The Rubidium (Rb) and the Strontium (Sr) are two chemical elements generally existing with the state of traces in the rocks. They replace partly for the Potassium for rubidium and the Calcium for strontium. Thus the minerals rich in potassium are generally rich in rubidium and those rich in calcium often present high percentages of strontium. It happens that strontium is a major element of certain minerals, it is the case in particular strontium carbonate of SrCO₃ formula (strontianite) or celestite SrSO₄ (célestite).

These two elements exist in nature in the form of several Isotope S, two for rubidium, ⁸⁵Rb and ⁸⁷Rb and four for strontium, ⁸⁴Sr, ⁸⁶Sr, ⁸⁷Sr and ⁸⁸Sr. Only one of them, the ⁸⁷Rb, is radioactive . It disintegrates in ⁸⁷Sr which, is to him a stable isotope of strontium like are, moreover, the three others. This Disintegration, for one, leads to the emission of an electron; it is thus a Radioactivité known as " beta less " that one can schematize by:

$\{\}\; ^\; \{\backslash \; rm\; \{has\}\}\; \_\; \{\backslash \; rm\; \{Z\}\}\; \backslash \; rm\; \{M\}\; \backslash \; longrightarrow\; \{\}\; ^\; \{\backslash \; rm\; \{has\}\}\; \_\; \{\backslash \; rm\; \{Z+1\}\}\; \backslash \; rm\; \{Me\}\; +\; e^\; \{-\}\; +\; \backslash \; naked\; bar\; \{\backslash \}\; \_\; \{E\}\; +\; \backslash \; mathbf\; \{Q\}$

$\{\}\; \_\; \{37\}\; ^\; \{87\}\; \backslash \; rm\; \{Rb\}\; \backslash \; longrightarrow\; \{\}\; \_\; \{38\}\; ^\; \{87\}\; \backslash \; rm\; \{Sr\}\; +\; e^-\; +\; \backslash \; naked\; bar\; \{\backslash \}\; \_\; \{E\}\; +\; \backslash \; mathbf\; \{Q\}$

Let us note as of now that ⁸⁷Rb and ⁸⁷Sr are two isobar S, i.e. two atomic species having the same mass number but differing by their numbers of protons. That poses a problem in mass spectrometry because the mass spectrometers used for the measurement of the isotopic reports/ratios of Sr generally have a weak resolution (300-400), which does not make it possible to separate ⁸⁷Rb from ⁸⁷Sr. It is thus essential to separate the two elements before measurement with the mass spectrometer. As in the case of the method of dating by the couple samarium-neodymium (Sm-Nd) it is generally necessary to dissolve the samples in order to carry out the separation of rudidium and strontium by ionic chromatography. This stage is carried out in clean room in order to limit the contamination of the sample.

The recent appearance of the mass spectrometers to plasma source coupled to a laser (LA-MC-ICPMS, Laser Ablation Multicollector Inductively Coupled Plasma Spectrometer Farmhouse) now makes it possible to carry out certain in-situ measurements on a polished section of rock, thus avoiding the complex phase of chemical dissolution-separation, but this method is still experimental for the couple Rb-Sr.

A certain number of conditions must be joined together so that the method Rb-Sr is applicable, in particular:

• the whole of the rocks or analyzed minerals must have crystallized starting from a common source of strontium, i.e. the initial reports/ratios ⁸⁷Sr/⁸⁶Sr are equal.
• the system must be remained closed since its formation, i.e. it did not lose or did not gain of rubidium or strontium. These exchanges are possible for example if the rock is crossed by fluids, when it is subjected to a metamorphic episode, or by deterioration on the surface.

At the end of the crystallization of a magmatic rock, each mineral constituting it integrated initial quantities different from the four isotopes of the strontium and both of rubidium.

Strontium 87 present today in a rock is thus the sum of strontium 87 present at the origin, with the formation of the rock and strontium 87 product by the disintegration of rubidium 87. We can write in a synthetic way:

$\{\}\; ^\; \{87\}\; \backslash \; rm\; \{current\; Sr\}\; \{\}\; \_\; \{\}\; =\; \{\}\; ^\; \{87\}\; \backslash \; rm\; \{initial\; Sr\}\; \{\}\; \_\; \{\}\; +\; \{\}\; ^\; \{87\}\; \backslash \; rm\; \{Sr\}$

When a radioactive isotope disintegrates, the variation of this isotope follows a function of the time NR (T) which obeys the law $N\text{'}\; (T)\; =\; -\; \backslash \; lambda\; NR\; (T)\; \backslash ,$. This differential equation has as a solution the functions of the type $N\; (T)\; =\; N\_0\; exp^\; \{-\; \backslash \; lambda\; T\}\; \backslash ,$.

