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JEE Main 202429 JanuaryMorning Shift
Exam
JEE Main
Year
2024
Date
29 January
Shift
Morning Shift
Subject
Physics
Chapter
Nuclear Physics

JEE Main 2024 · 29 January · Morning Shift · Physics · Nuclear Physics

The explosive in a Hydrogen bomb is a mixture of H 2 1 , H 3 1 and...

The explosive in a Hydrogen bomb is a mixture of H21,H31H 2 1 , H 3 1 and Li63Li 6 3 in some condensed form. The chain reaction is given by Li63+n10→He42+H31Li 6 3 + n 1 0 \to He 4 2 + H 3 1; H21+H31→He42+n10H 2 1 + H 3 1 \to He 4 2 + n 1 0

During the explosion the energy released is approximately [Given : M(Li)=6.01690amu,M(H21)=2.01471amu,M(He42)=4.00388amuM ( Li ) = 6 . 01690amu, M\left(H 2 1\right) = 2 . 01471amu, M\left(He 4 2\right) = 4 . 00388amu and 1amu=931.5MeV1amu = 931 . 5MeV]

Options

  1. A28.12MeV28 . 12MeV
  2. B12.64MeV12 . 64MeV
  3. C16.48MeV16 . 48MeV
  4. D22.22MeV22 . 22MeV

Correct answer

D. 22.22MeV22 . 22MeV

Step-by-step solution

Combining the reactions, it can be written that

Li63+n10→He42+H31Li 6 3 + n 1 0 \to He 4 2 + H 3 1

H21+H31→He42+n10H 2 1 + H 3 1 \to He 4 2 + n 1 0

_____________________ Li 6 3 + H 2 1 \to 2\left(He 4 2\right)

Hence, the energy released in process can be calculated as follows

{Q=\Deltamc2=[M(Li)+M(H21)−2×M(He42)]×931.5MeV=[6.01690+2.01471−2×4.00388]×931.5MeV=22.22MeV\begin{cases}Q & = & \Deltam{c}^{2} \\ & = & \left[M ( Li ) + M\left(H 2 1\right) - 2 \times M\left(He 4 2\right)\right] \times 931 . 5MeV \\ & = & [ 6 . 01690 + 2 . 01471 - 2 \times 4 . 00388 ] \times 931 . 5MeV \\ & = & 22 . 22MeV\end{cases}

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