Final answer:
The age of a substance can be determined by measuring the ratio of remaining radioactive parent isotope to the stable daughter product, and using the known half-life of the parent isotope to calculate how long it has been decaying.
Step-by-step explanation:
The amount of a radiometric decay product found in a substance can help determine the substance's age through a process known as radioactive dating. When a rock or mineral forms, it contains a known amount of a radioactive isotope, referred to as the parent isotope, which decays into a stable daughter product at a constant rate over time. This rate is characterized by the isotope's half-life, the time it takes for half of the parent atoms to decay into daughter atoms.
To estimate the age of a substance, geologists measure the ratio between the remaining parent atoms and the produced daughter atoms within the sample. If, for example, a rock contains uranium-238 (U-238), which decays to lead-206 (Pb-206) with a half-life of approximately 4.5 billion years, geologists can compute the rock's age by assessing the U-238 to Pb-206 ratio. The presence of a significant amount of daughter product alongside a decreased amount of the parent isotope indicates that multiple half-lives have passed, which allows for the calculation of the material's age.
It's important to note that radioactive dating assumes the material being tested has not been contaminated and that it remained a closed system since its formation. These conditions ensure the accuracy of the determined ages, making radiometric dating a powerful tool in geological and archaeological research.