## Radiometric dating

Substituting this in equation 6 gives. If one chooses to use P to designate the parent atom, the expression assumes its familiar form:. This pair of equations states rigorously what might be assumed from intuition , that minerals formed at successively longer times in the past would have progressively higher daughter-to-parent ratios. This follows because, as each parent atom loses its identity with time, it reappears as a daughter atom. Equation 8 documents the simplicity of direct isotopic dating. The time of decay is proportional to the natural logarithm represented by ln of the ratio of D to P.

In short, one need only measure the ratio of the number of radioactive parent and daughter atoms present, and the time elapsed since the mineral or rock formed can be calculated, provided of course that the decay rate is known. Likewise, the conditions that must be met to make the calculated age precise and meaningful are in themselves simple:. The rock or mineral must have remained closed to the addition or escape of parent and daughter atoms since the time that the rock or mineral system formed.

It must be possible to correct for other atoms identical to daughter atoms already present when the rock or mineral formed.

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The measurement of the daughter-to-parent ratio must be accurate because uncertainty in this ratio contributes directly to uncertainty in the age. Different schemes have been developed to deal with the critical assumptions stated above. In uranium-lead dating , minerals virtually free of initial lead can be isolated and corrections made for the trivial amounts present.

In whole-rock isochron methods that make use of the rubidium- strontium or samarium - neodymium decay schemes, a series of rocks or minerals are chosen that can be assumed to have the same age and identical abundances of their initial isotopic ratios. The results are then tested for the internal consistency that can validate the assumptions. In all cases, it is the obligation of the investigator making the determinations to include enough tests to indicate that the absolute age quoted is valid within the limits stated.

In other words, it is the obligation of geochronologists to try to prove themselves wrong by including a series of cross-checks in their measurements before they publish a result. Such checks include dating a series of ancient units with closely spaced but known relative ages and replicate analysis of different parts of the same rock body with samples collected at widely spaced localities.

The importance of internal checks as well as interlaboratory comparisons becomes all the more apparent when one realizes that geochronology laboratories are limited in number. Because of the expensive equipment necessary and the combination of geologic, chemical, and laboratory skills required, geochronology is usually carried out by teams of experts.

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Most geologists must rely on geochronologists for their results. In turn, the geochronologist relies on the geologist for relative ages. In order for a radioactive parent-daughter pair to be useful for dating, many criteria must be met. This section examines these criteria and explores the ways in which the reliability of the ages measured can be assessed. Because geologic materials are diverse in their origin and chemical content and datable elements are unequally distributed, each method has its strengths and weaknesses.

Of these, only the radioisotopes with extremely long half-lives remain. It should be mentioned in passing that some of the radioisotopes present early in the history of the solar system and now completely extinct have been recorded in meteorites in the form of the elevated abundances of their daughter isotopes.

Analysis of such meteorites makes it possible to estimate the time that elapsed between element creation and meteorite formation. Natural elements that are still radioactive today produce daughter products at a very slow rate; hence, it is easy to date very old minerals but difficult to obtain the age of those formed in the recent geologic past. This follows from the fact that the amount of daughter isotopes present is so small that it is difficult to measure. The difficulty can be overcome to some degree by achieving lower background contamination, by improving instrument sensitivity, and by finding minerals with abundant parent isotopes.

Geologic events of the not-too-distant past are more easily dated by using recently formed radioisotopes with short half-lives that produce more daughter products per unit time. Two sources of such isotopes exist. In one case, intermediate isotopes in the uranium or thorium decay chain can become isolated in certain minerals because of differences in chemical properties and, once fixed, can decay to new isotopes, providing a measure of the time elapsed since they were isolated. To understand this, one needs to know that though uranium U does indeed decay to lead Pb , it is not a one-step process.

In fact, this is a multistep process involving the expulsion of eight alpha particles and six beta particles , along with a considerable amount of energy. There exists a series of different elements, each of them in a steady state where they form at the same rate as they disintegrate. The number present is proportional to their decay rate, with long-lived members being more abundant. Because all these isotopes have relatively short half-lives, none remains since the formation of the elements, but instead they are continuously provided by the decay of the long-lived parent.

This type of dating, known as disequilibrium dating, will be explored below in the section Uranium-series disequilibrium dating. The amounts produced, although small, provide insight into many near-surface processes in the geologic past. The most widely used radioactive cosmogenic isotope is carbon of mass 14 14 C , which provides a method of dating events that have occurred over roughly the past 60, years.

