The rubidium–strontium dating method (Rb–Sr) is a radiometric dating technique, used by scientists to determine the age of rocks and minerals from their content of specific isotopes of rubidium (87Rb) and strontium (87Sr, 86Sr). One of the two naturally occurring isotopes of rubidium, 87Rb, decays to 87Sr with a half-life of 49.23 billion years. The radiogenic daughter, 87Sr, produced in this decay process is the only one of the four naturally occurring strontium isotopes that was not produced exclusively by stellar nucleosynthesis predating the formation of the Solar System. Over time, decay of 87Rb increases the amount of radiogenic 87Sr while the amount of other Sr isotopes remains unchanged. The ratio 87Sr/86Sr in a mineral sample can be accurately measured using a mass spectrometer. If the amount of Sr and Rb isotopes in the sample when it formed can be determined, the age can be calculated from the increase in 87Sr/86Sr. Different minerals that crystallized from the same silicic melt will all have the same initial 87Sr/86Sr as the parent melt. However, because Rb substitutes for K in minerals and these minerals have different K/Ca ratios, the minerals will have had different starting Rb/Sr ratios, and the final 87Sr/86Sr ratio will not have increased as much in the minerals poorer in Rb. Typically, Rb/Sr increases in the order plagioclase, hornblende, K-feldspar, biotite, muscovite. Therefore, given sufficient time for significant production (ingrowth) of radiogenic 87Sr, measured 87Sr/86Sr values will be different in the minerals, increasing in the same order. Comparison of different minerals in a rock sample thus allows scientists to infer the original 87Sr/86Sr ratio and determine the age of the rock. In addition, Rb is a highly incompatible element that, during partial melting of the mantle, prefers to join the magmatic melt rather than remain in mantle minerals. As a result, Rb is enriched in crustal rocks relative to the mantle, and 87Sr/86Sr is higher for crust rock than mantle rock. This allows scientists to distinguish magma produced by melting of crust rock from magma produced by melting of mantle rock, even if subsequent magma differentiation produces similar overall chemistry. Scientists can also estimate from 87Sr/86Sr when crust rock was first formed from magma extracted from the mantle, even if the rock is subsequently metamorphosed or even melted and recrystallized. This provides clues to the age of the Earth's continents. Development of this process was aided by German chemists Lise Meitner, Otto Hahn, and Fritz Strassmann, who discovered nuclear fission in December 1938.
Example For example, consider the case of an igneous rock such as a granite that contains several major Sr-bearing minerals including plagioclase feldspar, K-feldspar, hornblende, biotite, and muscovite. Each of these minerals has a different initial rubidium/strontium ratio dependent on their potassium content, the concentration of Rb and K in the melt and the temperature at which the minerals formed. Rubidium substitutes for potassium within the lattice of minerals at a rate proportional to its concentration within the melt. The ideal scenario according to Bowen's reaction series would see a granite melt begin crystallizing a cumulate assemblage of plagioclase and hornblende (i.e.; tonalite or diorite), which is low in K (and hence Rb) but high in Sr (as this substitutes for Ca), which proportionally enriches the melt in K and Rb. This then causes orthoclase and biotite, both K rich minerals into which Rb can substitute, to precipitate. The resulting Rb–Sr ratios and Rb and Sr abundances of both the whole rocks and their component minerals will be markedly different. This, thus, allows a different rate of radiogenic Sr to evolve in the separate rocks and their component minerals as time progresses.
Calculating the age The age of a sample is determined by analysing several minerals within multiple subsamples from different parts of the original sample. The 87Sr/86Sr ratio for each subsample is plotted against its 87Rb/86Sr ratio on a graph called an isochron. If these form a straight line then the subsamples are consistent, and the age probably reliable. The slope of the line dictates the age of the sample. Given the universal law of radioactive decay and the following rubidium beta decay: Rb 37 87 → β − 38 87 Sr + e − + ν ¯ e {\displaystyle {\ce {^{87}_{37}Rb->[{\beta ^{-}}]~_{38}^{87}Sr~+e^{-}\ +{\bar {\nu }}_{e}}}} , we obtain the expression which describes the growth of strontium-87 from the decay of rubidium-87: 38 87 Sr ( t ) = 38 87 Sr ( 0 ) + 37 87 Rb ( e λ t − 1 ) , {\displaystyle _{38}^{87}{\text{Sr}}(t)=~_{38}^{87}{\text{Sr}}(0)+~_{37}^{87}{\text{Rb}}(e^{\lambda t}-1)\ ,}
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