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How does radiometric dating assign numerical ages to rocks?

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Radiometric dating assigns numerical ages to rocks by measuring the ratio of radioactive parent isotopes to their stable daughter products within a sample. This method relies on the principle that radioactive isotopes decay into daughter atoms at a constant, known rate, which is expressed as a half-life—the time required for half of the parent atoms to decay.12

Because the rate of decay is immutable and unaffected by external conditions like heat or pressure, scientists can use the measured parent-to-daughter ratio to calculate the time elapsed since the rock or mineral formed. The process involves several key requirements:2
* The system must have remained closed, meaning no parent or daughter atoms were added or lost since formation.2
* Scientists must account for any initial daughter atoms present at the time of the rock's creation.23
* The decay constant for the specific isotope must be accurately known.2

Techniques such as the isochron method are often used to improve accuracy by analyzing multiple samples to test for internal consistency and account for initial isotopic ratios.23