In today’s XKCD What If column, Mr. Munroe examines how much wealth could be stored in a shoebox. He notes that one could store about 300 kilos of plutonium in one but that this far exceeds the critical mass. He then follows this passage with a cartoon of a mushroom cloud. I can’t see anything good happening from compiling 300 kilos of Pu-239 in a shoebox, but I don’t think that the result would be an explosion, at least not the spectacular kind. Wouldn’t it just get very hot and melt?
If you could actually cram 300 kg into a shoebox, you’d get a mushroom cloud. If you attempted to add a small amount at a time it’d get hot and melt itself and a lot of stuff around it, and kill you so you couldn’t add any more. But there has to be some interesting states between, add so slow there’s never much more than nearly critical amounts of Pu and full on explosion.
Plutonium atoms, like other radioactive atoms, spontaneously fission. This happens all the time, and it generates heat. If you gather enough plutonium into a lump, it gets warm, or even really hot, like this. You can use this heat to power an RTG. Presumably if you gathered a bit more Pu and made a somewhat larger mass (within limits - see below), you could come up with a lump whose surface-area-to-volume ratio was too low to shed adequate heat to the atmosphere, and it would melt, as you suggest.
The critical mass for a bare, solid plutonium sphere is a few kilograms, on up to about 100 kilograms, depending on which isotope you’re dealing with. For a spherical mass above that amount, each fission event triggers (on average) more than one additional fission event (in additional to all the spontaneous fission events that are happening all the time anyway). This means that within a very short amount of time (microseconds) after you’ve assembled this material, fission events are happening much more rapidly than they would happen spontaneously (see previous paragraph). The radioactivity ramps up in an exponential way, and before long (again, microseconds) there’s so much heat being released that your sphere of Pu doesn’t have time to melt and flow out of the way. Even if it manages to heat up and turn to liquid, gravity won’t pull your sphere apart quickly enough to prevent a further increase in radioactivity and energy release. Remember, all of this is happening in the few microseconds after you’ve assembled your sphere. It will explode violently (i.e. it will be a true nuclear explosion), unleashing all of the energy that has been released by the fission events so far.
A shoebox isn’t a sphere, but somewhere within the volume of that shoebox there is room for a sphere large enough to contain a critical mass of Pu - so your shoebox full of Pu will be supercritical; it will indeed explode.
At what point does it go from getting hot and melting and actually exploding? That is just a matter of energy density, no? I am imagining an array of hoppers each loaded with a subcritical mass of powdered plutonium oxide simultaneously being poured into the shoebox.
I will never “explode” unless the mass goes from subcritical to supercritical in less than a few hundred microseconds. If you dump plutonium into a box, it will reach a stage at which it becomes critical, but it won’t “explode” - it will “fizzle.” That will still release a huge amount of energy, and will most likely vaporize all of your carefully gathered Plutonuim, but it will be more of a pop than a bang. During the Manhattan project, Harry K. Daghlian, Jr. was killed when his hand slipped, and allowed two halves of a Plutonium core to come together and achieve barely critical mass. The resulting cascade of neutrons caused enough cellular damage that he died 25 days later, but the reaction was slow enough that he was able to knock the two halves apart with his hand. If the two halves had been bigger, they probably would have turned red (or even white) hot vey quickly, and contaminated all of Los Alamos.
Correction.
Louis Slotin died from radiation poisoning when he caused a criticality excursion by bringing two halves of a Plutonium core together - Daghlian died first (killed by the same core!) when he dropped a Tungsten block on his core, which acted as a neutron reflector, causing the core to go critical.
Correction to the correction: the Demon Core was a solid subcritical sphere of plutonium; neither accident involved two masses of plutonium coming together. Slotin was lowering a beryllium hemisphere (manually!) onto the core, using a screwdriver blade to prevent it from dropping into place completely. The screwdriver slipped, the shield dropped, the core went instantly supercritical, and the rest is history.
As an aside, I always thought it was a bit unfair to give it the name “Demon Core,” as though the accidents were somehow the fault of an inanimate lump of plutonium. It would be more accurate (though less kind to Slotin and Daghlian) to call it “The Idiot Magnet.”
One thing is that the explosive yield would be completely dependent on the speed and the geometry that the 300 kg of plutonium was put into the box with.
I think that if you’re assembling it into a box shape, that you won’t get a very efficient explosion at all- probably under a kiloton I’m guessing.
I think it’s more likely that he’s a lurker, or that he just occasionally comes across this site in Google searches often enough to remember us. If he were a member, then he’d be participating in the threads about XKCD, and would fall victim to the someone on the Internet is wrong trap and end up outing himself.
Of course, how do you add it? Criticality includes not just mass, but mass and geometry and other factors like reflectors and removing moderators like graphite rods. So it’s not like you’re pouring from one box into the other, the source box would have been critical long before. One concern that Feynman looked into in Tennessee was that the managers didn’t understand criticality and were storing drums of partially enriched uranium in adjacent rooms. they did not realize the walls did not count for much when maintaining separation between masses.
You would need a collection of widely dispersed tiny plutonium lego blocks, and fetch them one at a time to drop into the shoebox. As the mass builds up, the box would be hotter and more glowing on each return trip until it killed you and/or melted down.
