In the fission reaction \( {}^{236}_{92}\mathrm{U}\rightarrow{}^{117}\mathrm{X}+{}^{117}\mathrm{Y}+n+n \), the binding energy per nucleon of X and Y is 8.5 MeV, whereas that of \( {}^{236}\mathrm{U} \) is 7.6 MeV. The total energy liberated will be about
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 200 MeV
The energy liberated in fission equals the gain in total binding energy. The total binding energy of a nucleus is its binding energy per nucleon times the number of nucleons. The two free neutrons carry no binding energy.
The binding energy of the two fragments is:
\( \begin{aligned} E_{\mathrm{X+Y}} &= (117+117)\times8.5\,\mathrm{MeV} \\ &= 1989\,\mathrm{MeV} \end{aligned} \)
The binding energy of the uranium nucleus is:
\( \begin{aligned} E_{\mathrm{U}} &= 236\times7.6\,\mathrm{MeV} \\ &= 1793.6\,\mathrm{MeV} \end{aligned} \)
The energy liberated is the difference:
\( \begin{aligned} Q &= E_{\mathrm{X+Y}}-E_{\mathrm{U}} \\ &= 1989\,\mathrm{MeV}-1793.6\,\mathrm{MeV} \\ &\approx 195\,\mathrm{MeV} \end{aligned} \)
Therefore, about 200 MeV is liberated in each fission.