Dating with potassium-argon

The dating with potassium-argon (or K - Ar) is a radiometric method of Datation which makes it possible to determine the age of a sample of Roche by the measurement of the relative concentrations of the couple of Isotope S Potassium 40/Argon 40.

Description of the method

The method of dating K-Ar applies to a rock coming from the Solidification of a magma entirely degassed, and rests on the assumption that this rock did not contain argon at the time of its formation.

A dating of the rock is possible when one of the mineral constituting it contains potassium, and that the mineral trapped the totality of the argon formed during the disintegration of the ⁴⁰K.

The minerals are then dated by measuring the concentrations from the ⁴⁰K and the accumulated ⁴⁰Ar. The proportioning of the ⁴⁰K and the ⁴⁰Ar requires the use of refined techniques of Spectrometry mass implemented in specialized laboratories.

The radioactive Half-life of the ⁴⁰K is of 1,25 billion years; the method thus makes it possible to date from the rocks covering to it quasi totality of the geological ages with a good precision.

The minerals best adapted to this method are the Biotite, the Muscovite and the Feldspath S. the dating with potassium-argon makes it possible to date minerals from the metamorphic rocks and the volcanic rocks. It is particularly invaluable in prehistoric Archéologie , in particular in East Africa where the levels of volcanic ash are frequent in the archeological sites. It in particular made it possible to go back the sites to Olduvai and the prints of step of Laetoli.

Calculation of the age of the rock

Potassium 40 is a Isotope Radioactif which disintegrates according to the following modes of disintegration:

• $\{\}\; ^\; \{40\}\; \backslash \; mathrm\; \{K\}\; +\; \backslash \; mathrm\; \{E\}\; ^\; -\; \backslash \; rightarrow\; \{\}\; ^\; \{40\}\; \backslash \; mathrm\; \{Ar\}\; +\; \backslash \; gamma\; (1,505\; MeV)$

λ_ε = 0,581.10^-10/an

• $\{\}\; ^\; \{40\}\; \backslash \; mathrm\; \{K\}\; \backslash \; rightarrow\; \{\}\; ^\; \{40\}\; \backslash \; mathrm\; \{Ca\}\; +\; \backslash \; beta^\; \{-\}\; (1,311\; MeV)$

λ_β = 4,962.10^-10/an

The age of the sample is obtained by means of the following formula:

$t=\; \backslash \; frac\; \{1\}\; \{\backslash \; lambda\}\; \backslash \; cdot\; \backslash \; ln\; (1+\; \backslash \; frac\; \{\backslash \; lambda\}\; \{\backslash \; lambda\_\; \backslash \; epsilon+\; \backslash \; lambda\_\; \backslash \; beta\}\; \backslash \; cdot\; \backslash \; frac)$

When the report/ratio of the potassium 40 and argon 40 concentrations is sufficiently weak, the formula is simplified in:

$t=\; \backslash \; frac\; \{1\}\; \{0,1048\; \backslash \; times\; \backslash \; lambda\}\; \backslash \; cdot\; \backslash \; frac$

$t$ being the age of the sample, $\{\}\; ^\; \{40\}\; \backslash \; mathrm\; \{K\}\; \_t$et $\{\}\; ^\; \{40\}\; \backslash \; mathrm\; \{Ar\}\; \_t$ measured quantities of the isotopes father and wire.

See too

• Dating
• Carbon dating

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