500,000 Years to Safety
There is a minor problem with the common claim (repeated here) that plutonium takes 500,000 years to become allegedly safe. The 500,000-year figure is the amount of time that will reduce the number of plutonium-239 atoms to 1/1,000,000 of their original number. On the other hand, they will have turned into uranium-235, which is only 30,000 time less radioactive than the plutonium. The uranium atoms will be 1,000,000 as radioactive as the original plutonium after 3.5 billion years.
On the gripping hand, a typical nuclear reactor will produce somewhat fewer plutonium-239 atoms than it uses up uranium-235. Even breeder reactors will eventually have a steady amount of plutonium and continue using up uranium. If we assume that half as many plutonium-239 atoms are created as uranium-235 atoms are destroyed, it will take only a third of a million years to become less radioactive than the original uranium.
The above analysis assumes that the waste is merely buried (or dumped in Death Valley … which could turn it into a desert) instead of being reprocessed and burned up in more reactors. In the latter case, the fission products will become less radioactive than the uranium in much less time.