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JEE Main 20249 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Evening Shift
Subject
Physics
Chapter
Nuclear Physics

JEE Main 2024 · 9 April · Evening Shift · Physics · Nuclear Physics

The energy released in the fusion of 2 ~kg of hydrogen deep in the...

The energy released in the fusion of 2 kg2 \mathrm{~kg} of hydrogen deep in the sun is EHandtheenergyreleasedinthefissionofE_H and the energy released in the fission of2 \mathrm{~kg} of { }^{235} \mathrm{U}isisE_U.Theratio. The ratio\frac{E_H}{E_U}isapproximately:(Considerthefusionreactionasis approximately: (Consider the fusion reaction as4 \mid H+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 v+6 \gamma+26.7 \mathrm{MeV},energyreleasedinthefissionreactionof, energy released in the fission reaction of{ }^{235} \mathrm{U}isis200 \mathrm{MeV}perfissionnucleusandper fission nucleus and\mathrm{N}_{\mathrm{A}}= \left.6.023 \times 10^{23}\right)

Options

  1. A7.62
  2. B25.6
  3. C15.04
  4. D9.13

Correct answer

A. 7.62

Step-by-step solution

In each fusion reaction, 411H4{ }_1^1 \mathrm{H} nucleus are used. Energy released per Nuclei of 11H=26.74MeV∴{ }_1^1 \mathrm{H}=\frac{26.7}{4} \mathrm{MeV}\therefore Energy released by 2 kg2 \mathrm{~kg} hydrogen \left(\mathrm{E}_{\mathrm{H}}\right) =\frac{2000}{1} \times \mathrm{N}_{\mathrm{A}} \times \frac{26.7}{4} \mathrm{MeV} \qquad \qquad\quad \& ∴ Energy released by 2 kg Vranium (EV)=2000235×NA×200MeV\begin{aligned} & \therefore \text{ Energy released by } 2 \mathrm{~kg} \text{ Vranium }\left(\mathrm{E}_{\mathrm{V}}\right) \\ & =\frac{2000}{235} \times \mathrm{N}_{\mathrm{A}} \times 200 \mathrm{MeV}\end{aligned}So,So,\frac{E_H}{E_V}=235 \times \frac{26.7}{4 \times 200}=7.84\therefore$ Approximately close to 7.62
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