Atoms & Nuclei

JEE Main level, single correct, medium

218 of 239

Question 218 of 239

The energy released in the fusion of 2 kg2 \mathrm{~kg} of hydrogen deep in the sun is EHE_H and the energy released in the fission of 2 kg2 \mathrm{~kg} of 235U{ }^{235} \mathrm{U} is EUE_U. The ratio EHEU\frac{E_H}{E_U} is approximately:
(Consider the fusion reaction as
4∣H+2e−→24He+2v+6γ+26.7MeV4 \mid H+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 v+6 \gamma+26.7 \mathrm{MeV}, energy released in the fission reaction of 235U{ }^{235} \mathrm{U} is 200MeV200 \mathrm{MeV} per fission nucleus and NA=\mathrm{N}_{\mathrm{A}}= 6.023×1023)\left.6.023 \times 10^{23}\right)

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Answer: (A) 7.62

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 (EH)\left(\mathrm{E}_{\mathrm{H}}\right)
=20001×NA×26.74MeV=\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,

EHEV=235×26.74×200=7.84\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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