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{{Short description|Technique used to date materials such as rocks or carbon}}
{{Use dmy dates|date=August 2019}}
'''Radiometric dating''', '''radioactive dating''' or '''radioisotope dating''' is a technique which is used to [[Chronological dating|date]] materials such as [[Rock (geology)|rocks]] or [[carbon]], in which trace radioactive [[impurity|impurities]] were selectively incorporated when they were formed. The method compares the abundance of a naturally occurring [[Radionuclide|radioactive isotope]] within the material to the abundance of its [[Radioactive decay|decay]] products, which form at a known constant rate of decay.<ref>{{GoldBookRef|title=radioactive dating|file=R05082}}</ref> Radiometric dating of minerals and rocks was pioneered by [[Ernest Rutherford]] (1906) and [[Bertram Boltwood]] (1907).<ref name="Rutherford1906">{{cite book | url=https://archive.org/details/radioactivetrans00ruth/page/188/mode/2up?q=500+million | title=Radioactive Transformations | publisher=Archibald Constable and Co. Ltd | last=Rutherford | first=E. | author-link=Ernest Rutherford | year=1906 | location=London | page=186}}</ref><ref>{{ cite journal | author = Boltwood, Bertram | year = 1907 | title = The Ultimate Disintegration Products of the Radio-active Elements. Part II. The disintegration products of uranium | journal = American Journal of Science | series = 4 | volume = 23 | issue = 134 | pages = 77–88 | doi=10.2475/ajs.s4-23.134.78| bibcode = 1907AmJS...23...78B | s2cid = 131688682 | url = https://zenodo.org/record/1450152 }}</ref> Radiometric dating is now the principal source of information about the [[Absolute dating|absolute age]] of rocks and other [[Geology|geological features]], including the age of [[Paleontology|fossilized life forms]] or the [[age of Earth]] itself, and can also be used to date a wide range of natural and [[Artifact (archaeology)|man-made materials]].

Together with [[stratigraphy|stratigraphic principles]], radiometric dating methods are used in [[geochronology]] to establish the [[geologic time scale]].<ref>McRae, A. 1998. ''Radiometric Dating and the Geological Time Scale: Circular Reasoning or Reliable Tools?'' [http://www.talkorigins.org/faqs/dating.html Radiometric Dating and the Geological Time Scale], [[TalkOrigins Archive]]</ref> Among the best-known techniques are [[radiocarbon dating]], [[potassium–argon dating]] and [[uranium–lead dating]]. By allowing the establishment of geological timescales, it provides a significant source of information about the ages of [[fossil]]s and the deduced rates of [[evolution]]ary change. Radiometric dating is also used to date [[archaeology|archaeological]] materials, including ancient artifacts.

Different methods of radiometric dating vary in the timescale over which they are accurate and the materials to which they can be applied.

==Fundamentals==

===Radioactive decay===
[[File:Thorium decay chain from lead-212 to lead-208.svg|thumb|right|upright=1.35|Example of a radioactive [[decay chain]] from lead-212 (<sup>212</sup>Pb) to lead-208 (<sup>208</sup>Pb) . Each parent nuclide spontaneously decays into a daughter nuclide (the [[decay product]]) via an [[alpha decay|α decay]] or a [[beta decay|β<sup>−</sup> decay]]. The final decay product, lead-208 (<sup>208</sup>Pb), is stable and can no longer undergo spontaneous radioactive decay.]]
All ordinary [[matter]] is made up of combinations of [[chemical element]]s, each with its own [[atomic number]], indicating the number of [[proton]]s in the [[atomic nucleus]]. Additionally, elements may exist in different [[isotope]]s, with each isotope of an element differing in the number of [[neutron]]s in the nucleus. A particular isotope of a particular element is called a [[nuclide]]. Some nuclides are inherently unstable. That is, at some point in time, an atom of such a nuclide will undergo [[radioactive decay]] and spontaneously transform into a different nuclide. This transformation may be accomplished in a number of different ways, including [[alpha decay]] (emission of [[alpha particle]]s) and [[beta decay]] ([[electron]] emission, [[positron]] emission, or [[electron capture]]). Another possibility is [[spontaneous fission]] into two or more nuclides.<ref>{{cite web |title=Spontaneous fission |url=https://www.arpansa.gov.au/understanding-radiation/what-is-radiation/ionising-radiation/radiation-decay |website=Australian Radiation Protection and Nuclear Safety Agency |access-date=29 January 2025}}</ref>

