If 200 MeV energy is released in the fission of a single nucleus of uranium-235, how many fissions per second will produce a power of 32 kW?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 10^{15} \)
Power is the energy released per second. If \( N \) fissions take place every second, each releasing energy \( E \), the power is \( P = N E \), so the number of fissions per second is
\( \displaystyle N = \frac{P}{E} \)
\( E = 200\,\mathrm{MeV} = 200 \times 1.6\times10^{-13}\,\mathrm{J} = 3.2\times10^{-11}\,\mathrm{J} \)
\( P = 32\,\mathrm{kW} = 3.2\times10^{4}\,\mathrm{W} \)
\( \displaystyle N = \frac{3.2\times10^{4}\,\mathrm{J\,s^{-1}}}{3.2\times10^{-11}\,\mathrm{J}} = 10^{15}\ \text{fissions per second} \)