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 electric power. Assuming an average of 200 MeV of thermal energy is released from each fission event, determine the number of fission events that must take place every day.

Step-by-step solution

Total electric power required by the town, P_ e = 10⁶ 300 = 3 10⁸ W Since the efficiency of the reactor is 25 % , the thermal power required from the reactor is: P_ th = P_ e = 3 10⁸ 0.25 = 1.2 10⁹ W Energy released per fission event is: E = 200 MeV = 200 10⁶ 1.6 10⁻¹⁹ J = 3.2 10⁻¹¹ J Number of fissions taking place per second is: n = P_ th E = 1.2 10⁹ 3.2 10⁻¹¹ = 3.75 10¹⁹ s ⁻¹ Therefore, the number of fission events that must take place every day is: N = n 24 3600 = 3.75 10¹⁹ 86400 = 3.24 10²⁴