### Principles of isotopic dating

This time spans the historic record and a significant part of the prehistoric record of humans. We welcome suggested improvements to any of our articles. You can make it easier for us to review and, hopefully, publish your contribution by keeping a few points in mind. Your contribution may be further edited by our staff, and its publication is subject to our final approval.

Unfortunately, our editorial approach may not be able to accommodate all contributions. Our editors will review what you've submitted, and if it meets our criteria, we'll add it to the article. Please note that our editors may make some formatting changes or correct spelling or grammatical errors, and may also contact you if any clarifications are needed. Principles of isotopic dating All absolute isotopic ages are based on radioactive decay , a process whereby a specific atom or isotope is converted into another specific atom or isotope at a constant and known rate.

The recognition that the rate of decay of any radioactive parent atom is proportional to the number of atoms N of the parent remaining at any time gives rise to the following expression: With t made explicit and half-life introduced, equation 4 is converted to the following form, in which the symbols have the same meaning: Since the initial number of parent atoms present at time zero N 0 must be the sum of the parent atoms remaining N and the daughter atoms present D , one can write: Substituting this in equation 6 gives If one chooses to use P to designate the parent atom, the expression assumes its familiar form: Likewise, the conditions that must be met to make the calculated age precise and meaningful are in themselves simple: The decay constant must be known.

Olson Thomas Edvard Krogh Evaluation and presentation schemes in dating Origin of radioactive elements used In order for a radioactive parent-daughter pair to be useful for dating, many criteria must be met. Principal cosmogenic and uranium-thorium series radioisotopes Source: Major decay schemes for isotopic dating parent isotope daughter isotope half-life in years applicable materials U Pb 4. Page 3 of 8. Next page The isochron method. Learn More in these related Britannica articles: The possible confounding effects of 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.

It is therefore essential to have as much information as possible about the material being dated and to check for possible signs of alteration. 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. This can reduce the problem of contamination. In uraniumâ€”lead dating , the concordia diagram is used which also decreases the problem of nuclide loss.

Finally, correlation between different isotopic dating methods may be required to confirm the age of a sample. For example, the age of the Amitsoq gneisses from western Greenland was determined to be 3. Accurate radiometric dating generally requires that the parent has a long enough half-life that it will be present in significant amounts at the time of measurement except as described below under "Dating with short-lived extinct radionuclides" , the half-life of the parent is accurately known, and enough of the daughter product is produced to be accurately measured and distinguished from the initial amount of the daughter present in the material.

The procedures used to isolate and analyze the parent and daughter nuclides must be precise and accurate. This normally involves isotope-ratio mass spectrometry. The precision of a dating method depends in part on the half-life of the radioactive isotope involved. For instance, carbon has a half-life of 5, years. After an organism has been dead for 60, years, so little carbon is left that accurate dating cannot be established.

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On the other hand, the concentration of carbon falls off so steeply that the age of relatively young remains can be determined precisely to within a few decades. 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 closure temperature or blocking temperature and is specific to a particular material and isotopic system.

These temperatures are experimentally determined in the lab by artificially resetting sample minerals using a high-temperature furnace. As the mineral cools, the crystal structure begins to form and diffusion of isotopes is less easy. At a certain temperature, the crystal structure has formed sufficiently to prevent diffusion of isotopes. This temperature is what is known as closure temperature and represents the temperature below which the mineral is a closed system to isotopes.

Thus an igneous or metamorphic rock or melt, which is slowly cooling, does not begin to exhibit measurable radioactive decay until it cools below the closure temperature. The age that can be calculated by radiometric dating is thus the time at which the rock or mineral cooled to closure temperature.

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This field is known as thermochronology or thermochronometry. The mathematical expression that relates radioactive decay to geologic time is [12] [15]. The equation is most conveniently expressed in terms of the measured quantity N t rather than the constant initial value N o. The above equation makes use of information on the composition of parent and daughter isotopes at the time the material being tested cooled below its closure temperature. This is well-established for most isotopic systems. Plotting an isochron is used to solve the age equation graphically and calculate the age of the sample and the original composition.

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## Radiometric dating - Wikipedia

Radiometric dating has been carried out since when it was invented by Ernest Rutherford as a method by which one might determine the age of the Earth. In the century since then the techniques have been greatly improved and expanded. The mass spectrometer was invented in the s and began to be used in radiometric dating in the s.