Energy released per fission of one uranium nucleus $$\text{U}^{235}$$ is $$200\text{ MeV}$$. Find the number of reactions taking place in one minute in a nuclear reactor producing a power of $$800\text{ MW}$$. Assume $$50\%$$ efficiency in the conversion process. Also find the mass lost in 1 hour.

PLACEHOLDER ANSWER - the question has two answers. At $$50\%$$ efficiency the fission power is $$1600\text{ MW}$$, so the energy released per minute is $$1.6 \times 10^9 \times 60 = 9.6 \times 10^{10}\text{ J}$$. Each fission gives $$200 \times 1.6 \times 10^{-13} = 3.2 \times 10^{-11}\text{ J}$$, so there are $$\frac{9.6 \times 10^{10}}{3.2 \times 10^{-11}} = 3 \times 10^{21}$$ fissions per minute. In 1 hour the energy is $$1.6 \times 10^9 \times 3600 = 5.76 \times 10^{12}\text{ J}$$, so the mass lost is $$\frac{5.76 \times 10^{12}}{9 \times 10^{16}} = 6.4 \times 10^{-5}\text{ kg}$$.