While the moment in time at which a particular nucleus decays is unpredictable, a collection of atoms of a radioactive nuclide decays [[exponential decay|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 nuclide in question will have decayed into a "daughter" nuclide or [[decay product]]. In many cases, the daughter nuclide itself is radioactive, resulting in a [[decay chain]], eventually ending with the formation of a stable (nonradioactive) daughter nuclide; each step in such a chain is characterized by a distinct half-life. In these cases, usually the half-life of interest in radiometric dating is the longest one in the chain, which is the rate-limiting factor in the ultimate transformation of the radioactive nuclide into its stable daughter. Isotopic systems that have been exploited for radiometric dating have half-lives ranging from only about 10 years (e.g., [[tritium]]) to over 100 billion years (e.g., [[samarium-147]]).<ref name="Bernard-Griffiths1989">{{cite book|last1=Bernard-Griffiths|first1=J.|last2=Groan|first2=G.|editor1-last=Roth|editor1-first=Etienne|editor2-last=Poty|editor2-first=Bernard|title=Nuclear Methods of Dating|date=1989|publisher=Springer Netherlands|isbn=978-0-7923-0188-2|pages=53–72|chapter=The samarium–neodymium method}}</ref>

For most radioactive nuclides, the half-life depends solely on nuclear properties and is essentially constant.<ref>{{cite journal|last1=Pommé|first1=S.|last2=Stroh|first2=H.|last3=Altzitzoglou|first3=T.|last4=Paepen|first4=J.|last5=Van Ammel|first5=R.|last6=Kossert|first6=K.|last7=Nähle|first7=O.|last8=Keightley|first8=J. D.|last9=Ferreira|first9=K. M.|last10=Verheyen|first10=L.|last11=Bruggeman|first11=M.|date=2018-04-01|title=Is decay constant?|journal=Applied Radiation and Isotopes|series=ICRM 2017 Proceedings of the 21st International Conference on Radionuclide Metrology and its Applications|volume=134|pages=6–12|doi=10.1016/j.apradiso.2017.09.002|pmid=28947247|doi-access=free|bibcode=2018AppRI.134....6P }}</ref> This is known because decay constants measured by different techniques give consistent values within analytical errors and the ages of the same materials are consistent from one method to another. It is not affected by external factors such as [[temperature]], [[pressure]], chemical environment, or presence of a [[magnetic field|magnetic]] or [[electric field]].<ref>{{cite journal|doi=10.1146/annurev.ns.22.120172.001121|doi-access=free |title=Perturbation of Nuclear Decay Rates |year=1972 |author=Emery, G T |journal=[[Annual Review of Nuclear Science]] |volume=22|issue=1 |pages=165–202|bibcode = 1972ARNPS..22..165E }}</ref><ref>{{cite journal|doi=10.1038/264340a0 |title=Direct test of the constancy of fundamental nuclear constants |year=1976 |author=Shlyakhter, A. I. |journal=Nature |volume=264|issue=5584 |page=340 |bibcode=1976Natur.264..340S|s2cid=4252035 |doi-access=free }}</ref><ref>Johnson, B. (1993). ''How to Change Nuclear Decay Rates'' [http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/decay_rates.html Usenet Physics FAQ]</ref> The only exceptions are nuclides that decay by the process of electron capture, such as [[beryllium-7]], [[strontium-85]], and [[zirconium-89]], whose decay rate may be affected by local electron density. For all other nuclides, the proportion of the original nuclide to its decay products changes in a predictable way as the original nuclide decays over time.{{Citation needed|date=October 2022}} This predictability allows the relative abundances of related nuclides to be used as a [[clock]] to measure the time from the incorporation of the original nuclides into a material to the present.

