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Radiometric dating is a technique used to date materials based on a knowledge of the decay rates of naturally occurring isotopes, and the current abundances. It is our principal source of information about the age of the Earth and a significant source of information about rates of evolutionary change.

Various methods exist differing in accuracy, cost and applicable time scale.

All ordinary matter is made up of combinations of chemical elements, each with its own atomic number, indicating the number of protons in the atomic nucleus. Additionally, elements may exist in different isotopes, with each isotope of an element differing only in the number of neutrons in the nucleus. A particular isotope of a particular element is called a nuclide. Some nuclides are inherently unstable. That is, at some random point in time, an atom of such a nuclide will be transformed into a different nuclide by the process known as radioactive decay. This transformation is accomplished by the emission of particles such as electrons (known as beta decay) or alpha particles.

While the moment in time at which a particular nucleus decays is random, a collection of atoms of a radioactive nuclide decays exponentially at a rate described by a parameter known as the half-life, usually given in units of years when discussing dating techniques. After one half-life has elapsed, one half of the atoms of the substance in question will have decayed. Many radioactive substances decay from one nuclide into a final, stable decay product (or "daughter") through a series of steps known as a decay chain. In this case, usually the half-life reported is the dominant (longest) for the entire chain, rather than just one step in the chain. Nuclides useful for radiometric dating have half-lives ranging from a few thousand to a few billion years.

In most cases, the half-life of a nuclide depends solely on its nuclear properties; it is not affected by temperature, chemical environment, magnetic and electric fields, or any other external factors.[1] The half-life of any nuclide is also believed to be constant through time. Although decay can be accelerated by radioactive bombardment, such bombardment tends to leave evidence of its occurrence. Therefore, in any material containing a radioactive nuclide, the proportion of the original nuclide to its decay product(s) changes in a predictable way as the original nuclide decays. This predictability allows the relative abundances of related nuclides to be used as a clock that measures the time from the incorporation of the original nuclide(s) into a material to the present.

The processes that form specific materials are often conveniently selective as to what elements they incorporate during their formation. In the ideal case, the material will incorporate a parent nuclide and reject the daughter nuclide. In this case, the only daughter nuclides to be found through examination of a sample must have been created since the sample was formed. When a material incorporates both the parent and daughter nuclides at the time of formation, it may be necessary to assume that the initial proportions of a radioactive substance and its daughter are known. The daughter product should not be a small-molecule gas that can leak out of the material, and it must itself have a long enough half-life that it will be present in significant amounts. In addition, the initial element and the decay product should not be produced or depleted in significant amounts by other reactions. The procedures used to isolate and analyze the reaction products must be straightforward and reliable.

If a material that selectively rejects the daughter nuclide is heated, any daughter nuclides that have been accumulated over time will be lost through diffusion, setting the isotopic "clock" to zero. The temperature at which this happens is known as the "blocking temperature" and is specific to a particular material.

In contrast to the most simple radiometric dating techniques, isochron dating, which can be used for many isotopic decay sequences (e.g. rubidium-strontium decay sequence), does not require knowledge of the initial proportions. Also the argon-argon dating technique can be used for the potassium-argon sequence to ensure that no initial 40Ar was present.

#### The age equation

Considering that radioactive parent elements decay to stable daughter elements [2], the mathematical expression that relates radioactive decay to geologic time, called the age equation, is [3]:

$t = \frac{1}{\lambda} {\ln \left(1+\frac{D}{P}\right)}$
where
$t =$age of the sample
$D =$number of atoms of the daughter isotope in the sample
$P =$number of atoms of the parent isotope in the sample
$\lambda =$decay constant of the parent isotope
$\ln =$natural logarithm

The decay constant (or rate of decay[4]) is the fraction of a number of atoms of a radioactive nuclide that disintegrates in a unit of time. The decay constant is inversely proportional to the radioactive half-life.[5]

and $t_{1/2} =$ half-life of the parent isotope, which can be obtained from tables such as the one given in [1]:

### Limitation of techniques

Although radiometric dating is accurate in principle, the precision is very dependent on the care with which the procedure is performed. The possible confounding effects of initial contamination of parent and daughter isotopes have to be considered, as do the effects of any loss or gain of such isotopes since the sample was created. Additionally, measurement in a mass spectrometer is subject to isotopic interference of other nuclides with the same mass number. Corrections may have to be performed by measuring isotopic ratios of elements which interfere with the target isotope.

