I assume you mean this question to be after the event of a nuclear weapon or nuclear powerplant meltdown. It all depends on the half-life of the element used. There are several different forms of uranium and plutonium which are used for power, and each have different half-lifes. Uranium-235 is the most common isotope used for nuclear power generation. It has a half life of about 700 million years. So to answer your question, in the event of a nuclear meltdown, the radiation will stay there for millions of years after the fact if it has the half life (which is the time it takes for the element to decay to half of its original mass). If there is cleanup of the radioactive material left over, this number can be greatly reduced.
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