===Decay constant determination===
{{See also|Radioactive decay law}}
The radioactive decay constant, the probability that an atom will decay per year, is the solid foundation of the common measurement of radioactivity. The accuracy and precision of the determination of an age (and a nuclide's half-life) depends on the accuracy and precision of the decay constant measurement.<ref>{{cite journal|last1=Begemann|first1=F.|last2=Ludwig|first2=K.R.|last3=Lugmair|first3=G.W.|last4=Min|first4=K.|last5=Nyquist|first5=L.E.|last6=Patchett|first6=P.J.|last7=Renne|first7=P.R.|last8=Shih|first8=C.-Y.|last9=Villa|first9=I.M.|last10=Walker|first10=R.J.|date=January 2001|title=Call for an improved set of decay constants for geochronological use|journal=Geochimica et Cosmochimica Acta|volume=65|issue=1|pages=111–121|doi=10.1016/s0016-7037(00)00512-3|bibcode=2001GeCoA..65..111B}}</ref> The in-growth method is one way of measuring the decay constant of a system, which involves accumulating daughter nuclides. Unfortunately for nuclides with high decay constants (which are useful for dating very old samples), long periods of time (decades) are required to accumulate enough decay products in a single sample to accurately measure them. A faster method involves using particle counters to determine alpha, beta or gamma activity, and then dividing that by the number of radioactive nuclides. However, it is challenging and expensive to accurately determine the number of radioactive nuclides. Alternatively, decay constants can be determined by comparing isotope data for rocks of known age. This method requires at least one of the isotope systems to be very precisely calibrated, such as the [[lead–lead dating|Pb–Pb system]].{{Citation needed|date=October 2022}}

===Accuracy of radiometric dating===
[[File:Thermal ionization mass spectrometer.jpg|thumb|[[Thermal ionization mass spectrometer]] used in radiometric dating.]]
The basic equation of radiometric dating requires that neither the parent nuclide nor the daughter product can enter or leave the material after its formation. 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 [[Metasomatism|alteration]].<ref>{{cite journal|doi=10.1016/0012-821X(96)00132-X |title=3-D, <sup>40</sup>Ar-<sup>39</sup>Ar geochronology in the Paraná continental flood basalt province |year=1996 |journal=Earth and Planetary Science Letters |volume=143|issue=1–4 |pages=95–109 |bibcode=1996E&PSL.143...95S|last1=Stewart |first1=Kathy |last2=Turner |first2=Simon |last3=Kelley |first3=Simon |last4=Hawkesworth |first4=Chris |last5=Kirstein |first5=Linda |last6=Mantovani |first6=Marta }}</ref> Precision is enhanced if measurements are taken on multiple samples from different locations of the rock body. 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 dating|isochron]]. This can reduce the problem of [[contamination]]. In [[uranium–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 [[Geology of Greenland|Amitsoq gneisses from western Greenland]] was determined to be 3.60 ± 0.05 [[Gigaannum|Ga]] (billion years ago) using uranium–lead dating and 3.56 ± 0.10 Ga (billion years ago) using lead–lead dating, results that are consistent with each other.<ref>{{cite book|last1=Dalrymple|first1=G. Brent|title=The age of the earth|date=1994|publisher=Stanford Univ. Press|location=Stanford, Calif.|isbn=978-0-8047-2331-2}}</ref>{{rp|142–143}}

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]].<ref>{{cite book|last1=Dickin|first1=Alan P.|title=Radiogenic isotope geology|date=2008|publisher=Cambridge Univ. Press|location=Cambridge|isbn=978-0-521-53017-0|pages=15–49|edition=2nd}}</ref>

The precision of a dating method depends in part on the half-life of the radioactive isotope involved. For instance, carbon-14 has a half-life of 5,730 years. After an organism has been dead for 60,000 years, so little carbon-14 is left that accurate dating cannot be established. 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.<ref>{{cite journal|year=2004
|title=INTCAL04 Terrestrial Radiocarbon Age Calibration, 0–26 Cal Kyr BP
|journal=Radiocarbon
|volume=46
|issue=3
|pages=1029–1058
|doi=10.1017/S0033822200032999
|doi-access=free
|bibcode=2004Radcb..46.1029.
|hdl=10289/3690
|hdl-access=free
}}</ref>

