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Considering that the spontaneous fission rate of uranium 235 is 0.00563 fissions per Kg per second, why does this not cause small explosions or "fizzles" of the sub-critical fuel mass(s) in an atom bomb in the hours before the assembly of the critical mass is triggered? By similar reasoning, why doesn't spontaneous fission cause explosions in sub-critical stockpiles of uranium and plutonium fuels?

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An explosion requires a runaway chain reaction, where each fission reaction triggers more than one other fission reaction, causing exponential growth in the amount of energy released. The amount of material required for a sustained chain reaction is the critical mass. A sub-critical mass does not have enough material to maintain a chain reaction. One fission event is not likely to trigger another, so an explosion doesn't happen. A single fission releases a large amount of energy for its mass, but in an absolute sense, the amount of energy released is rather small - around 32 pJ of energy.

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  • $\begingroup$ I understand that a nuclear explosion requires a critical fuel mass. My question referred to the effect of the spontaneous fissions on the sub-critical material. I know they will not lead to a sustained chain reaction, but what is the effect of all of these fissions on the sub-critical mass? $\endgroup$ May 24, 2020 at 20:00
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    $\begingroup$ @BarrieLawson That was my point, the spontaneous fission of one nucleus is not likely to trigger another fission event. In the event that it does, it's unlikely that the fission of that nucleus triggers another fission event. Generally, if one fission event has probability $p<1$ of triggering another fission event, then the probability of triggering $n$ fission events from a spontaneous fission is $p^n$, which gets very small very quickly. $\endgroup$ May 24, 2020 at 20:05
  • $\begingroup$ Also, most U-235 decays are alpha emission. The branching ratio for spontaneous fission is ~$7×10^{-9}$%. $\endgroup$
    – PM 2Ring
    Nov 6, 2023 at 5:55
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Because a single decay event can't be stored for later use. There is nothing from the event that can "build up" over time.

Every fission decay event releases neutrons. For the purpose of this scenario, we can imagine the neutrons have only two outcomes: they reach a fissile nucleus and cause a reaction (releasing additional neutrons), or they miss everything and escape into the environment.

If the number of neutrons that each decay event is likely to release additionally is less than one, then over time the neutrons from the event are lost. They leave the material and either interact with the environment or decay. In either event, they don't contribute to further reactions in the fissile material. This is similar to what is happening to uranium in the earth's crust. Some atom of U-235 might by chance be induced to fission by a wandering neutron every now and again. But because the density of the fissile material is so low, the decay is very unlikely to reach another atom. The chain is broken.

Only in a "critical mass" of the material can the chain continue. In a sub-critical mass, the total rate of reactions might be increased (potentially with a measurable change in temperature or heat flow), but still insufficient for the reaction to accelerate. In this sub-critical mass nothing (other than heat) is accumulating. In fact, the fissile material is decaying at a slightly greater-than-normal rate.

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  • $\begingroup$ Thank you for your explanation. Does this mean that despite the sub-critical mass generating 486 fissions per hour there is a negligible risk of even a minor event being initiated when a bomb is being transported to its target? What would the probability of such an event be and what could its magnitude be? $\endgroup$ May 24, 2020 at 22:14
  • $\begingroup$ Assuming folks have done the sums properly in creating the assembly, the risk is zero. The crust of the earth has much more uranium and many more fissions per hour. But because the density of fissile material and neutron absorbers is insufficient for sustained fission, the decays do not propagate. $\endgroup$
    – BowlOfRed
    May 24, 2020 at 22:44

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