# What is the shelf-life of a gravity-powered uranium bomb?

Inspired by this Worldbuilding question about making a booby-trap with a very long shelf life. The idea is to suspend one lump of fissile material say $3/4$ of a critical mass above another of the same mass. When one is dropped on the other there is some sort of violent reaction.

Let's not worry about how effective the trap would be. I am principally interested in how quickly it decays over time. Let's say the elements are made of $U$-$235$ whose half-life is about $700$ million years. Naievely you would expect the two elements to last about $500$ million years before the total mass becomes subcritical.

But I understand it's more complicated than that because the half-life formula doesn't account for the interaction between the atoms. Obviously when a uranium atom decay it shoots out particles which make nearby atoms more likely to decay. So a $2$ kg element should decay to $1$ kg faster than a $1$ kg element decays to $1/2$ kg. And an element of critical mass will decay suddenly and explosively.

So how long should we expect the booby-trap to remain viable? Of course there are loads of variables I have not considered or specified like the density or shape of the elements or how reflective the surroundings are. Feel free to set those variables to whatever is most convenient to getting a broad estimate. Are we talking one year or are we talking a hundred million years?

• A.V.S. pointed this out in a comment on my incorrect answer: "Spontaneous fission constitutes only a small fraction of all decays. So, even if each event causes some additional reactions, the overall effect would still be small." A.V.S., I think that should be an answer. – Ben Crowell Apr 22 '18 at 19:57
• I don't understand how that answers the question either. – Daron Apr 23 '18 at 11:59
• For U-235, the spontaneous fission half-life is nine orders of magnitude longer than that of other decay modes. Even when there is a spontaneous fission event, there are on average 1.86 neutrons emitted into the assembly, which will produce (on average) less than 1 additional fission because the assembly is subcritical. Basically, the effect of spontaneous fission on the total amount of material in the context of this question is negligible. – whit May 21 '18 at 16:09
• This question is also asking about a supercritical assembly, NOT a bomb: The device described would release a considerable amount of prompt radiation into the vicinity (enough to be lethal to people close by), but would heat up and become subcritical (by melting and flowing into a different geometry or by kinetic disassembly) in moments. In order to be a "bomb", the assembly must be held together long enough for considerably more yield to be released. – whit May 21 '18 at 16:16
• So how long would you expect it to last? – Daron May 21 '18 at 16:43