Radioactive Equilibrium

An equilibrium as old as the Earth

Establishing a radioactive equilibrium
The radioactive equilibrium takes about 2 million years to form in the lineage of uranium 238, at which point the activities of these descendants become equal to that of uranium 238. The short half-lives of the first two descendants, thorium 234 and protactinium 234, mean that this equilibrium is reached quickly. It takes much longer for the next descendants, uranium 234 (with a half-life of 246,000 years) and thorium 230 (with a half-life of 75,000 years) to reach equilibrium. Radium and radon, the next descendants in the chain, have much shorter half-lives, and reach equilibrium at about the same time as the thorium. Two million years represent a brief instant for uranium 238, whose half-life is 4.5 billion years. The activity of the ancestor nucleus will not even have had time to diminish.


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Radioactive lineage is the term given to the chain of successive radioactive disintegrations that some nuclei undergo. In nature, radioactive lineage is particularly relevant for three heavy elements with half-lives of the order of billions of years: uranium 238, uranium 235 and thorium 232. The descendants of these three nuclei, present in trace quantities in rocks, make a substantial contribution to the natural levels of radioactivity.

Over the 4.5 billion years of the Earth’s history, all three of these decay chains have reached equilibria between the parent nucleus and the various descendants. The ratios evolve very slowly, ensuring that at any given moment the number of nuclei being formed is identical to the number of nuclei decaying. The activities are all practically invariant, and equal to the activity of the ‘ancestor’ nucleus.

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