===Closure temperature===
{{Main|Closure temperature}}

The closure temperature or blocking temperature represents the temperature below which the mineral is a closed system for the studied isotopes. If a material that selectively rejects the daughter nuclide is heated above this temperature, any daughter nuclides that have been accumulated over time will be lost through [[diffusion]], resetting the isotopic "clock" to zero. 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. 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.<ref name=Faure>{{cite book|first=Gunter |last=Faure |title=Principles and applications of geochemistry: a comprehensive textbook for geology students |publisher=[[Prentice Hall]] |location=[[Englewood Cliffs, New Jersey]] |year=1998 |edition=2nd |isbn=978-0-02-336450-1 |oclc=37783103}}{{Page needed|date=September 2010}}</ref><ref name=Rollinson>{{cite book|first=Hugh R. |last=Rollinson |title=Using geochemical data: evaluation, presentation, interpretation |publisher=[[Longman]] |location=[[Harlow]] |year=1993 |isbn=978-0-582-06701-1 |oclc=27937350}}{{Page needed|date=September 2010}}</ref> This temperature varies for every mineral and isotopic system, so a system can be [[Closed system|closed]] for one mineral but [[Open system (thermodynamics)|open]] for another. Dating of different minerals and/or isotope systems (with differing closure temperatures) within the same rock can therefore enable the tracking of the thermal history of the rock in question with time, and thus the history of metamorphic events may become known in detail. These temperatures are experimentally determined in the lab by [[Petrology#Branches|artificially resetting sample minerals]] using a high-temperature furnace. This field is known as [[thermochronology]] or thermochronometry.{{Citation needed|date=October 2022}}

===The age equation===
[[File:Figure 2 High res Debaille et al (2017) The role of phosphates for the Lu–Hf chronology of meteorites.gif|class=skin-invert-image|thumb|[[Samarium–neodymium dating|Lu-Hf]] isochrons plotted of meteorite samples. The age is calculated from the slope of the isochron (line) and the original composition from the intercept of the isochron with the y-axis.]]
The mathematical expression that relates radioactive decay to geologic time is<ref name=Faure/><ref name="Cornell">{{cite web|first=W. M. |last=White |year=2003 |title=Basics of Radioactive Isotope Geochemistry |publisher=[[Cornell University]] |url=https://www.geo.cornell.edu/geology/classes/Geo656/656notes03/656%2003Lecture04.pdf}}</ref>

{{block indent|em=1.2|{{math|1=''D''* = ''D''<sub>0</sub> + ''N''(''t'') (''e''<sup>''λt''</sup> − 1)}}}}

where
* {{mvar|t}} is age of the sample,
* {{math|''D''*}} is number of atoms of the radiogenic daughter isotope in the sample,
* {{math|''D''<sub>0</sub>}} is number of atoms of the daughter isotope in the original or initial composition,
* {{math|''N''(''t'')}} is number of atoms of the parent isotope in the sample at time {{var|t}} (the present), given by {{math|1=''N''(''t'') = ''N''<sub>0</sub>''e''<sup>−''λt''</sup>}}, and
* {{mvar|λ}} is the [[decay constant]] of the parent isotope, equal to the inverse of the radioactive [[half-life]] of the parent isotope<ref name=usgs>{{cite web| url=https://pubs.usgs.gov/gip/geotime/radiometric.html |title=Geologic Time: Radiometric Time Scale |publisher=[[United States Geological Survey]] |date=16 June 2001}}</ref> times the natural logarithm of 2.

The equation is most conveniently expressed in terms of the measured quantity ''N''(''t'') rather than the constant initial value ''N<sub>o</sub>''.{{Citation needed|date=October 2022}}

To calculate the age, it is assumed that the system is [[Closed system|closed]] (neither parent nor daughter isotopes have been lost from system), ''D''<sub>0</sub> either must be negligible or can be accurately estimated, ''λ'' is known to high precision, and one has accurate and precise measurements of D* and ''N''(''t'').{{Citation needed|date=October 2022}}

