In the process, these so-called parent radioisotopes transform, or decay, into daughter isotopes containing different numbers of protons and neutrons.
These may become parent isotopes to their own daughter isotopes.
Parent and daughter isotopes are often different elements with different physical and chemical properties.
where D is the present amount of daughter isotope in a sample at present and D0 is the amount of daughter isotope in the sample at the time of formation.
Because absolute numbers of atoms of some isotopes are difficult to measure, and because ratios of isotopes with very similar atomic masses can be measured accurately and precisely with a mass spectrometer, equation (5) may be modified while preserving the equality of both sides of the equation by dividing each side by the identical amount of a stable non-radiogenic isotope (d) of the same element as the daughter isotope. A stable non-radiogenic isotope is not radioactive, and it is either not produced by decay of a radioactive isotope at all or else it is produced at an exceedingly slow rate by a radioactive isotope with a half-life that far exceeds the age of the universe.
To calculate the age of the sample, therefore, we must also know [D.sub.0]/[d.sub.0], the ratio of daughter isotope and the stable non-radiogenic isotope in the sample at the time of its origin.
In this case, the problem of knowing the initial isotope ratios or amounts is avoided because essentially no daughter isotope is initially present ([sup.40]A[r.sub.0] = 0)6.
In the other three methods, however, if lead is lost at all, a mineral will yield a spuriously young age because a daughter isotope, either [sup.208]Pb, [sup.207]Pb, or [sup.206]Pb, is lost, and the ages are based on the ratios of 238U/[sup.206]Pb, 235U/[sup.207]Pb, or [sup.232]Th/[sup.208]Pb.
As a result, the atomic number (Z) of a daughter isotope such Ca (Z = 20) is one more than that of the parent K (Z = 19) whereas the atomic mass remains the same (40) because the sum of protons and neutrons remains constant, a neutron being replaced by a proton.