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(2) Geochronology

Introduction to Geophysics and Planetary Physics

Decay Laws

Radioactive elements follow an exponential decay law. After one half-life half of the atoms are left, after another half-life „half of the half“, i.e. on quarter (Source: www.noezsv.at). Exponential decay appears frequently in nature - barometric formula, Beer-Lambert-Bouguer law, beer froth (IGNobel Prize 2001), number of students in lectures …

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Isotopes of Chemical Elements

The chemical properties of an element are ultimately determined by the number of protons in the nucleus, since they determine the number of electrons in the shell of a (neutral) atom, and the structure of the electron shell is responsible for the chemical properties. Most elements have different Isotopes. All Isotopes of an element share the same number of protons (and have therefore the same chemical properties), but they have different numbers of neutrons. Light elements tend to have equal numbers of neutrons and protons. The most common isotopes of Helium, Carbon, Nitrogen an Oxygen are, e.g., 4He, 12C, 14N und 16O – but in case of Hydrogen 1H is most abundant (Source: Univ. Heidelberg)

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Parent and Daughter Isotopes

(„True“) Radioactive decay results in the transformation of a parent isotope into a daughter isotope („gamma decay“ is not a decay). Time can therefore be measured by counting both isotopes, like in the symbolic “hourglass” representation. Source: Univ. Heidelberg, Geochronology Lab.

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Decay Chain – Radium Series

Most radioactive nuclei (like Uranium-238) undergo a series of decays („chain“) until a stable isotope (here Lead-206) is reached Note the different half-lives (Source: Univ. Heidelberg, Geochronology Lab).

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Usable Isotopes

(Some) radioactive isotopes that are used in geochronology: Parent and daughter isotopes with associated half-lives (Source: Univ. Heidelberg, Geochronology Lab).

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Uranium-Lead-Dating

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Left: Uranium-Lead age of a zircon crystal. The two parallel Uranium chains allow for the representation in the concordia diagram. Undisturbed samples should lie on the (curved) concordia-line. Leakage of lead affects both lead isotopes in the same way – disturbed samples therefore lie on a straight line – the discordia. Ideally, the upper intercept corresponds to the age of formation, the lower intercept to the age of the metamorphose event (Univ. Heidelberg, Geochronology Lab).

Potassium-Argon-Dating

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Potassium („Kalium“) is an abundant element in Earth‘s crust. Argon as a noble gas is chemically inert, it usually (entirely) escapes from molten lava. K-Ar-Dating therefore gives the age of crystallization. Contamination with atmospheric Argon is possible (Uni. Heidelberg, Geochron. Lab. ).

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Footprints in Laetoli, Tanzania

A fortunate coincidence delivered the proof that our ancestors (here: Australopithecus afarensis) walked upright already 3.6 Million years ago. Rain converted freshly deposited volcanic ash into mud – which was crossed by an elephant, a rhino, some guinea fowls – and by two Hominids (apparently side-by-side), who all left their footprints. The sun dried and hardened the mud (almost like cement), which was then covered – and preserved – by other ash layers. Volcanic ash can be dated very accurately with the Potassium-Argon-Method.

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Left: An example for 40Ar/39Ar Dating of a Paleozoic muscovite – the constant plateau age suggests a closed system. In this variant of the K-Ar method, the mineral is sample is put in a neutron beam, which converts Potassium-39 into Argon-39 – therefore only Argon ratios have to be measured. Right: Thin-section of a Muscovite in polarized light (Univ. of Heidelberg, Geochronology Lab).

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Argon-Argon-Dating

Different Methods in Comparison

Age of the Amitsoq-Gneiss in Western Greenland: Different methods give different results – with different uncertainties (error bars). In general, isotopes with shorter half-lives can be expected to yield smaller absolute errors (Source: Univ. Heidelberg).

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Half-Lives and Range of Use

Different decay rates (half lives) correspond to different time ranges, where a dating method can be reasonably used. „Ga“ means giga-annum (= one billion (109) years). The 14C-Method can just be used for the last ~60 000 years. On the other hand it is pointless to apply the Rubidium-Strontium method to samples from the recent past (Source: Uni-Heidelberg, Geochronology Lab).

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The Origin of Radioactive Carbon

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The unstable carbon isotope Carbon-14 is constantly produced in the Earth‘s atmosphere.Responsible are Cosmic Rays – not the protons of the primary cosmic rays, but the neutrons of the secondary cosmic rays.C-14 (or radiocarbon) is therefore called a cosmogenic nuclide. (Does anybody know Viktor Franz Hess?)

Radiocarbon Dating

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Carbon-14 is built in the atmosphere when neutrons of the secondary cosmic rays react with nitrogen. C-14 decays to Nitrogen-14 via β–decay. The production rate turned out not to be time-constant, but radiocarbon ages can be calibrated with the aid of dendrochronology.

Radiocarbon Dating – „Ötzi“, the Iceman

On September 19, 1991 a German couple discovered a mummified body in the Ötztal Alps on Tisenjoch (at ~3200 m), close to the Similaun summit. Just by chance Reinhold Messner showed up. Radiocarbon Dating revealed the sensation: The body was more than 5000 years old, yielding (together with the surprisingly functional equipment) an unprecedented look on the Neolithic period.

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