The atomic mass of _6 C^12 is 12.000000 ~u and that of _6 C^13 is 13.003354 ~u . The required energy to remove a neutron from _6 C^13 , if mass of neutron is 1.008665 ~u , will be :

Atoms and Nuclei PYQ — JEE Main 2024 · 27 Jan · Shift 2 · Q68 with Solution

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Correct answer: C

Removing one neutron from ${}_6\mathrm{C}^{13}$ gives ${}_6\mathrm{C}^{12}$ :

{}_6\mathrm{C}^{13} \rightarrow {}_6\mathrm{C}^{12} + {}_0n^1

The required energy is the neutron separation energy:

S_n = \left[M({}^{12}\mathrm{C}) + m_n - M({}^{13}\mathrm{C})\right]c^2

Since atomic masses are given, electron masses cancel on both sides.

Given:

M({}^{12}\mathrm{C}) = 12.000000\,u

M({}^{13}\mathrm{C}) = 13.003354\,u

m_n = 1.008665\,u

So,

\Delta m = 12.000000 + 1.008665 - 13.003354

\Delta m = 13.008665 - 13.003354 = 0.005311\,u

Using:

1\,u = 931.5\,\text{MeV}

Therefore,

S_n = 0.005311 \times 931.5

S_n \approx 4.95\,\text{MeV}

The correct option is:

\boxed{\text{C: } 4.95\,\text{MeV}}