# Peter Lux

## Secular Equilibrium

The reason for this post is to help people understand ‘secular equilibrium’. The reason for people interest is mainly due to this report which is based on data here. I have a bit to say about this data but will not go into it now.

If you want a more mathematical explanation the see here (warning uses a lot of calculus – A-level mathematics)

If we have a long lived isotope such as U-238 then as it decays the activity (i.e. the number of decays per second) of its daughter products becomes the same as the activity of the U-238.

To understand this let us think of a widget factory. It produces 100 widgets per week but they are not very good widgets and 10% of the break every week. The first week we have 100 widgets produced and 10 break leaving 90 widgets. The next week we have another 100 widgets produced and 20 break leaving 170. If we go on then when we have 1000 widgets then 100 break every week. This is the same as the number being produced every week. As you can see from the graph below there comes a point when there is no increase in the number of widgets.

If we have a decay chain

P â†’ D â†’ G

i.e. where the parent isotope (P) has a very long lifetime compared to the daughter isotope (D) a similar thing happens. D builds up until it decays as fast as it forms. The rate of production of D can be measured by the rate of decay of P and is the number of disintegrations per second of P. The rate of destruction of DÂ  is the number of disintegrations of D. So when we reach this equilibrium then the activity of D equals the activity of P.

An example of how this is useful is that you want to know if some uranium is of natural origin or not. If the uranium is naturally occurring then it should have been there for a very long time and secular equilibrium would have been established. If it has arrived recently then it would not be in secular equilibrium with its daughter products.

If you have secular equilibrium then that indicates that the the parent isotope has been there for a long time. However, the opposite is not necessarily true. The reason is that the two isotopes have different chemical properties and the daughter product may have dissolved and migrated away from the sample area.

The problem with the data used by EdF from Hinkley is that it claims to have found secular equilibrium when careful analysis of the data shows that this is not true. There has been a lot of comment about Dr Busby’s report saying that the data is not good enough to draw any conclusions. This may or may not be the case. However, if the data is not good enough it cannot be used by EdF in their safety case.

I will give the formula for secular equilibrium in another post – some people may find it useful and the derivation is just A level mathematics although the solution to the differential equations is usually just given and not derived.