Why do fuel rods have to be cooled for so long after being not actively used anymore?
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Because they’re still actively generating a lot of heat and it takes a long time for that to stop. Nuclear reactors use radioactive fuel to generate heat which boils water. When the reactor is running, the fuel rods are actively undergoing nuclear fission, but even when the reactor is shut down and the fission has stopped, the fuel is still radioactive and is still emitting heat from that radioactive decay. That radioactive decay continues (and thus the heat it generated continues) until the isotopes responsible for that heat have decayed.
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