The fusion reaction in the sun involves the following set of reactions. Identify \( X \), \( Y \) and \( Z \)
\( {}_{1}\mathrm{H}^{1} + {}_{1}\mathrm{H}^{1} \rightarrow X + e^{+} + \nu + 0.42\ \mathrm{MeV} \)
\( e^{+} + e^{-} \rightarrow \gamma + \gamma + 1.02\ \mathrm{MeV} \)
\( {}_{1}\mathrm{H}^{2} + {}_{1}\mathrm{H}^{1} \rightarrow Y + \gamma + 5.49\ \mathrm{MeV} \)
\( {}_{2}\mathrm{He}^{3} + {}_{2}\mathrm{He}^{3} \rightarrow Z + {}_{1}\mathrm{H}^{1} + {}_{1}\mathrm{H}^{1} + 12.86\ \mathrm{MeV} \)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( X = {}_{1}\mathrm{H}^{2},\ Y = {}_{2}\mathrm{He}^{3},\ Z = {}_{2}\mathrm{He}^{4} \)
In every nuclear reaction the mass number (superscript) and the charge number (subscript) balance. The positron \( e^{+} \) has charge \( +1 \) and mass number 0; the neutrino and gamma photons carry neither.
First reaction: mass \( 1 + 1 = A_{X} + 0 \), charge \( 1 + 1 = Z_{X} + 1 \), so \( X = {}_{1}\mathrm{H}^{2} \) (deuterium).
Third reaction: mass \( 2 + 1 = A_{Y} \), charge \( 1 + 1 = Z_{Y} \), so \( Y = {}_{2}\mathrm{He}^{3} \).
Fourth reaction: mass \( 3 + 3 = A_{Z} + 1 + 1 \), charge \( 2 + 2 = Z_{Z} + 1 + 1 \), so \( Z = {}_{2}\mathrm{He}^{4} \).
This is the proton-proton cycle: four protons end up as one helium-4 nucleus.
NCERT (2026-27):
Nuclear Fusion – Energy Generation in Stars – “… The fusion reaction in the sun is a multi-step process in which the hydrogen is burned into helium. Thus, the fuel in the sun is the hydrogen in its core. The proton-proton (p, p) cycle by which this occurs is represented by the following sets of reactions:
\( \displaystyle {}_{1}^{1}\mathrm{H} + {}_{1}^{1}\mathrm{H} \rightarrow {}_{1}^{2}\mathrm{H} + e^{+} + \nu + 0.42\,\mathrm{MeV} \qquad \text{(i)} \)
\( \displaystyle e^{+} + e^{-} \rightarrow \gamma + \gamma + 1.02\,\mathrm{MeV} \qquad \text{(ii)} \)
\( \displaystyle {}_{1}^{2}\mathrm{H} + {}_{1}^{1}\mathrm{H} \rightarrow {}_{2}^{3}\mathrm{He} + \gamma + 5.49\,\mathrm{MeV} \qquad \text{(iii)} \)
\( \displaystyle {}_{2}^{3}\mathrm{He} + {}_{2}^{3}\mathrm{He} \rightarrow {}_{2}^{4}\mathrm{He} + {}_{1}^{1}\mathrm{H} + {}_{1}^{1}\mathrm{H} + 12.86\,\mathrm{MeV} \qquad \text{(iv)} \qquad (13.14) \)”