Radiometric dating estimates elapsed time from changes in radionuclide populations, using a known nuclear decay constant and assumptions about the initial composition and subsequent closure to matter exchange.
With no initial radiogenic argon-40 and complete daughter retention, the surviving potassium-40 population is and the accumulated daughter population is . Here is the total nuclear decay constant and is the argon-producing branching fraction. Their ratio gives the displayed age. The result measures closure of the mineral's isotope system under those assumptions.
Radiocarbon dating uses the loss of carbon-14 relative to stable carbon after carbon exchange stops. It can measure either an isotope ratio by accelerator mass spectrometry or radioactive activity per fixed carbon content. Interpreting an age requires radiocarbon calibration and control of contamination and reservoir differences.
A radiocarbon age estimates elapsed time from a measured carbon-14 ratio , an assumed initial ratio and a specified nuclear decay constant . The displayed exponential decay inversion gives the age on that model's timescale. A conventional radiocarbon age uses a prescribed reference and decay convention; it is not generally a calendar age. Radiocarbon calibration accounts for changes in the atmospheric isotope ratio and maps the measurement to a calendar-age estimate.
Radiocarbon calibration converts conventional radiocarbon ages into calendar-age information using independently dated material and models of changes in reservoir isotope ratios. Conventional ages use the historical -year half-life, whereas the physical carbon-14 half-life is about years.[ref]
Radiocarbon calibration by Oxford Radiocarbon Accelerator Unit. Half-life conventions, changing atmospheric ratios and tree-ring calibration
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Radiometric dating is a technique used to date materials such as rocks or carbon by measuring the abundance of specific radioactive isotopes within the sample. This method relies on the principle of radioactive decay, where unstable isotopes (parent isotopes) transform into stable isotopes (daughter isotopes) over time at a known rate, characterized by their half-lives. For example, in carbon dating, carbon-14 (a radioactive isotope of carbon) decays into nitrogen-14 over time.