The uranium-lead dating is an absolute dating method , in which the radioactive decay series of uranium are exploited to date samples. With this method z. B. earthly rocks or meteorites dated. The age of the earth assumed today of 4.55 billion years was first determined by Fritz Houtermans and Clair Cameron Patterson using uranium-lead dating. Using this dating method, the age of the solar system , applied to what is probably the oldest minerals formed in our solar system, the calcium-aluminum-rich inclusions in meteorites, was determined to be 4.567 billion years. The oldest minerals formed on earth, zircons , which were found in rocks in Australia , were found to be up to 4.404 billion years old.

## Basics

There are two series of decays, each starting with uranium isotopes and ending with lead isotopes via several intermediate steps:

The various unstable decay products in these series are much more short-lived than the respective uranium isotope at the beginning of the series. Therefore, only the half-lives of the uranium isotopes play an essential role in determining the age. According to the law of decay:

${\ displaystyle {} ^ {206} \ mathrm {Pb} = {} ^ {238} \ mathrm {U} \ cdot (1-e ^ {- \ lambda _ {238} t}), \ quad {\ lambda } _ {238} = 1 {,} 55125 \ cdot 10 ^ {- 10} \, {\ frac {1} {\ mathrm {year}}}}$
${\ displaystyle {} ^ {207} \ mathrm {Pb} = {} ^ {235} \ mathrm {U} \ cdot (1-e ^ {- \ lambda _ {235} t}), \ quad {\ lambda } _ {235} = 9 {,} 8485 \ cdot 10 ^ {- 10} \, {\ frac {1} {\ mathrm {year}}}}$

This means that the age can be calculated in three different ways from the measurement of the lead isotope ratios and the Pb / U ratio. The first two methods result directly from the transformation of the respective law of decay:

${\ displaystyle t = {\ frac {1} {\ lambda _ {238}}} \ cdot \ ln \ left (1 + {\ frac {{} ^ {206} \ mathrm {Pb}} {{} ^ { 238} \ mathrm {U}}} \ right)}$
${\ displaystyle t = {\ frac {1} {\ lambda _ {235}}} \ cdot \ ln \ left (1 + {\ frac {{} ^ {207} Pb} {{} ^ {235} \ mathrm {U}}} \ right)}$

The third equation for age can easily be derived from both laws of decay, in which there are no ratios of isotopes of different elements, but only ratios of isotopes of one element:

${\ displaystyle {\ frac {{} ^ {207} \ mathrm {Pb}} {{} ^ {206} \ mathrm {Pb}}} = {\ frac {{} ^ {235} \ mathrm {U}} {{} ^ {238} \ mathrm {U}}} \ cdot {\ frac {(e ^ {\ lambda _ {235} t} -1)} {(e ^ {\ lambda _ {238} t} - 1)}}}$

The age can be determined from this equation by iterative numerical or graphic processes . In principle, only the ratio of the lead isotopes 207 Pb:  206 Pb needs to be measured, assuming that the current natural uranium isotope ratio on earth is homogeneous. This has long been assumed, the value should be 235 U:  238 U = 1: 137.88. However, new measurements put it at 235 U:  238 U = 1: 137.818 ± 0.045 (2σ), it can also be slightly different depending on the location. Since isotope ratios of an element can be determined much more precisely than the ratio of different elements, this method is very precise. The prerequisite for this method is that the current uranium isotope ratio in the sample is known. In particular, the application for dating meteorites requires a homogeneity of the uranium isotopes in the solar nebula , as long as the terrestrial uranium isotope ratio is used to calculate the age. However, the required uranium isotope ratio can in principle also be determined in each individual sample, so that this assumption is not absolutely necessary or can even be checked directly. A meaningful method to check whether the necessary prerequisites are met for a specific sample is to use the Konkordia diagram. ${\ displaystyle t}$

Another advantage of this method is that the decay constants of uranium are known with an accuracy in the per thousand range, while the decay constants of other radioactive elements used for dating are usually only known with an accuracy in the percentage range.

## Konkordia diagram

The Konkordia diagram is a way of checking the reliability of the measured U-Pb ages. If the measured 206 Pb / 238 U ratio and the 207 Pb / 235 U ratio of a measured sample are entered in the Konkordia diagram, the data point should ideally lie on the curve called the Concordia. This is the case, for example, with crystals that only have a one-step history behind them, i.e. after their crystallization no longer experienced any disturbance in the uranium-lead isotope system. If the measured isotope ratios are on the Konkordia, a one-step history can be assumed and the age can be regarded as very reliable.

A disruption of the U-Pb isotope system by an event later than the one to be dated can occur, for B. a metamorphosis of the rock or lead loss due to diffusion. If the sample has been disturbed, the data point is next to it d. i.e., he is discordant. Also non-radiogenic lead components, i. H. Lead from sources other than uranium decay (e.g. primordial lead) can cause a deviation from the Concordia if they are not sufficiently corrected in the lead isotope measurements. In fact, many rocks have a complex history behind them, which is why a large number of the uranium-lead ratios measured in practice turn out to be discordant.