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.<ref name="Rollinson" /><ref>{{cite journal|doi=10.1016/0012-821X(75)90088-6 |title=Approximation of terrestrial lead isotope evolution by a two-stage model |date=June 1975 |first=J. S. |last=Stacey |author2=J. D. Kramers |journal=Earth and Planetary Science Letters |volume=26 |issue=2 |pages=207–221 |bibcode=1975E&PSL..26..207S}}</ref> However, construction of an isochron does not require information on the original compositions, using merely the present ratios of the parent and daughter isotopes to a standard isotope. An [[Isochron dating|isochron plot]] is used to solve the age equation graphically and calculate the age of the sample and the original composition.{{Citation needed|date=October 2022}}

==Modern dating methods==
Radiometric dating has been carried out since 1905 when it was [[Age of the Earth#Invention of radiometric dating|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.<ref name=usgs/> Dating can now be performed on samples as small as a nanogram using a [[mass spectrometer]]. The mass spectrometer was invented in the 1940s and began to be used in radiometric dating in the 1950s. It operates by generating a beam of [[ion|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 cup]]s," 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.{{Citation needed|date=October 2022}}

===Uranium–lead dating method===
{{Main|Uranium–lead dating}}
[[File:Pfunze belt concordia.png|class=skin-invert-image|thumb|upright=1.8|A concordia diagram as used in [[uranium–lead dating]], with data from the [[Pfunze Belt]], [[Zimbabwe]].<ref>{{cite journal|doi=10.1016/S0899-5362(01)90021-1 |title=U–Pb zircon ages from a craton-margin archaean orogenic belt in northern Zimbabwe |year=2001 |first=M. L. |last=Vinyu |author2=R. E. Hanson |author3=M. W. Martin |author4=S. A. Bowring |author5=H. A. Jelsma |author6=P. H. G. M. Dirks |journal=[[Journal of African Earth Sciences]] |volume=32|issue=1 |pages=103–114|bibcode = 2001JAfES..32..103V }}</ref> All the samples show loss of lead isotopes, but the intercept of the errorchron (straight line through the sample points) and the concordia (curve) shows the correct age of the rock.<ref name=Rollinson/>]]

[[Uranium–lead radiometric dating]] involves using uranium-235 or uranium-238 to date a substance's absolute age. This scheme has been refined to the point that the error margin in dates of rocks can be as low as less than two million years in two-and-a-half billion years.<ref name="Oberthuer">{{cite journal|year=2002|title=Precise U–Pb mineral ages, Rb–Sr and Sm–Nd systematics for the Great Dyke, Zimbabwe—constraints on late Archean events in the Zimbabwe craton and Limpopo belt|journal=Precambrian Research|volume=113|issue=3–4|pages=293–306|bibcode=2002PreR..113..293O|doi=10.1016/S0301-9268(01)00215-7|last1=Oberthür |first1=Thomas |last2=Davis |first2=Donald W. |last3=Blenkinsop |first3=Thomas G. |last4=Höhndorf |first4=Axel }}</ref><ref>{{cite journal|doi=10.1016/j.jafrearsci.2004.12.003 |title=The age and petrology of the Chimbadzi Hill Intrusion, NW Zimbabwe: first evidence for early Paleoproterozoic magmatism in Zimbabwe |year=2004 |first=Tawanda D. |last=Manyeruke |author2=Thomas G. Blenkinsop |author3=Peter Buchholz |author4=David Love |author5=Thomas Oberthür |author6=Ulrich K. Vetter |author7=Donald W. Davis |journal=Journal of African Earth Sciences |volume=40|issue=5 |pages=281–292|bibcode = 2004JAfES..40..281M }}</ref> An error margin of 2–5% has been achieved on younger [[Mesozoic]] rocks.<ref>{{cite journal|doi=10.1016/S0009-2541(00)00394-6 |title=Precise <sup>206</sup>Pb/<sup>238</sup>U age determination on zircons by laser ablation microprobe-inductively coupled plasma-mass spectrometry using continuous linear ablation |year=2001 |first1=Xian-hua |last1=Li |first2=Xi-rong|last2=Liang|first3=Min|last3=Sun|first4=Hong|last4=Guan|first5=J. G.|last5=Malpas |journal=Chemical Geology |volume=175|issue=3–4 |pages=209–219|bibcode=2001ChGeo.175..209L}}</ref>

