[Karsten (OP)]

My students asked me this twice now and I did not have a good answer. I hate when that happens.

The trouble with radioactive material seems to be that some of it stays radioactive quite long. Other materials decay in milliseconds. Why do we use the materials that take so long to decay in a nuclear power plant? Could we use some that have a much shorter half life?

My guess is that the material has to be radioactive to be useful in a nuclear power situation and if it has a very short half life it is basically already gone by the time we find it in the ground. All that is left is the stuff with the half life of millions of years. But that is just a guess.

Any real answers?

[Bored chemist]

Essentially you already have the right answer. Very nearly all the radioactivity on earth is derived from  uranium and thorium which have long enough half lives not to have already decayed.
There are traces of things like carbon 14 made by cosmic / solar ray interactions in the upper atmosphere but these are too rare to generate any useful power.

[RD]

Short lived radioactive isotopes are used in medicine ... http://en.wikipedia.org/wiki/Technetium-99m_generator

[Karsten (OP)]

Short lived radioactive isotopes are used in medicine ... http://en.wikipedia.org/wiki/Technetium-99m_generator

And we cannot run nuclear reactors with those short-lived isotopes?

[Bored chemist]

The only way to make them is to use a nuclear reactor based on uraninum.

[Karsten (OP)]

Aha. Very good. This makes sense. Thanks.

[swansont]

We don't run most reactors on decay, we use induced fission (except for things like radioisotope thermal generators, which convert the heat from decay into electricity).  Fission has the advantages of being able to control the output, so you can effectively shut it down when you want to, and releasing more energy than in a typical decay, by a large factor (decay energies are typically several MeV, while fission of U-235 releases about 200 MeV).

So the materials used in the power plant have to have the long half-life.  If they had decayed away, there would be no fuel.