Let's face it: radiation is forever

Chernobyl reactor after the 1986 explosion

Uranium-235 ha a half life of 700 million years, more that all human existence and even all primate existence. It is in practical terms forever.

And half-life is only half of it, as the name says. Like the sophists' turtle which lightfooted Achilles could never reach, that only means loss of half of its radioactivity, it needs another such time to reach to 1/4, etc. 

The other usual component of nuclear fuel, Plutonium-239, has a much shorter half-life, "only" 24,200 years, which is like the span from the Last Glacial Maximum to now, a little bit more actually. 

Even radioactive cesium's effective half-life in the wild is above 180 years.

Radioactivity is forever and we can do little about it but dig a huge hole somewhere that is considered geologically stable and desertic (like in the middle of the Sahara or Siberia), dump everything there in the best containers we can conceive and bury it many kilometers under the soil. 

But what we cannot do is to keep producing radioactive materials and assuming unacceptable risks with them. Chernobyl and Fukushima are there to stay, forever. We can (at a high cost of lives) bury them maybe but we cannot guarantee that we can forget about them ever in the future. 

Russian doll nuclear logic: containment for the containment

Chernobyl still needs a new better sarcophagus and even this one will need replacement in the future. Chernobyl's radioactivity still haunts Central Europe and even Scotland, thousands of kilometers away from the doomed reactor. Much of the same can be said of other sites, like Chelyabinsk, where much of the Soviet nuclear arsenal was developed.

See also: Wikipedia - Chernobyl disaster effects, Chernobyl's New Safe Confinement. 

Thanks to Xdrfox posting at EnergyNews comment section with a bunch of useful links, and to Energy News itself, which is replacing the emergency effort of Florida Oil Spill Law on the Fukushima catastrophe, not their focus of attention (it is the Deepwater Horizon catastrophe instead).