Uranium–lead dating is often performed on the [[mineral]] [[zircon]] (ZrSiO<sub>4</sub>), though it can be used on other materials, such as [[baddeleyite]] and [[monazite]] (see: [[monazite geochronology]]).<ref>{{cite journal|doi=10.2113/104.1.13 |title=SHRIMP baddeleyite and zircon ages for an Umkondo dolerite sill, Nyanga Mountains, Eastern Zimbabwe |year=2001 |first=M.T.D. |last=Wingate |journal=South African Journal of Geology |volume=104|issue=1 |pages=13–22|bibcode=2001SAJG..104...13W }}</ref> Zircon and baddeleyite incorporate uranium atoms into their crystalline structure as substitutes for [[zirconium]], but strongly reject lead. Zircon has a very high closure 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]] or [[Secondary ion mass spectrometry|SIMS]] techniques.<ref>{{cite journal|doi=10.1126/science.286.5448.2289 |title=Isotope Geochemistry: New Tools for Isotopic Analysis |date=December 1999 |first=Trevor |last=Ireland |journal=Science |volume=286 |issue=5448 |pages=2289–2290|s2cid=129408440 }}</ref>

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. This can be seen in the concordia diagram, where the samples plot along an errorchron (straight line) which intersects the concordia curve at the age of the sample.{{Citation needed|date=October 2022}}

===Samarium–neodymium dating method===
{{Main|Samarium–neodymium dating}}

This involves the [[alpha decay]] of <sup>147</sup>Sm to <sup>143</sup>Nd with a [[half-life]] of 1.06 x 10<sup>11</sup> years. Accuracy levels of within twenty million years in ages of two-and-a-half billion years are achievable.<ref>{{cite journal|doi=10.1016/S0012-821X(98)00228-3 |title=A multielement geochronologic study of the Great Dyke, Zimbabwe: significance of the robust and reset ages |date=December 1998 |first=S. B. |last=Mukasa |author2=A. H. Wilson |author3=R. W. Carlson |journal=Earth and Planetary Science Letters |volume=164 |issue=1–2 |pages=353–369 |bibcode=1998E&PSL.164..353M}}</ref>

===Potassium–argon dating method===
{{Main|Potassium–argon dating}}

This involves [[electron capture]] or [[positron]] decay of potassium-40 to argon-40. Potassium-40 has a half-life of 1.3 billion years, so this method is applicable to the oldest rocks. Radioactive potassium-40 is common in [[mica]]s, [[feldspar]]s, and [[hornblende]]s, though the closure temperature is fairly low in these materials, about 350&nbsp;°C (mica) to 500&nbsp;°C (hornblende).{{Citation needed|date=October 2022}}

===Rubidium–strontium dating method===
{{Main|Rubidium–strontium dating}}

This 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 rock|igneous]] and [[metamorphic rock]]s, and has also been used to date [[moon rock|lunar samples]]. Closure 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. Application of in situ analysis (Laser-Ablation ICP-MS) within single mineral grains in faults have shown that the Rb-Sr method can be used to decipher episodes of fault movement.<ref>{{cite journal|doi=10.1038/s41598-019-57262-5|title=In situ Rb-Sr dating of slickenfibres in deep crystalline basement faults |year=2020 |last1=Tillberg |first1=Mikael |last2=Drake |first2=Henrik |last3=Zack |first3=Thomas |last4=Kooijman |first4=Ellen |last5=Whitehouse |first5=Martin J. |last6=Åström |first6=Mats E. |journal=Scientific Reports |volume=10 |issue=1 |page=562 |pmid=31953465 |bibcode=2020NatSR..10..562T |s2cid=210670668 |pmc=6969261 }}</ref>

===Uranium–thorium dating method===
{{Main|Uranium–thorium dating}}

A relatively short-range dating technique is based on the decay of uranium-234 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 32,760 years.{{Citation needed|date=October 2022}}

While [[uranium]] is water-soluble, [[thorium]] and [[protactinium]] are not, and so they are selectively precipitated into ocean-floor [[sediment]]s, from which their ratios are measured. The scheme has a range of several hundred thousand years. A related method is [[ionium–thorium dating]], which measures the ratio of [[ionium]] (thorium-230) to thorium-232 in [[ocean sediment]].{{Citation needed|date=October 2022}}

