When \( {}^{235}_{92}\mathrm{U} \) undergoes fission, 0.1% of its original mass is changed into energy. How much energy is released if 1 kg of \( {}^{235}_{92}\mathrm{U} \) undergoes fission?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 9\times10^{13}\,\mathrm{J} \)
In fission, a small mass \( \Delta m \) disappears. It appears as energy, given by Einstein’s mass–energy relation \( E=\Delta m\,c^2 \). Here \( c=3\times10^{8}\,\mathrm{m\,s^{-1}} \).
The mass changed into energy is 0.1% of 1 kg:
\( \begin{aligned} \Delta m &= \frac{0.1}{100}\times1\,\mathrm{kg} \\ &= 1\times10^{-3}\,\mathrm{kg} \end{aligned} \)
The energy released is:
\( \begin{aligned} E &= \Delta m\,c^2 \\ &= 1\times10^{-3}\,\mathrm{kg}\times(3\times10^{8}\,\mathrm{m\,s^{-1}})^2 \\ &= 1\times10^{-3}\times9\times10^{16}\,\mathrm{J} \\ &= 9\times10^{13}\,\mathrm{J} \end{aligned} \)