A town has a population of 1 million. The average electric power needed per person is 300 W . A reactor is designed to supply power to this town, with an aimed efficiency of 25\% for converting thermal power into

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Quantrex Academy · Accepted Answer

Correct answer: B. 3.24 × 10^ 24

Total electric power required by the town,

P_{e} = 10^{6} \times 300 = 3 \times 10^{8} \text{ W}

Since the efficiency of the reactor is

25\%

, the thermal power required from the reactor is:

P_{th} = \dfrac{P_{e}}{\eta} = \dfrac{3 \times 10^{8}}{0.25} = 1.2 \times 10^{9} \text{ W}

Energy released per fission event is:

E = 200 \text{ MeV} = 200 \times 10^{6} \times 1.6 \times 10^{-19} \text{ J} = 3.2 \times 10^{-11} \text{ J}

Number of fissions taking place per second is:

n = \dfrac{P_{th}}{E} = \dfrac{1.2 \times 10^{9}}{3.2 \times 10^{-11}} = 3.75 \times 10^{19} \text{ s}^{-1}

Therefore, the number of fission events that must take place every day is:

N = n \times 24 \times 3600 = 3.75 \times 10^{19} \times 86400 = 3.24 \times 10^{24}

A town has a population of 1 million. The average electric power...

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