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How do radioactive isotopes help determine the ages of rocks and fossils?

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detector output connected to a measuring circuit — radiation measurement Figure 1: (A) A simple equivalent circuit for the development of a voltage pulse at the output of a detector. R represents the resistance and C the capacitance of the circuit; V(t) is the time (t)-dependent voltage produced. (B) A representative current pulse due to the interaction of a single quantum in the detector. The total charge Q is obtained by integrating the area of the current, i(t), over the collection time, t_c. (C) The resulting voltage pulse that is developed across the circuit of (A) for the case of a long circuit time constant. The amplitude (V_max) of the pulse is equal to the charge Q divided by the capacitance C.

Radioactive isotopes allow scientists to determine the age of rocks and fossils through a process known as radiometric dating. This method relies on the principle that radioactive isotopes (parent atoms) decay into stable daughter products at a constant, known rate, characterized by a specific half-life—the time required for half of the parent atoms to decay.12

By measuring the ratio of parent isotopes to daughter isotopes within a sample using a mass spectrometer, researchers can calculate the time elapsed since the material formed. Because different isotopes have varying half-lives, scientists select specific pairs based on the age of the sample:13

Carbon-14 dating: Used for organic materials (fossils) typically up to 50,000–60,000 years old.14
Uranium-Lead dating: Used for much older igneous and metamorphic rocks, as these isotopes have extremely long half-lives.124

For these measurements to be accurate, the sample must have remained a closed system, preventing the addition or escape of parent or daughter atoms since its formation.3