system
Given the following post, respond as if you're commenting on Reddit:
human
Does all the nuclear fuel in an atomic bomb undergo fission, or is some scattered before it can go critical?

Is it possible that some fissile material is blown away by the force of the explosion before it can start reacting itself? On a related note, could the detonation of a nuclear weapon in close proximity to a reactor's fuel rods (unshielded for this hypothetical) cause them to explode?
gpt
Most of it does not undergo fission, only a small fraction actually does.

It takes about 0.22 Moles of fission reactions to produce 1 kiloton of energy. So for the nuclear weapon that destroyed Nagasaki (21 kilotons) it took about 4.6 Moles of fission reactions to produce that amount of destructive power. Pu-239 has an atomic weight of... 239 amu, so 4.6 Moles would weigh very close to 1.1 kilogram (about 55 cm^3 or just under 2 tablespoons). In comparison, about 6.2 kilograms of Plutonium were used in that bomb, so only about 17% of the fissionable material underwent fission.

In the case of the "Little Boy" bomb dropped on Hiroshima about 0.8 kilograms out of 64 kg of Uranium fissioned, or about 1.25% of the total.

As far as a bomb going off near fuel rods, there are interesting aspects to that. The thing that makes a fission bomb "go" is that the population of neutrons grows at a geometric rate. And this occurs because when the bomb has been assembled and is detonating a neutron produced via fission is about as likely to run into another fissionable nucleus as it is to escape from the core. This is as much a function of density as it is of sheer size, which is what implosion assembly (which increases density) is all about.

So if you have a hunk of fissionable mass nearby that isn't at the proper density you aren't going to magically be able to get it to start magnifying the number of neutrons just by throwing more at it. If that could happen it could happen with the number of neutrons already in the reactor.

However, that doesn't mean nothing happens, something actually will happen. If you increase the neutron flux on fission fuel rods you won't get them to spontaneously have fission chain reactions that spiral out of control. But what could happen is that for some of the neutrons that left the bomb they could multiply their energy release by causing a fission reaction.

In general you'll have on the order of as many neutrons produced as the number of fission reactions that have taken place, so if you have a huge amount of fissionable material packed tight around a bomb you could easily double the yield in this way.

Note that because we're just talking about one off fission reactions from fast neutrons and not multiplying neutrons this can happen even with natural U-238.

And this is exactly how real bombs work. Often they use a "tamper" of heavy metal round the core of the bomb to delay the bomb blowing itself apart quickly (so that the nuclear reactions have more time to run before everything is too spread out). And if a natural Uranium tamper is used then you can increase yield.

The Tsar Bomba bomb, for example, was designed to use Uranium around the 3rd fusion stage, to make use of the neutrons produced by the fusion reactions. Such a design would have doubled the yield of the bomb (to 100 MT). But in testing the Soviets decided to avoid producing so much radioactive fallout from all of those fission reactions and instead used a different material for the tamper, resulting in a 50 MT yield in the test.