Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Energy is released when two deuterons fuse to form a \( {}^{4}_{2}\mathrm{He} \) nucleus.
Reason (R): In this fusion the total number of nucleons decreases, and the mass of the nucleons that disappear is converted into energy.
In the light of the above statements, choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) is true but (R) is false.
Assertion (A) Energy is released when two deuterons fuse to form a \( {}^{4}_{2}\mathrm{He} \) nucleus. — True. The binding energy per nucleon of \( {}^{4}_{2}\mathrm{He} \) (about 7 MeV) is far greater than that of the deuteron (about 1.1 MeV). The helium nucleus is more tightly bound than the two deuterons, so the fusion gives out energy.
Reason (R) In this fusion the total number of nucleons decreases, and the mass of the nucleons that disappear is converted into energy. — False. Two deuterons carry 2 protons and 2 neutrons, and the \( {}^{4}_{2}\mathrm{He} \) nucleus has the same 2 protons and 2 neutrons. No nucleon disappears. The total binding energy increases. Binding energy lowers the mass of a nucleus, so the helium nucleus is lighter than the two deuterons. This mass difference, \( \Delta m \), appears as the energy \( \Delta m\,c^{2} \).
NCERT (2026-27):
Nuclear Fusion – Energy Generation in Stars – “When two light nuclei fuse to form a larger nucleus, energy is released, since the larger nucleus is more tightly bound …”
Example 13.4 – “(b) We know that the binding energy of a nucleus gives a negative contribution to the mass of the nucleus (mass defect). Now, since proton number and neutron number are conserved in a nuclear reaction, the total rest mass of neutrons and protons is the same on either side of a reaction. But the total binding energy of nuclei on the left side need not be the same as that on the right hand side. The difference in these binding energies appears as energy released or absorbed in a nuclear reaction. …”