According to radiometric dating estimates the earth is approximately
Since both decay series contain a unique set of intermediate radioactive isotopes, and because each has its own half-life, independent age calculations can be made from each (Dalrymple 20).
However, without any uranium present, accumulation of daughter isotopes ceases even though time continues to pass.The use of lead isotope ratios makes this isochron self-checking.A large scattering of measurements would indicate the sample is multi-stage rather than single-stage, making the isochron unreliable.The resulting line drawn through the plotted points will pass through a point representing the initial lead composition of the system.Although this point cannot be determined, the isochron will rotate about it as the rock ages because the initial amount of lead is constant regardless of age.Houtermans calculated the time required for lead composition of primordial lead samples to decay to the lead composition of young ores.
He used young terrestrial ores to obtain data for young ores and assumed the lead composition of the meteorite Canyon Diablo was representative of primordial lead.
These plots are also self-checking and are useful for dating old rocks with complex histories.
The plots can still produce valuable and accurate data using rocks that have been subjected to heating and metamorphic events (Dalrymple 20).
The difficulties with single-stage systems can be circumnavigated with multi-stage systems.
Though multi-stage lead samples cannot be used for generating isochrons, they can be used to produce valuable information through concordia-discordia plots.
An example isochron from Dalrymple (2004) is shown in Figure 4.8 below. Unlike other isochrons, the slope of the Pb-Pb isochron decreases with increasing age.