The way that a nuclear reaction works is that a stable nucleus absorbs an extra neutron, and that causes the nucleus to become unstable, thus undergoing radioactive decay – becoming a different element, releasing more neutrons, and releasing a bunch of energy.
In a nuclear power plant, it’s desirable to have a chain reaction, where you have sufficient amounts of the radioactive material so that each decaying atom launches a neutron at another nucleus, causing it to delay in turn.
What makes the waste, well, waste, is that it will still undergo radioactive decay, but it won’t sustain a chain reaction, and it won’t produce enough energy to power the reactor.
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