Mass spectrometers are liable to interferences and inaccuracies. Primary amongst these is the quality of the vacuum. Poor vacuum permits gaseous atoms to intercept ionised atoms which are meant to be measured. The resolution of the receptor is also a factor, but modern equipment is greatly improved on previous editions.

Precision is enhanced if measurements are taken on different samples taken from the same rock body but at different locations. Alternatively, if several different minerals can be dated from the same sample and are assumed to be formed by the same event and were in equilibrium with the reservoir when they formed, they should form an isochron. Finally, correlation between different isotopic dating methods may be required to confirm the age of a sample.

The precision of a method of dating depends in part on the half-life of the radioactive isotope involved. For instance, carbon-14 has a half-life of less than 6000 years. After an organism has been dead for 60,000 years, so little carbon-14 is left in it that accurate dating becomes impossible. On the other hand, the concentration of carbon-14 falls off so steeply that the age of relatively young remains can be determined precisely to within a few decades. The isotope used in uranium-thorium dating has a longer half-life, but other factors make it more accurate than radiocarbon dating.

## Modern dating techniques

Radiometric dating can be performed on samples as small as a billionth of a gram using a mass spectrometer. The mass spectrometer was invented in the 1940s and began to be used in radiometric dating in the 1950s. The mass spectrometer operates by generating a beam of ionized atoms from the sample under test. The ions then travel through a magnetic field, which diverts them into different sampling sensors, known as "Faraday cups", depending on their mass and level of ionization. On impact in the cups, the ions set up a very weak current that can be measured to determine the rate of impacts and the relative concentrations of different atoms in the beams.

The uranium-lead radiometric dating scheme is one of the oldest available, as well as one of the most highly respected. It has been refined to the point that the error in dates of rocks about three billion years old is no more than two million years.

Uranium-lead dating is usually performed on the mineral "zircon" (ZrSiO4), though it can be used on other materials. Zircon incorporates uranium atoms into its crystalline structure as substitutes for zirconium, but strongly rejects lead. It has a very high blocking temperature, is resistant to mechanical weathering and is very chemically inert. Zircon also forms multiple crystal layers during metamorphic events, which each may record an isotopic age of the event. In situ micro-beam analysis can be achieved via laser ICP-MS orSIMS tecniques [6] .

One of its great advantages is that any sample provides two clocks, one based on uranium-235's decay to lead-207 with a half-life of about 700 million years, and one based on uranium-238's decay to lead-206 with a half-life of about 4.5 billion years, providing a built-in crosscheck that allows accurate determination of the age of the sample even if some of the lead has been lost.

Two other radiometric techniques are used for long-term dating. Potassium-argon dating involves electron capture or positron decay of potassium-40 to argon-40. Potassium-40 has a half-life of 1.3 billion years, and so this method is applicable to the oldest rocks. Radioactive potassium-40 is common in micas, feldspars, and hornblendes, though the blocking temperature is fairly low in these materials, about 125 °C (mica) to 450 °C (hornblende).

Rubidium-strontium dating is based on the beta decay of rubidium-87 to strontium-87, with a half-life of 50 billion years. This scheme is used to date old igneous and metamorphic rocks, and has also been used to date lunar samples. Blocking temperatures are so high that they are not a concern. Rubidium-strontium dating is not as precise as the uranium-lead method, with errors of 30 to 50 million years for a 3-billion-year-old sample.

## Short-range dating techniques

There are a number of other dating techniques that have short ranges and are so used for historical or archaeological studies. One of the best-known is the carbon-14 (C14) radiometric technique.

Carbon-14 is a radioactive isotope of carbon, with a half-life of 5,730 years (very short compared with the above). In other radiometric dating methods, the heavy parent isotopes were synthesized in the explosions of massive stars that scattered materials through the Galaxy, to be formed into planets and other stars. The parent isotopes have been decaying since that time, and so any parent isotope with a short half-life should be extinct by now.

