Question

A reactor is developing energy at the rate of $32MW$. Calculate the required number of fissions per second of ${}_{92}{U}^{235}$. Assume that energy per fission is $200MeV$

Answer 1

Rate at which the energy is developed at the reactor $=32MW=32\times {10}^{6}J/s$

Energy per fission $=200MeV$

Required number of fissions per second $=?$

Since the two energies are in different units, we must convert them into the same unit.

$\therefore$ energy released per fission $=200MeV$

$=200\times {10}^{6}eV$

$=200\times {10}^6\times 1.6\times {10}^{-19}J(\because 1eV=1.6\times {10}^{-19}J)$

$=320\times {10}^{-13}Joules$.

Let $N$ be the number of fissions per second producing $32MW$.

Energy per fission $\times N=$ Total energy released per second

$\therefore 320\times {10}^{-13}\times N=32\times {10}^{6}J/s$

$N=\frac{32\times {10}^6}{320\times {10}^{-13}}={10}^{18}fissions$

$\therefore$ The no. of fissions per second to produce the required power $={10}^{18}$ fissions per second.