Atomic dating using isotopes
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 made explicit and half-life introduced, equation 4 is converted to the following form, in which the symbols have the same meaning: Alternatively, because the number of daughter atoms is directly observed rather than to designate the parent atom, the expression assumes its familiar form: and 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 measurement of the daughter-to-parent ratio must be accurate because uncertainty in this ratio contributes directly to uncertainty in the age.
isotope is converted into another specific atom or isotope at a constant and known rate.
Most elements exist in different atomic forms that are identical in their chemical properties but differ in the number of neutral particles— neutrons—in the nucleus.
The results show that there is no known process that can alter the rate of radioactive decay.Two alterations are generally made to equation 4 in order to obtain the form most useful for radiometric dating.In the first place, since the unknown term in radiometric dating is obviously ) rather than through the decay constant λ.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 (see below Use of mass spectrometers).