Secular equilibrium is a specific condition of radioactive equilibrium in which the activity of a daughter radionuclide becomes equal to that of its parent radionuclide. This occurs when the half-life of the parent is significantly longer than that of the daughter (typically by a factor of 10,000 or more).
In a decay chain where a long-lived parent () decays into a short-lived daughter ():
Since Activity () is defined as , this simplifies to:
In this state, the quantity of the daughter radionuclide remains constant because its rate of production (from the parent's decay) is exactly balanced by its own rate of decay.
Secular equilibrium is a fundamental concept in managing NORM. In many geological formations, the Uranium Decay Series and Thorium Decay Chain are in secular equilibrium. However, industrial processes like oil extraction or mineral processing can break this equilibrium by chemically separating elements (e.g., leaching Radium but leaving Uranium behind). This leads to concentrated "disequilibrium" NORM, such as radioactive scale.