The fission of a \({}^{235}_{92}\mathrm{U}\) nucleus by a slow neutron releases about 200 MeV of energy. The nucleus that splits, \({}^{236}_{92}\mathrm{U}\), has a mass of about 236 u. About what percentage of its mass changes into energy in this fission?
(Take \(1\ \mathrm{u}=931.5\ \mathrm{MeV}/c^{2}\).)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.09%
The energy given out in fission comes from a small loss of mass. By \( E=mc^{2} \), a mass of 1 u is the same as 931.5 MeV of energy. So the whole mass \( M \) of the nucleus is worth an energy \( Mc^{2} \). The part of the mass that turns into energy is \( E/Mc^{2} \).
\( \begin{aligned} Mc^{2} &= 236\times931.5\ \mathrm{MeV} \\ &\approx 2.2\times10^{5}\ \mathrm{MeV} \end{aligned} \)
\( \begin{aligned} \frac{E}{Mc^{2}}\times100 &= \frac{200}{2.2\times10^{5}}\times100 \\ &\approx 0.09\% \end{aligned} \)
From the above, about 0.09% of the mass changes into energy. Hence, only a very small part of the mass of the uranium nucleus turns into energy in one fission.
NCERT (2026-27):
Mass – Energy – “Einstein gave the famous mass-energy equivalence relation”
\( E=mc^{2} \)\( \qquad (13.6) \)
Example 13.3 – “… = 0.9315 × 109 eV = 931.5 MeV or, 1u = 931.5 MeV/c2”