Konkordia diagram

Even with discordant uranium-lead measurements, the history of a rock can often be reconstructed. This is the case if, after the original crystallization, crystals of a rock were caused by another singular event, e.g. B. a metamorphosis, have been disturbed, so have a two-stage history. Then the data points of such crystals in the Konkordia diagram lie on a straight line which intersects the Konkordia at the times of the first event (crystallization) and the second event (metamorphosis). Such a straight line is called a discordia. So if you measure several crystals from a rock, which all have the same two-stage history behind them, the discordia can be adapted to the data points, and thus the intersection points with the concordia and their associated points in time can be determined.

A possible problem here can be that if the uranium-lead isotope system has been disturbed by a continuous loss of lead, the data points can also lie in a wide range approximately on a straight line and only at small 207 Pb / 235 U ratios to the origin of the diagram turn towards. The danger here is that a straight line adapted to such data can be incorrectly interpreted as a discordia.

In addition to a discordant data point in the Konkordia diagram, which can be caused by non-radiogenic (also called primordial) lead, the lead isotope 204 Pb is an important indicator for the presence of non-radiogenic lead in a sample. This is because there is no natural series of decays into the isotope 204 Pb and therefore also no radiogenic 204 Pb, but this lead isotope is completely primordial and the frequency is therefore a direct measure of the proportion of non- radiogenic lead in the sample.

In the case of samples or mineral separations in which non-radiogenic lead represents a non-negligible proportion, this must be corrected before the age calculation. This is usually done by determining the primordial 206 Pb and 207 Pb frequencies with the measured 204 Pb frequency and the known isotope ratios of the primordial lead and subtracting them from the corresponding measured frequencies of these isotopes. The result is the radiogenic 206 Pb and 207 Pb frequencies with which the ages can then be calculated.

When making this correction, it is important to know the isotope ratios of primordial lead. These were for example by Tatsumoto et al. determined and published in 1973 and later by Göpel et al. (1985) confirmed. The studies by Göpel et al. also strongly support the assumption that the primordial lead was homogeneous in the protoplanetary disk .

Dating due to radioactive decay of uranium was first suggested by Ernest Rutherford in 1905 . After Bertram B. Boltwood had proven lead as the end product of uranium decay in 1907, Arthur Holmes gave ages of up to 1.64 billion years for some rocks in 1911 . These ages were too high, however, because they were not based on isotope ratios, but on the chemical ratios of uranium and lead. Isotopes were still unknown at the time.

Isotope ratios of lead were not measured until 1927 by Francis William Aston . In 1930 Otto Hahn determined the age of the earth with the uranium-lead method at 1.5 to 3 billion years, although he still used chemical ratios instead of isotope ratios for the calculation and made the assumption that no primordial lead in the rocks he was looking at were present. From 1937, Alfred Nier undertook measurements of lead isotope ratios with mass spectrometers . He also tried to determine the isotope ratios of primordial lead. The development of the atomic bomb, particularly as part of the Manhattan Project , also led to the development of improved techniques for determining isotope ratios and better understanding of uranium decay, greatly accelerating the development of the uranium-lead dating technique. In 1953 Clair Cameron Patterson published, based on lead isotope measurements in a meteorite, the still accepted age of the earth of 4.55 billion years.

## literature

• JM Mattinson (2013): Revolution and evolution: 100 years of U-Pb geochronology . Elements 9, 53-57
• B. Heuel-Fabianek (2017): Natural radioisotopes: the “atomic clock” for determining the absolute age of rocks and archaeological finds . Radiation Protection Practice, 1/2017, pp. 31–42.

## Individual evidence

1. Determination of the Age of the Earth from the Isotopic Composition of Meteoritic Lead. In: Nuovo Cimento. 10, 1953, pp. 1623-1633, doi: 10.1007 / BF02781658
2. ^ Patterson C., Tilton G. and Inghram M. (1955): Age of the Earth , Science 121, 69-75, doi: 10.1126 / science.121.3134.69 .
3. ^ Patterson C. (1956): Age of meteorites and the Earth , Geochimica et Cosmochimica Acta 10, 230-237
4. Amelin Y., Krot AN, Hutcheon ED, and Ulyanov AA (2002): Lead isotopic ages of chondrules and calcium-aluminum-rich inclusions , Science, 297 , 1678–1683, doi : 10.1126 / science.1073950 .
5. SA Wilde, JW Valley, WH Peck, CM Graham (2001): Evidence from detrital zircons for the existence of continental crust and oceans on the Earth 4.4 Gyr ago , Nature, 409, 175-178. (PDF file; 197 kB)
6. Steiger and Jäger: Submission on geochronology: Convention on the use of decay constants in geo- and cosmochronology , Earth and Planetary Science Letters, 36, 1977, 359-362
7. Hiess et al .: 238U / 235U Systematics in Terrestrial Uranium-Bearing Minerals , Science, 335, 2012, 1610–1614, doi : 10.1126 / science.1215507
8. Tatsumoto et al., Science, 180, 1973, 1278-1283
9. Göpel et al .: U-Pb systematics in iron meteorites - Uniformity of primordial lead , Geochimica et Cosmochimica Acta, 49, 1985, 1681-1695
10. Otto Hahn: The age of the earth. Die Naturwissenschaften 18 (1930) Issue 47-49, pp. 1013-1019