Definition

Radiometric dating is a way to find out how many years old a rock or fossil is: some atoms inside rocks slowly change into other atoms at a steady rate, so scientists count how many have changed to work out the age. The method relies on the constant decay rate of a radioactive parent isotope into a stable daughter isotope; by measuring the ratio of parent to daughter atoms and knowing the half-life, scientists calculate the time since the material formed. Carbon-14 (half-life $5{,}730$ years) dates organic remains up to about $50{,}000$ years, while potassium-40 and uranium-238 date igneous rocks that are millions to billions of years old. Decay follows first-order kinetics, $N = N_0 e^{-\lambda t}$, so the age is $t = \frac{1}{\lambda}\ln\left(1 + \frac{D}{N}\right)$, where $D$ is the daughter atoms produced and $\lambda$ is the decay constant. Reliable dating requires a closed system since formation and a known or negligible initial daughter content; isochron methods remove the initial-daughter assumption. Systems include $^{238}U \rightarrow ^{206}Pb$ (half-life $4.47$ billion years), $^{40}K \rightarrow ^{40}Ar$ ($1.25$ billion years), $^{87}Rb \rightarrow ^{87}Sr$ ($48.8$ billion years), and $^{14}C \rightarrow ^{14}N$ ($5{,}730$ years).