Which of the following nuclear reactions is possible?

The correct answer is Option (2) → \( {}^{12}_{6}\mathrm{C}+{}^{1}_{1}\mathrm{H}\rightarrow{}^{13}_{7}\mathrm{N}+2\,\mathrm{MeV} \)

In a nuclear reaction, the number of protons and the number of neutrons are each conserved. So the mass numbers (upper indices) and the atomic numbers (lower indices) must add up to the same totals on the two sides.

Option (1) \( {}^{13}_{6}\mathrm{C}+{}^{1}_{1}\mathrm{H}\rightarrow{}^{14}_{6}\mathrm{C}+4.3\,\mathrm{MeV} \) — Incorrect. The mass numbers balance, \( 13+1=14 \), but the atomic numbers do not. They are \( 6+1=7 \) on the left against 6 on the right.

Option (2) \( {}^{12}_{6}\mathrm{C}+{}^{1}_{1}\mathrm{H}\rightarrow{}^{13}_{7}\mathrm{N}+2\,\mathrm{MeV} \) — Correct. The mass numbers give \( 12+1=13 \) and the atomic numbers give \( 6+1=7 \). So both balance. The 7 protons and 6 neutrons on the left make up the nitrogen-13 nucleus on the right.

Option (3) \( {}^{14}_{7}\mathrm{N}+{}^{1}_{1}\mathrm{H}\rightarrow{}^{16}_{8}\mathrm{O}+7.3\,\mathrm{MeV} \) — Incorrect. The atomic numbers balance, \( 7+1=8 \), but the mass numbers do not. They are \( 14+1=15 \) on the left against 16 on the right.

Option (4) \( {}^{235}_{92}\mathrm{U}+{}^{1}_{0}n\rightarrow{}^{144}_{56}\mathrm{Ba}+{}^{89}_{36}\mathrm{Kr}+2\,{}^{1}_{0}n+200\,\mathrm{MeV} \) — Incorrect. The atomic numbers balance, \( 56+36=92 \), but the mass numbers do not. They are \( 235+1=236 \) on the left against \( 144+89+2=235 \) on the right. The balanced form of this fission reaction releases three neutrons.

NCERT (2026-27):
Example 13.4 – “… In a nuclear reaction, elements may be transmuted. Thus, the number of atoms of each element is not necessarily conserved in a nuclear reaction. However, the number of protons and the number of neutrons are both separately conserved in a nuclear reaction.”