ~N and ₈¹⁵ O are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u, respectively. Given that the radii of both the ₇¹⁵ ~N and ₈¹⁵ O nuclei are same, 1 u=931.5 MeV / c² (c is the speed of light) and e² /(4 π ε₀)=1.44 MeV fm. Assuming that the difference between the binding energies of ₇¹⁵ ~N and ₈¹⁵ O is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm=10⁻¹⁵ ~m)

JEE Advanced 2016 Atoms and Nuclei Question with Answer (JEE Adv 2016 Paper 2 Paper 2, Q1)

JEE Advanced 2016JEE Adv 2016 Paper 2, Paper 2PhysicsHardAtoms and Nuclei183× since 2002

The electrostatic energy of

Z

protons uniformly distributed throughout a spherical nucleus of radius

R

is given by \[ E=\frac{3}{5} \frac{Z(Z-1) e²}{4 \pi \varepsilon_{0} R} \] The measured masses of the neutron,

{ }_{1}^{1} \mathrm{H},{ }_{7}^{15} \mathrm{~N}

and

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

are

1.008665 \mathrm{u}, 1.007825 \mathrm{u}

15.000109 \mathrm{u}

and

15.003065 \mathrm{u}

, respectively. Given that the radii of both the

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

and

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

nuclei are same,

1 \mathrm{u}=931.5 \mathrm{MeV} / c^{2}

(

c

is the speed of light) and

e^{2} /\left(4 \pi \varepsilon_{0}\right)=1.44 \mathrm{MeV} \mathrm{fm}

. Assuming that the difference between the binding energies of

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

and

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

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

\left(1 \mathrm{fm}=10^{-15} \mathrm{~m}\right)