<P> Accurate radiometric dating generally requires that the parent has a long enough half - life that it will be present in significant amounts at the time of measurement (except as described below under "Dating with short - lived extinct radionuclides"), the half - life of the parent is accurately known, and enough of the daughter product is produced to be accurately measured and distinguished from the initial amount of the daughter present in the material . The procedures used to isolate and analyze the parent and daughter nuclides must be precise and accurate . This normally involves isotope - ratio mass spectrometry . </P> <P> The precision of a dating method depends in part on the half - life of the radioactive isotope involved . For instance, carbon - 14 has a half - life of 5,730 years . After an organism has been dead for 60,000 years, so little carbon - 14 is left that accurate dating cannot be established . On the other hand, the concentration of carbon - 14 falls off so steeply that the age of relatively young remains can be determined precisely to within a few decades . </P> <P> If a material that selectively rejects the daughter nuclide is heated, any daughter nuclides that have been accumulated over time will be lost through diffusion, setting the isotopic "clock" to zero . The temperature at which this happens is known as the closure temperature or blocking temperature and is specific to a particular material and isotopic system . These temperatures are experimentally determined in the lab by artificially resetting sample minerals using a high - temperature furnace . As the mineral cools, the crystal structure begins to form and diffusion of isotopes is less easy . At a certain temperature, the crystal structure has formed sufficiently to prevent diffusion of isotopes . This temperature is what is known as closure temperature and represents the temperature below which the mineral is a closed system to isotopes . Thus an igneous or metamorphic rock or melt, which is slowly cooling, does not begin to exhibit measurable radioactive decay until it cools below the closure temperature . The age that can be calculated by radiometric dating is thus the time at which the rock or mineral cooled to closure temperature . Dating of different minerals and / or isotope systems (with differing closure temperatures) within the same rock can therefore enable the tracking of the thermal history of the rock in question with time, and thus the history of metamorphic events may become known in detail . This field is known as thermochronology or thermochronometry . </P> <P> The mathematical expression that relates radioactive decay to geologic time is </P>

How does the emission of radioactive isotopes relate to this event