When a nuclear reactor is in a critical state, the

Chapter , Problem 30

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When a nuclear reactor is in a critical state, the neutrons released in each fi ssion trigger an average of exactly one additional fi ssion. If the average number of additional fi ssions triggered rises above one, the reactor enters a supercritical state in which the fi ssion rate and the power output grow very rapidly. A reactor in a critical state has a power output of 25 kW. The reactor then enters a supercritical state in which each fi ssion triggers an average of 1.01 additional fi ssions. The average time for the neutrons released by one generation of fi ssions to trigger the next generation of fi ssions is 1.2 3 1028 s. How much time elapses before the power output from a single generation of fi ssions grows to 3300 MW (roughly the normal output of a commercial reactor)?

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