Nuclear physics: critical state and fission

1. May 1, 2013

lovelyrwwr

When a nuclear reactor is in a critical state, the neutrons released in each fission trigger an average of exactly one additional fission. If the average number of additional fissions triggered rises above one, the reactor enters a supercritical state in which the fission rate and the thermal power output both 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 fission triggers an average of 1.01 additional fissions. The average time it takes for the neutrons released by one generation of fissions to trigger the next generation of fissions is 1.3 × 10-8 s. How much time elapses before the reactor's power output from a single generation of fissions grows to 3800 MW (which is roughly the normal output of a commercial reactor)?

My attempt
[(1.3E-8 seconds)(3800MW)(1000)] / [1.01(25KW)] = 0.00196 seconds but this answer is wrong according to my online homework site.

2. May 1, 2013

voko

Why are you using that formula?

3. May 1, 2013

SteamKing

Staff Emeritus
Hint: Let x0 = number of fissions which equals a power output of 25 kW.
Let x1 = number of fissions which equals a power output of 3800 kW.

What is the ratio of x1 to x0? If x0 grows by 1% every 1.3*10^-8 s, how long does it take x0 to increase to x1?