I am now going to get a rough idea of how much caesium 137 there is in spent nuclear fuel. One reason for choosing Cs-137 is that it is a major fission product, it has a reasonably long half-life (30.17 years), it has a low melting and boiling point and is readily absorbed by the human body.

I am going to assume that the Cs-137 does not decay to any appreciable amount while it is in the reactor. This is just to make this post a bit simpler, and I have shown how to take this into account in this post if anyone is interested.

I have shown how to get a rough idea of how many fission events are necessary to produce a certain amount of energy, and expressed this as fissions per tonne of Uranium in a Rough Model of a Nuclear Reactor.I have also given data on now many atoms of a particular isotope is produced per fission in Composition of Spent Fuel.

So now we can simply multiply the two numbers – i.e. number of fissions per tonne of Uranium by the probability that a certain isotope (in this case Cs-137) will be produced.

For example, if there are 1.33×10²⁶ fissions per tonne of uranium and 6% of them result in an atom of Cs-137 then we would expect 1.33×10²⁶ x 0.06 = 7.97 x 10²⁴ atoms of Cs-137 to be produced. We can then compare it with published data.

The basic model is where I have assumed that the Cs-137 does not undergo decay in the reactor whereas the more advanced model takes this decay into account.

Not bad for such a rough model. However, this is the amount of Cs-137 in the fuel as it leaves the reactor. Once out of the reactor it is no longer being produced but simply decays. I shall look at this in a later post.

1 Irradiated Fuel Measurements, J. Parker (http://www.fas.org/sgp/othergov/doe/lanl/lib-www/la-pubs/00326413.pdf)