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Half-life is defined as the time period that must elapse in order to halve the initial number of radioactive atoms.
The half-life and the decay constant are inversely proportional because rapidly decaying radioisotopes have a high decay constant but a short half-life.
With This pair of equations states rigorously what might be assumed from intuition, that minerals formed at successively longer times in the past would have progressively higher daughter-to-parent ratios.
This follows because, as each parent atom loses its identity with time, it reappears as a daughter atom. In short, one need only measure the ratio of the number of radioactive parent and daughter atoms present, and the time elapsed since the mineral or rock formed can be calculated, provided of course that the decay rate is known.
The age calculated is only as good as the existing knowledge of the decay rate and is valid only if this rate is constant over the time that elapsed.
Fortunately for geochronology, the study of radioactivity has been the subject of extensive theoretical and laboratory investigation by physicists for almost a century.
For a single element, these atoms are called isotopes.
Because isotopes differ in mass, their relative abundance can be determined if the masses are separated in a mass spectrometer ( Radioactive decay can be observed in the laboratory by either of two means: (1) a radiation counter (e.g., a Geiger counter), which detects the number of high-energy particles emitted by the disintegration of radioactive atoms in a sample of geologic material, or (2) a parent atoms.
The situation is analogous to the death rate among human populations insured by an insurance company.Such checks include dating a series of ancient units with closely spaced but known relative ages and replicate analysis of different parts of the same rock body with samples collected at widely spaced localities.The importance of internal checks as well as interlaboratory comparisons becomes all the more apparent when one realizes that geochronology laboratories are limited in number.In turn, the geochronologist relies on the geologist for relative ages.Radioactive isotope, also called radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.