Radioactive equilibrium for a decay chain occurs when the each radionuclide decays at the same rate it is produced. At equilibrium, all radionuclides decay at the same rate. Understanding the equilibrium for a given decay series, helps scientists estimate the amount of radiation that will be present at various stages of the decay.

For example, as uranium-238 begins to decay to thorium-234, the amount of thorium and its activity increase. Eventually the rate of thorium decay equals its production its concentration then remains constant. As thorium decays to proactinium-234, the concentration of proactinium-234 and its activity rise until its production and decay rates are equal. When the production and decay rates of each radionuclide in the decay chain are equal, the chain has reached radioactive equilibrium.

Equilibrium occurs in many cases. However if the half-life of the decay product is much longer than that of the original radionuclide, equilibrium cannot occur. The graphs below illustrate the progress of ingrowth, and its effect on overall activity, and the potential for radioactive equilibrium in three general cases.

For simplicity's sake, the illustrations assume that the decay chain is only two steps the decay product decays to a stable nuclide. As decay chains lengthen, the calculations become more complex.

### Radionuclide and Decay Product Half-Lives Are Similar

When the half-life of the original radionuclide is only slightly longer or about the same as the half life of the decay product, the total activity rises initially. This results from the combined decay of both radionuclides. (It peaks slightly before the activity of the decay product does.) Eventually a balance (equilibrium) is reached.

The total activity then decays at about the same rate as the original radionuclide. This is known as "transient equilibrium.

### Radionuclide Has a Much Longer Half-Life

When the half-life of the original radionuclide is much longer than the half-life of the decay product, the decay product generates radiation more quickly. Within about 7 half lives of the decay product, their activities are equal, and the amount of radiation (activity) is doubled. Beyond this point, the decay product decays at the same rate it is produced a state called "secular equilibrium.

### Decay Product Has a Longer Half-Life

If the half-life of the decay products is much longer than that of the original radionuclide, its activity builds up to a maximum and then declines. The original radionuclide eventually decays away and no equilibrium occurs.