$\backslash \; lambda\; \backslash ,$ is called " constant of disintegration ". It is related to another constant characteristic of this disintegration, T , called " period of half-life " , time with the end of which there remains nothing any more but half of the isotope present at the beginning.

We thus have: $\backslash \; frac\; \{N\_0\}\; \{2\}\; =\; N\_0\; exp^\; \{-\; \backslash \; lambda\; T\}$ from where $\backslash \; lambda\; =\; \backslash \; frac\; \{ln\; (2)\}\{T\}$.

For the couple (⁸⁷Rb/⁸⁷Sr), T are worth approximately 49 billion years and thus λ = 1,42 10^-11/an .

The equation above becomes:

$\{\}^\{87\}\backslash !Current\; Sr\_\; \{\}\; =\; \{\}\; ^\; \{87\}\; \backslash !\; Initial\; Sr\_\; \{\}\; +\; \{\}\; ^\; \{87\}\; \backslash !\; Current\; Rb\_\; \{\}\; (exp^\; \{\backslash \; lambda\; T\}\; -\; 1)$
Indeed, the desinteration partial of ⁸⁷Rb_initial results in the difference: ⁸⁷Rb_initial - ⁸⁷Rb_actuel and like ⁸⁷Rb_actuel = ⁸⁷Rb_initiale^-λt, we have well:

$\{\}^\{87\}\backslash !Initial\; Rb\_\; \{\}\; -\; \{\}\; ^\; \{87\}\; \backslash !\; Current\; Rb\_\; \{\}\; =\; \{\}\; ^\; \{87\}\; \backslash !\; Current\; Rb\_\; \{\}\; (exp^\; \{\backslash \; lambda\; T\}\; -\; 1)$
The problem is that we are opposite two unknown factors: ⁸⁷Sr_initial and T; however, we have only one equation…

This problem will be skilfully solved by knowing that the isotopic report/ratio ⁸⁷Sr_initial/⁸⁶Sr_initial remained identical since the origin and that the quantity of isotope ⁸⁶Sr (stable isotope) does not vary during time.

By dividing the equation above by ⁸⁶Sr_actuel which is equal to ⁸⁶Sr_initial besides, we obtain:

$\{\}^\{87\}\backslash !Current\; Sr\_\; \{\}/\{\}\; ^\; \{86\}\; \backslash !\; Current\; Sr\_\; \{\}\; =\; \{\}\; ^\; \{87\}\; \backslash !\; Initial\; Sr\_\; \{\}/\{\}\; ^\; \{86\}\; \backslash !\; Current\; Sr\_\; \{\}\; +\; (\{\}\; ^\; \{87\}\; \backslash !\; Current\; Rb\_\; \{\}/\{\}\; ^\; \{86\}\; \backslash !\; Current\; Sr\_\; \{\})\; (exp^\; \{\backslash \; lambda\; T\}\; -\; 1)$
Two rocks resulting from the same magma will present the same initial report/ratio ⁸⁷Sr_initial/⁸⁶Sr_actuel but of the ⁸⁷Sr_actuel ratios/⁸⁶Sr_actuel and ⁸⁷Rb_actuel/⁸⁶Sr_actuel different.

We will have two unknown factors then but also here, in this case, two equations… It is necessary then:

• to measure the concentrations of rubidium and strontium in the total rock and/or separate minerals (muscovite, biotite…) what can be carried out various manners. The method generally considered most reliable is the measurement of the concentrations of rubidium and strontium by isotopic dilution. In the case of strontium if the tracer used for the isotopic measurement of dilution is enriched in ⁸⁴Sr and gauged well, only one measurement with the mass spectrometer makes it possible to obtain the measurement of the ⁸⁷Sr/⁸⁶Sr report/ratio and the Sr content of the sample.
• to measure the isotopic composition of strontium in la/les rock total and the mineral fractions
• to then place on the x-axis the values of the ⁸⁷Rb_actuel ratios/⁸⁶Sr_actuel and to place on the y-axis the values of the corresponding ⁸⁷Sr_actuel ratios/⁸⁶Sr_actuel,

• to release the line of tendency which emerges from the group of dots,
• to calculate the slope " of it; p"
• and finally to deduce the age from it from the rocks by the equation $t\; =\; \{ln\; (p+1)\}/\backslash \; lambda$.