radiometric dating using Sr, Pb, and Ag isotope ratios - the basic idea behind using isotope ratios of certain elements for dating is that the abundance of daughter isotopes produced by radioactive decay change with time, such that the abundance ratio of a daughter isotope relative to a reference isotope of the same element will change as a function of time. For example, the following decay schemes correspond to the daughter isotopes of Sr, Pb, and Ag mentioned in the text:
87Rb --> 87Sr (half-life ~ 48.8 Ga)
238U --> 206Pb (half-life ~4.51 Ga)
235U --> 207Pb (half-life ~0.71 Ga)
107Pd --> 107Ag (half-life ~ 7 Ma)
where Ga = giga-aeon (billions of years) and Ma = mega-aeon (millions of years). The first three examples show decay schemes that continue to this day. The last shows the decay for a so-called extinct radionuclide, one that occurs so fast that none of the parent remains. Extinct radionuclides offer a powerful tool for studying early solar system events, as we shall see, but for now let's focus on the more conventional examples.
Conisdering conventional systems, more of the daughter isotope is produced as decay proceeds so the ratio of the daughter to a reference isotope (e.g., the 87Sr/86Sr ratio) in a sample increases as time elapses. The ratio that is relevant for chronology is the so-called initial ratio. The initial ratio is the ratio of the daughter isotope to reference isotope at the time of isotopic closure.
The diagram below shows how the initial ratio of 87Sr/86Sr differs for two rocks that have almost identical ages (within errors). The absolute sample ages are derived from the slope of the isochron lines for each rock (shown as best-fit lines through points, where the points were determined in this case by measuring 87Sr, 86Sr and 87Rb isotope abundances in multiple minerals from the rocks), whereas the initial ratios are determined by the intersection of the isochrons with the y-axis. Even in cases such as this where the absolute ages of two samples overlap, differences in the intial ratio tell us which sample is older. Thus, the initial ratio can be a more precise indicator of sample age. (For the Rb-Sr system, much of the uncertainty in formal ages derives from uncertainty in the decay rate. In the particular example below, a problem also arises in the limited spread of values for the lower rock, which contributes to an error in determining the isochron slope and hence the absolute age.)
For more on how the Rb-Sr system is used to obtain dates, click here. (The link leads to a series of pages produced by Prof. Cowley from the University of Michigan).