>>631>>641>recycling of nuclear waste
Blog post coming up.
Natural uranium is mostly U238, with some U235 mixed in. U238 can't be used as fuel, so it has to go through isotope separation first - throwing away some of the U238 makes it enriched, i.e. the relative amount of U235 goes up as U238 goes down. This is the part where you'd use things like centrifuges.
What goes into a reactor is like >>637
said still mostly U238, but there's enough U235 to sustain a chain reaction.
When fuel comes out, some of the U235 has fissioned and become "real" waste, it's been split in half into elements with half the atomic weight and is extremely radioactive. But there's still U235 left, just not enough to keep things going. Additionally some of the U238 will have swallowed neutrons and have become plutonium, Pu239.
Plutonium is more radioactive than uranium 235, which is more radioactive than uranium 238. None of those are "kill you instantly" dangerous, and of course uranium already exists in nature. The split-in-half fission products are the real nasty stuff, but they only make up something like 1% of the total.
This also means that only about 1% of the fuel going in has been consumed. Reprocessing is the idea that you could pull out the remaining U235 and get fuel efficiency up to about 5%, or better yet, chemically separate the plutonium and use that as fuel. That way we could, in theory, turn all the U238 into plutonium and then use that as fuel, getting us close to 100% efficiency.
Sounds great! But plutonium equals bombs for most people, and uranium is cheap enough that we don't absolutely have to try to be efficient, so in practice reprocessing isn't done and we end up with 100 times more waste than we need to.
The other thing is that the most radioactive part of waste, the fission products, are not dangerous for tens of thousands of years, they're radiating and decaying so hard that they're mostly harmless after a few hundred years. Plutonium is the long-lasting stuff that causes the apparent problem that would have us need geological storage. But it can be used as fuel!
So we can't reprocess Pu because bombs, and we have a waste problem because we don't reprocess. Meanwhile, countries that use nuclear energy already have bombs, or have made the choice not to develop them, but somehow it's still absolutely vital that we prevent the US, France and Japan from getting their hands on plutonium.