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David’s fright

Dear reader,

Some time ago recently I commented on the fright that David Hahn gave himself, this fright lead to his arrest and the uncovering of his nuclear experiments. What I think may have happened was that when David did the chemical conversion of thorium dioxide into thorium metal that he removed the radium from the thorium.

Some of you will know the equation for simple radioactive decay.

A = Ao e λt

Where λ is the radioactive decay constant, which is equal to ln 2 / the half life = ln 2 / t½

For some thing simple like a cobalt-60 source in a cancer treatment machine this simple equation is all you need to predict the radioactivity level at a future date.

But for the more complex system where one thing decays into another thing which decays into another thing …….. ad nauseum something else is needed. For the next step up in complexity (two radioisotopes)

Here you need to use

Ay = Axo . (λy / λy –λx) . (e –λxt – e – λyt)

Which is a bit more maths, but I shudder at three radioisotopes in a series. If any of you feel up to it then please mail me your equation.

For natural thorium we have the following decay series.

Isotope Half life Mode
232Th 1.405 x 1010 years α
228Ra 6 years β
228Ac 6 hours β
228Th 1.9 years α
224Ra 3.7 days α
220Rn 1 minute α
216Po 0.2 seconds α
212Pb 10.6 hours β
212Bi 61 minutes β
212Po Short α
208Pb Stable

Looking at the decay series I think it was the ingrowth of the radium isotopes which was responsible for giving David his fright, all the other isotopes seem too short lived to be important in the kinetics. But I am sure that someone out there wants to be clever by using a more mathematically rigorous method.

If we assume that David started with a thorium which reached a secular radioactive equilibrium between the two thorium isotopes then we can start. Lets assume that David has 1 kBq of each of the thorium isotopes in his stash of gas mantles and at time zero he does the separation. Then if we consider only the thorium-228, radium-224, radon-220 and polonium-216 then we can make a graph. We will assume that none of the radon-220 is lost from the thorium “fuel” then if we just consider the four alpha emitters which I have mentioned in the last sentence then the graph of the total alpha activity of the thorium-228, radium-224, radon-220 and polonium-216 against time will look like this.

The change in alpha activity for Th-228, Ra-224, Rn-220 and Po-216 after the chemical separation of 1 kBq of Th-228 with time.

I am sure that we can get a even better set of graphs by adding more of the radioactive isotopes to it, but while the better graphs might be more useful for radiation protection purposes I think that this simple graph can show you the general idea of what can happen if you purify thorium and then leave it to stand. It is possible that David’s neutron source may have induced some radioactivity by activation but I suspect that his neutron source was quite weak. To know for sure we would need to have obtained his neutron source and then tested it with a series of target materials to see how much activity it could induce. On the top of my hit list of targets for the test would be sulphur, silver, rhodium and iridium. I would use a range of solid targets to allow an estimate to be made of the neutron flux for a series of different energies.


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