Rubidium-87 decays to Strontium-87 by beta decay according to the following equation:
Some background on Rubidium and Strontium:
Rb is a highly incompatible element. Sr is fairly incompatible in mafic systems
and relatively incompatible in silica-rich systems. This means that as partial
melting occurs, Rb is going to partition to the melt in greater proportion than
Sr will. From this partitioning, the mantle will become depleted in Rb relative
to Sr. Concurrently, the crust will become enriched in Rb relative to Sr.
A brief introduction to the radiogenic relationship between Rb and
Sr:
Rubidium-87 decays to Strontium-87 by beta decay according to the following
equation:
The amount of 87Sr found in a sample at any time is determined by the decay
constant of 87Rb, the initial amount of 87Sr in the sample, the time since the
initial time and the ratio of Rb to Sr in the system. This can be seen in the
equation below.
Where lambda is the decay constant and t is the age of the system.
The above equation tells us the absolute amount of Strontium-87 in the rock
sample. However, because this is a small number and counting atoms isn’t
easy, it is more useful to use the ratio of one isotope to another. By dividing
the above equation by a common factor, a more useful equation can be created:
This ratio of radiogenic strontium to a non-radiogenic isotope, Strontium-86, over time is more useful than the absolute amount of Strontium present in a sample.
Putting all this information together can tell us the history of a rock sample. We know that Rb preferentially goes into the crust. We also know that Rb-87 decays to Sr-87 over time. Thus, the Sr-87/Sr-86 ratio of the crust increases over time. Likewise, because the mantle is depleted in Rb, the Sr-87/Sr-86 ratio of the mantle decreases over time. This can be seen in the following figure from White (2005).
The crust has an increasing ratio of Sr-87/Sr-86 over time compared to the bulk earth composition, while the mantle has a decreasing ratio.
A few problems with the Rb-Sr system are that both elements are mobile during weathering and metamorphism, so their concentrations can be affected by these processes. In addition, Rb is a volatile element so the ratio of Sr-87/Sr-86 is not chondritic since some Rb was lost during the formation of the earth.
From White, 2005 and Dickin, 2002
neodymium