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JEE Advance2016
Paper-2
Question
The electrostatic energy of $Z$ protons uniformly distributed throughout a spherical nucleus of radius $R$ is given by $E=\frac{3}{5} \frac{Z(Z-1) e^2}{4 \pi \varepsilon_0 R}$ The measured masses of the neutron, ${ }_1^1 \mathrm{H},,{ }_7^{15} \mathrm{~N}$ and ${ }_8^{15} \mathrm{O}$ are $1.008665 \mathrm{u}, 1.007825 \mathrm{u}, 15.000109$ u and 15.003065 u , respectively. Given that the radii of both the ${ }_7^{15} \mathrm{~N}$ and ${ }_8^{15} \mathrm{o}$ nuclei are same, 1 $\mathrm{u}=931.5 \mathrm{MeV} / \mathrm{c}^2\left(\mathrm{c}\right.$ is the speed of light) and $\mathrm{e}^2 /\left(4 \pi \varepsilon_0\right)=1.44 \mathrm{MeV} \mathrm{fm}$. 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 ( $1 \mathrm{fm}=10^{-15} \mathrm{~m}$ )
Select the correct option:
A
2.85 fm
B
3.03 fm
C
3.42 fm
D
3.80 fm
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