Nuclear weapons use and nuclear meltdown don't have comparable radiation fallout. It's not even remotely similar. Nuclear bombs release radiation in a bang (usually disappearing in a couple days, IIRC), but nuclear melt downs release materials that continue to be radioactive (for an eternity).
Think about Chernobyl vs Hiroshima. Chernobyl is uninhabitable and will remain so for a very long time. Hiroshima was rebuilt in the exact same spot that was destroyed and is a healthy, thriving city, by all accounts.
Even in some far out place, nuclear fallout in some far out place will eventually make its way into the air and water of the world, count on it.
Could you expand on why the disappearance time is so much faster for a bomb than for a power plant? If 1kg of uranium undergoes fission, I would expect there to be a little less then 1kg of fission products resulting from it. No matter if it were a bomb or a power plant, the amount and lifetime of the fission products would be the same. There would have to be something else going on, like the bomb only splitting a tiny fraction of its uranium, or maybe something about the environment of the explosion destroying fission products?
At a very high level bombs are trying to convert as much of their fuel into energy as possible. The ideal bomb consumes most of the fuel and produces a lot of very nasty extremely short lived nuclear waste thus making a big detonation over a small fraction of a second. Waste products should be short lived isotopes to make them even more deadly weapons.
Meltdowns aren’t controlled reactions the waste includes perfectly useful fuel, short and long lived waste products, plus a mix of things such as control rods and the walls of the reactor etc. https://en.wikipedia.org/wiki/Corium_(nuclear_reactor)
There’s a few other effects such as mushroom clouds moving material away from the blast location, and reactors containing more nuclear fuel.
Do we actually have that much control over what the fission products are? My impression was that you hit U-235 with a neutron, and you get the same kinds of fission products out whether it's a bomb or a reactor. It's just determined by physics what kinds of isotopes are likely to come out, and my impression was that we don't know how to influence it so that only the shorter-lived kinds are created. Bombs may be designed to consume a very high fraction of the fuel, but that would tend to make them worse, since the fission products are more radioactive than the starting Uranium, and there will be more of them. The mushroom cloud thing does make sense as an explanation for why Hiroshima is still inhabited, though. And it's clear that Corium wouldn't be able form in the middle of a nuclear bomb explosion.
We don’t have direct control over the specific products, but as I understand it the extreme amounts of neurons in a nuclear bomb destabilize large atoms.
Think about Chernobyl vs Hiroshima. Chernobyl is uninhabitable and will remain so for a very long time. Hiroshima was rebuilt in the exact same spot that was destroyed and is a healthy, thriving city, by all accounts.
Even in some far out place, nuclear fallout in some far out place will eventually make its way into the air and water of the world, count on it.