In a nuclear reactor, \(3.125\times10^{16}\) uranium nuclei undergo fission every second. Each fission releases 200 MeV of energy. The power output of the reactor is
(Take \(1\ \mathrm{MeV}=1.6\times10^{-13}\ \mathrm{J}\).)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(1.0\times10^{6}\ \mathrm{W}\)
Power is the energy released per second. It equals the number of fissions per second multiplied by the energy of one fission in joule.
\( \begin{aligned} E &= 200\times1.6\times10^{-13} \\ &= 3.2\times10^{-11}\ \mathrm{J} \end{aligned} \)
\( \begin{aligned} P &= nE \\ &= 3.125\times10^{16}\times3.2\times10^{-11} \\ &= 1.0\times10^{6}\ \mathrm{W} \end{aligned} \)
From the above, \( P=1.0\times10^{6}\ \mathrm{W} \). Hence, the reactor gives a power of 1 MW.
NCERT (2026-27):
Fission – “The energy released (the Q value ) in the fission reaction of nuclei like uranium is of the order of 200 MeV per fissioning nucleus. …”