The neutron generation time in a reactor is the average time between one fission and the fissions induced by the neutrons emitted in that fission. Suppose that the power output of a reactor at time is . We have to show that the power output a time t later is , where

,

where k is the multiplication factor. Note that for constant power output .

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The multiplication factor in a nuclear power reactor is the ratio of number of neutrons present at the beginning of a particular generation to the number of neutrons present at the beginning of the next generation.

Let the number of neutrons present which trigger nuclear fission process at be N. It is given that the power output at is .

The neutron generation time in a reactor is the average time between a fission and the fissions induced by the neutrons emitted in that fission.
Between the times and later, fission generations would have occurred. Therefore, at time t the number of neutrons present for triggering the nuclear fission process then will be

.

The power output due to fission in the nuclear reactor at time t will therefore be

.