Carbon-14 is an exception. It is continuously created through collisions of neutrons generated by cosmic rays with nitrogen in the upper atmosphere. The carbon-14 ends up as a trace component in atmospheric carbon dioxide (CO2).

An organism acquires carbon from carbon dioxide during its lifetime. Plants acquire it through photosynthesis, and animals acquire it from consumption of plants and other animals. When an organism dies, it ceases to intake new carbon-14 and the existing isotope decays with a characteristic half-life (5730 years). The proportion of carbon-14 left when the remains of the organism are examined provides an indication of the time lapsed since its death. The carbon-14 dating limit lies around 58,000 to 62,000 years [2].

The rate of creation of carbon-14 appears to be roughly constant, as cross-checks of carbon-14 dating with other dating methods show it gives consistent results. However, local eruptions of volcanoes or other events that give off large amounts of carbon dioxide can reduce local concentrations of carbon-14 and give inaccurate dates. The releases of carbon dioxide into the biosphere as a consequence of industrialization have also depressed the proportion of carbon-14 by a few percent; conversely, the amount of carbon-14 was increased by above-ground nuclear bomb tests that were conducted into the early 1960s. Also, an increase in the solar wind or the earth's magnetic field above the current value would depress the amount of carbon-14 created in the atmosphere. These effects are corrected for by the calibration of the radiocarbon dating scale. See the article on radiocarbon dating.

Another relatively short-range dating technique is based on the decay of uranium-238 into thorium-230, a substance with a half-life of about 80,000 years. It is accompanied by a sister process, in which uranium-235 decays into protactinium-231, which has a half-life of 34,300 years.

While uranium is water-soluble, thorium and protactinium are not, and so they are selectively precipitated into ocean-floor sediments, from which their ratios are measured. The scheme has a range of several hundred thousand years.

Natural sources of radiation in the environment knock loose electrons in, say, a piece of pottery, and these electrons accumulate in defects in the material's crystal lattice structure. When the sample is heated, at a certain temperature it will glow from the emission of electrons released from the defects, and this glow can be used to estimate the age of the sample to a threshold of a few hundred thousand years. This is termed thermoluminescence.

Finally, fission track dating involves inspection of a polished slice of a material to determine the density of "track" markings left in it by the spontaneous fission of uranium-238 impurities.

The uranium content of the sample has to be known, but that can be determined by placing a plastic film over the polished slice of the material, and bombarding it with slow neutrons. This causes induced fission of U-235, as opposed to the spontaneous fission of U-238. The fission tracks produced by this process are recorded in the plastic film. The uranium content of the material can then be calculated from the number of tracks and the neutron flux.

This scheme has application over a wide range of geologic dates. For dates up to a few million years micas, tektites (glass fragments from volcanic eruptions), and meteorites are best used. Older materials can be dated using zircon, apatite, titanite, epidote and garnet which have a variable amount of uranium content. Because the fission tracks are healed by temperatures over about 200 °C the technique has limitations as well as benefits. The technique has potential applications for detailing the thermal history of a deposit.

Large amounts of otherwise rare Cl-36 were produced by irradiation of seawater during atmospheric detonations of nuclear weapons between 1952 and 1958. The residence time of Cl-36 in the atmosphere is about 1 week. Thus, as an event marker of 1950s water in soil and ground water, Cl-36 is also useful for dating waters less than 50 years before the present. Cl-36 has seen use in other areas of the geological sciences, including dating ice and sediments.

## Dating with shortlived extinct radionuclides

At the beginning of the solar system there were several relatively shortlived radionuclides like 26Al, 60Fe, 53Mn, and 129I present within the solar nebula. These radionuclides—possibly produced by the explosion of a supernova—are extinct today but their decay products can be detected in very old material such as meteorites. Measuring the decay products of extinct radionuclides with a mass spectrometer and using isochronplots it is possible to determine relative ages between different events in the early history of the solar system. Dating methods based on extinct radionuclides can also be calibrated with the U-Pb method to give absolute ages.