radiation - Why is nuclear waste more dangerous than the original nuclear fuel?

I know the spent fuel is still radioactive. But it has to be more stable than what was put in and thus safer than the uranium that we started with. That is to say, is storage of the waste such a big deal? If I mine the uranium, use it, and then bury the waste back in the mine (or any other hole) should I encounter any problems? Am I not doing the inhabitants of that area a favor as they will have less radiation to deal with than before?

Answer

Typical nuclear power reactions begin with a mixture of uranium-235 (fissionable, with a half-life of 700 Myr) and uranium-238 (more common, less fissionable, half-life 4 Gyr) and operate until some modest fraction, 1%-5%, of the fuel has been expended. There are two classes of nuclides produced in the fission reactions:

1. 
   

   Fission products, which tend to have 30-60 protons in each nucleus. These include emitters like strontium-90 (about 30 years), iodine-131 (about a week), cesium-137 (also about 30 years). These are the main things you hear about in fallout when waste is somehow released into the atmosphere.

   
   
   

   For instance, after the Chernobyl disaster, radioactive iodine-131 from the fallout was concentrated in people's thyroid glands using the same mechanisms as the usual concentration natural iodine, leading to acute and localized radiation doses in that organ. Strontium behaves chemically very much like calcium, and there was a period after Chernobyl when milk from dairies in Eastern Europe was discarded due to high strontium content. (Some Norwegian reindeer are still inedible.)

   
   


2. 
   

   Activation products. The reactors operate by producing lots of free neutrons, which typically are captured on some nearby nucleus before they decay. For most elements, if the nucleus with $N$ neutrons is stable, the nucleus with $N+1$ neutrons is radioactive and will decay after some (possibly long) time. For instance, neutron capture on natural cobalt-59 in steel alloys produces cobalt-60 (half-life of about five years); Co-60 is also produced from multiple neutron captures on iron.

   
   

   In particular, a series of neutron captures and beta decays, starting from uranium, can produce plutonium-239 (half-life 24 kyr) and plutonium-240 (6 kyr).

   
   

What sometimes causes confusion is the role played by the half-life in determining the decay rate. If I have $N$ radionuclides, and the average time before an individual nuclide decays is $T$, then the "activity" of my sample is $$ \text{activity, } A= \frac NT. $$

So suppose for the sake of argument that I took some number $N_\mathrm{U}$ of U-238 atoms and fissioned them into $2N_\mathrm{U}$ atoms of cobalt-60. I've changed by population size by a factor of two, but I've changed the decay rate by a factor of a billion.

The ratio of the half-lives $T_\text{U-238} / T_\text{Pu-240}$ is roughly a factor of a million. So if a typical fuel cycle turns 0.1% of the initial U-238 into Pu-240, the fuel leaves the reactor roughly a thousand times more radioactive than it went in --- and will remain so for thousands of years.