Consider the reaction \({}^{2}_{1}\mathrm{H}+{}^{2}_{1}\mathrm{H}\rightarrow{}^{3}_{1}\mathrm{H}+{}^{1}_{1}\mathrm{H}\). The masses are \(m({}^{2}_{1}\mathrm{H})=2.014102\ \mathrm{u}\), \(m({}^{3}_{1}\mathrm{H})=3.016049\ \mathrm{u}\) and \(m({}^{1}_{1}\mathrm{H})=1.007825\ \mathrm{u}\). Taking \(1\ \mathrm{u}=931.5\ \mathrm{MeV}/c^{2}\), the Q-value of the reaction is about
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(+4.03\ \mathrm{MeV}\)
The Q-value of a reaction is the energy it gives out. It equals the loss in total mass multiplied by \( c^{2} \). A positive Q-value means that energy is released.
\( \begin{aligned} m_i &= 2\times2.014102 \\ &= 4.028204\ \mathrm{u} \end{aligned} \)
\( \begin{aligned} m_f &= 3.016049+1.007825 \\ &= 4.023874\ \mathrm{u} \end{aligned} \)
\( \begin{aligned} Q &= (m_i-m_f)c^{2} \\ &= (4.028204-4.023874)\times931.5\ \mathrm{MeV} \\ &= 0.004330\times931.5\ \mathrm{MeV} \\ &= +4.03\ \mathrm{MeV} \end{aligned} \)
From the above, \( Q \) is positive. Hence, the fusion of two deuterons into a triton and a proton releases about 4.03 MeV.
NCERT (2026-27):
Summary – “9. The Q-value of a nuclear process is Q = final kinetic energy – initial kinetic energy. Due to conservation of mass-energy, this is also,”
\( Q=(\text{sum of initial masses}-\text{sum of final masses})c^{2} \)
Nuclear fusion – energy generation in stars – “… Some examples of such energy liberating nuclear fusion reactions are :”
\( {}^{2}_{1}\mathrm{H}+{}^{2}_{1}\mathrm{H}\rightarrow{}^{3}_{1}\mathrm{H}+{}^{1}_{1}\mathrm{H}+ \)\( 4.03\ \mathrm{MeV} \)\( \qquad [13.13(c)] \)