Question
Energy released in the fission of a single $$_{92}{U^{235}}$$ nucleus is $$200\,MeV.$$ The fission rate of a $$_{92}{U^{235}}$$ filled reactor operating at a power level of $$5\,W$$ is
A.
$$1.56 \times {10^{ - 10}}{s^{ - 1}}$$
B.
$$1.56 \times {10^{11}}{s^{ - 1}}$$
C.
$$1.56 \times {10^{ - 16}}{s^{ - 1}}$$
D.
$$1.56 \times {10^{ - 17}}{s^{ - 1}}$$
Answer :
$$1.56 \times {10^{11}}{s^{ - 1}}$$
Solution :
Fission rate = $$\frac{{{\text{total nuclear power}}}}{{{\text{energy produced/fission}}}}$$
Here, total nuclear power $$= 5\,W$$
Energy released per fission $$= 200\,MeV$$
∴ Fission rate $$ = \frac{5}{{200\,MeV}}$$
$$\eqalign{
& = \frac{5}{{200 \times 1.6 \times {{10}^{ - 13}}}}\,\,\left[ {\because 1\,MeV = 1.6 \times {{10}^{ - 13}}J} \right] \cr
& = 1.56 \times {10^{11}}{s^{ - 1}} \cr} $$