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Reactor grade plutonium and its poor quaility for bomb making

It has been said that reprocessing is bad for world peace, and that it will make it easier for a bomb maker to obtain the plutonium needed for a bomb. I hold the view that a PWR or BWR is strongly optimised for making electricity rather than bomb useable plutonium.

In a CANDU, RBMK, MAGNOX or AGR reactor it is possible to refuel the reactor while it is running, this allows short irradiation times which favour plutonium production for bombs. But in a BWR and PWR it is not possible to refuel it while it is running; this feature of the design makes it harder to make bomb grade plutonium using one of these reactors.

This is because the isotope signature of plutonium for a bomb making becomes worse with an increased irradiation time and burn up in the reactor. On the other hand an electric power company wants to get the most energy out of each fuel element, so they will want to get the highest burn up possible out of the fuel during a long irradiation time. These two considerations oppose each other.

In a recent paper the isotope signature of a used PWR fuel was given in a paper, this was fuel which had a burn up of 27.3 megawatt days per ton of uranium.

238Pu              0.27 g per Kg

239Pu              5.40 g per Kg

240Pu              2.06 g per Kg

241Pu              0.55 g per Kg

242Pu              0.39 g per Kg 

This works out as plutonium which by weight is

238Pu 3.1%

239Pu 62.3 %

240Pu 23.8 %

241Pu 6.3 %

242Pu 4.5 %

You might ask why this is important, it is important in the design of an atomic bomb to make sure that the implosion occurs faster than the generation of neutrons by spontaneous fission in the nuclear fuel used to make the bomb. If we assume that we need 10 kilos of plutonium to build a bomb then we can calculate based on the isotope signature how quickly neutrons will be generated by spontaneous fission in the fuel.

If we have ten kilos of the plutonium then we will have 310 grams of 238Pu. This isotope of Pu has a half life of 88 years and 1.9 x 10-7 of decays are spontaneous fissions.

The half life is 2777068800 seconds

So as the decay constant is ln 2 / half life = 2.49597 x 10-10 s-1.

As we have 1.3 moles of this plutonium isotope we have 7.84378 x 1023 atoms of the plutonium, which means that we have 1,95778 x 1014 Bq (196 TBq) of activity. As the branch ratio for spontaneous fission is 1.9 x 10-7 then we will have 3.72 x107 fissions per second.

We can repeat the maths for the other plutonium isotopes present.

Overall for this plutonium we can calculate that 1.87 x 108 spontaneous fission events will occur per second. So a bomb based on this plutonium would have to be imploded in less than 5.34 nanoseconds. Which is a very short length of time.

If we repeat the calculation using the isotope signature for the plutonium (99% Pu-239 and 1% Pu-240) used for the first ever atom bomb test (trinity), then we get a time of 209 nanoseconds. This is a much longer time which will make the task of the bomb maker much easier.

If the bomb design fails to implode in the time between the spontaneous fissions then it will give either a zero explosive yield or a very small yield.

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