There are two primary forces at work in a nucleus; electromagnetic force and strong nuclear force. Gravity is too weak to matter at such a scale and the weak force is too complicated for me to talk about, although admittedly it is important.
The strong nuclear force actually holds the nucleus together, with protons and neutrons exchanging virtual mesons (quark-antiquark pairs) in order to stick together. The positive charge of the protons, however, introduces a pressure trying to drive the nucleus apart, though this doesn’t typically matter as the strong force is MUCH stronger (hence the name). However, the EM force maintains its strength over significantly larger distances than the strong force, and this adds up the larger the atoms get.
Uranium (the heaviest of the naturally occurring elements) and plutonium (a manmade element just above uranium) are big enough that when we compress them like springs, the EM force overpowers the strong force and the nucleus breaks like a rubber band ball. Particles ejected from this reaction will crash into other radioactive particles nearby causing a chain reaction.
There’s a lot of refinement to ensure you have enough of the unstable particles, but once you have that enriched product, it’s really down to compressing it. Some designs have a lump of material being shot like a gun into a bigger lump. A better design was a shell of conventional explosives around a radioactive core. We’ve since moved on to thermonuclear weaponry, which uses the fission reaction to trigger a fusion reaction for an even more energetic explosion.
Scary thing is, we can keep stacking them almost indefinitely; fission triggers fusion bomb to trigger bigger fission reaction to trigger bigger fusion reaction and so on.
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