The explosive in a Hydrogen bomb is a mixture of 1 H 2 , 1 H 3 and 3 Li 6 in some condensed form. The chain reaction is given by 3 Li 6 + 0 n 1 rightarrow 2 He 4 + 1 H 3 1 H 2 + 1 H 3 rightarrow 2 He 4 + 0 n 1 During the explosion the energy released is approximately [Given : M ( Li )=6.01690 amu . M ( 1 H 2 )=2.01471 amu. M ( 2 He 4 )=4.00388 amu , and 1 amu =931.5 MeV ]

Physics · Nuclear Physics

JEE Main 2024 — 29 January, Shift 1 — Question 47

The explosive in a Hydrogen bomb is a mixture of ${ }_{1} \mathrm{H}^{2},{ }_{1} \mathrm{H}^{3}$ and ${ }_{3} \mathrm{Li}^{6}$ in some condensed form. The chain reaction is given by

${ }_{3} \mathrm{Li}^{6}+{ }_{0} \mathrm{n}^{1} \rightarrow{ }_{2} \mathrm{He}^{4}+{ }_{1} \mathrm{H}^{3}$

${ }_{1} \mathrm{H}^{2}+{ }_{1} \mathrm{H}^{3} \rightarrow{ }_{2} \mathrm{He}^{4}+{ }_{0} \mathrm{n}^{1}$

During the explosion the energy released is approximately [Given : $\mathrm{M}(\mathrm{Li})=6.01690 \mathrm{amu} . \mathrm{M}\left({ }_{1} \mathrm{H}^{2}\right)=2.01471$ amu. $\mathrm{M}\left({ }_{2} \mathrm{He}^{4}\right)=4.00388 \mathrm{amu}$ , and $1 \mathrm{amu}=931.5$ $\mathrm{MeV}]$

Option A:
28.12 MeV
Option B:
12.64 MeV
Option C:
16.48 MeV
Option D:
22.22 MeV
Correct

Answer: D

Step-by-step solution

${ }_{3} \mathrm{Li}^{6}+{ }_{0} \mathrm{n}^{1} \rightarrow{ }_{2} \mathrm{He}^{4}+{ }_{1} \mathrm{H}^{3}$

${ }_{1} \mathrm{H}^{2}+{ }_{1} \mathrm{H}^{3} \rightarrow{ }_{2} \mathrm{He}^{4}+{ }_{0} \mathrm{n}^{1}$

${ }_{3} \mathrm{Li}^{6}+{ }_{1} \mathrm{H}^{2} \rightarrow 2\left({ }_{2} \mathrm{He}^{4}\right)$

Energy released in process

$\mathrm{Q}=\Delta \mathrm{mc}^{2}$

$\mathrm{Q}=\left[\mathrm{M}(\mathrm{Li})+\mathrm{M}\left({ }_{1} \mathrm{H}^{2}\right)-2 \times \mathrm{M}_{2}\left(\mathrm{He}^{4}\right)\right] \times 931.5 \mathrm{MeV}$

$\mathrm{Q}=[6.01690+2.01471-2 \times 4.00388] \times 931.5 \mathrm{MeV}$

$\mathrm{Q}=22.216 \mathrm{MeV}$ $\mathrm{Q}=22.22 \mathrm{MeV}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 29 January, Shift 1
Subject: Physics
Chapter: Nuclear Physics
Topic: Mass Defect, Binding Energy and Q-Value of Nuclear Reaction