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.