If a number of samples are analyzed and the results are shown to define a straight line within error, then a precise age is defined because this is only possible if each is a closed system and each has the same initial ratio and age.
The uncertainty in determining the slope is reduced because it is defined by many points.
When a single body of liquid rock crystallizes, parent and daughter elements may separate so that, once solid, the isotopic data would define a series of points, such as those shown as open circles designated R.
A specific datable mineral like lead of mass 206 relative to that of mass 204 has changed from an initial value of about 10 present when the Earth was formed to an average value of about 19 in rocks at the terrestrial surface today.Similar studies have shown that the samarium–neodymium (Sm–Nd) parent–daughter pair is more resistant to secondary migration but that, in this instance, sufficient initial spread in the abundance of the parent isotope is difficult to achieve.trace minerals may form, each concentrating certain elements and radioactive trace elements within the rock.By careful selection, certain minerals that contain little or no daughter element but abundant parent element can be analyzed.If the Earth’s interior were a simple and homogeneous reservoir with respect to the ratio of uranium to lead, a single sample extracted by a volcano would provide the time of extraction. No parent–daughter value for a closed system is involved, rather just a single isotopic measurement of lead viewed with respect to the expected evolution of lead in the Earth.Unfortunately the simplifying assumption in this case is not true, and lead model ages are approximate at best.In this case, the slope of the line in potassium–argon (K–Ar) dating, for example, because most minerals do not take argon into their structures initially.In rubidium–strontium dating, micas exclude strontium when they form, but accept much rubidium.Should a point plot below the line, it could indicate that a particular sample was open to migration of the dating elements or that the sample was contaminated and lay below the isochron when the rock solidified.Rubidium–strontium (Rb–Sr) dating was the first technique in which the whole rock isochron method was extensively employed.In uranium–lead (U–Pb) dating of zircon, the zircon is found to exclude initial lead almost completely.Minerals, too, are predictable chemical compounds that can be shown to form at specific temperatures and remain closed up to certain temperatures if a rock has been reheated or altered.