===Radiocarbon dating method===
{{Main|Radiocarbon dating}}
[[File:Ales stenar bred.jpg|upright=1.35|thumb|right|[[Ale's Stones]] at Kåseberga, around ten kilometres south east of [[Ystad]], [[Sweden]] were dated back to approximately 1,400 years ago using the carbon-14 method on organic material found at the site.<ref>{{cite web |url=http://www.raa.se/cms/extern/en/places_to_visit/our_historical_sites/ales_stenar.html |title=Ales stenar |publisher=The Swedish National Heritage Board |date=11 October 2006 |access-date=9 March 2009 |archive-url=https://web.archive.org/web/20090331132307/http://www.raa.se/cms/extern/en/places_to_visit/our_historical_sites/ales_stenar.html |archive-date=31 March 2009 }}</ref>]] [[Radiocarbon dating]] is also simply called carbon-14 dating. Carbon-14 is a radioactive isotope of carbon, with a half-life of 5,730 years<ref>{{cite journal|last=Clark |first=R. M. |year=1975 |title=A calibration curve for radiocarbon dates |journal=Antiquity |volume=49 |issue=196 |pages=251–266 |url=http://www.antiquity.ac.uk/ant/049/Ant0490251.htm|doi=10.1017/S0003598X00070277 |s2cid=161729853 |url-access=subscription }}</ref><ref>{{cite journal|doi=10.5194/angeo-20-115-2002 |first=S. S. |last=Vasiliev |author2=V. A. Dergachev |year=2002 |title=The ~2400-year cycle in atmospheric radiocarbon concentration: Bispectrum of <sup>14</sup>''C'' data over the last 8000 years |journal=Annales Geophysicae |volume=20|issue=1 |pages=115–120 |bibcode = 2002AnGeo..20..115V |url=http://hal.archives-ouvertes.fr/docs/00/31/69/27/PDF/angeo-20-115-2002.pdf |doi-access=free }}</ref> (which is very short compared with the above isotopes), and decays into nitrogen.<ref>{{cite web|url=http://www.chem.uwec.edu/Chem115_F00/nelsolar/chem.htm|title=Carbon-14 Dating|website=www.chem.uwec.edu|access-date=2016-04-06}}</ref> In other radiometric dating methods, the heavy parent isotopes were produced by [[nucleosynthesis]] in supernovas, meaning that any parent isotope with a short half-life should be extinct by now. Carbon-14, though, is continuously created through collisions of neutrons generated by [[cosmic rays]] with nitrogen in the [[upper atmosphere]] and thus remains at a near-constant level on Earth. The carbon-14 ends up as a trace component in atmospheric [[carbon dioxide]] (CO<sub>2</sub>).<ref>{{Cite web |date=2022-10-12 |title=How do we know the build-up of carbon dioxide in the atmosphere is caused by humans? |url=https://www.climate.gov/news-features/climate-qa/how-do-we-know-build-carbon-dioxide-atmosphere-caused-humans |archive-url=https://web.archive.org/web/20201125150315/https://climate.gov/news-features/climate-qa/how-do-we-know-build-carbon-dioxide-atmosphere-caused-humans |archive-date=25 November 2020 |access-date=2024-10-21 |website=www.climate.gov |language=en}}</ref>

A carbon-based life form acquires carbon 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 take in 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 elapsed since its death. This makes carbon-14 an ideal dating method to date the age of bones or the remains of an organism. The carbon-14 dating limit lies around 58,000 to 62,000 years.<ref>{{cite journal|first=Wolfango |last=Plastino |author2=Lauri Kaihola |author3=Paolo Bartolomei |author4=Francesco Bella |year=2001 |title=Cosmic background reduction in the radiocarbon measurement by scintillation spectrometry at the underground laboratory of Gran Sasso |url=http://digitalcommons.library.arizona.edu/objectviewer?o=http%3A%2F%2Fradiocarbon.library.arizona.edu%2FVolume43%2FNumber2A%2Fazu_radiocarbon_v43_n2A_157_161_v.pdf |journal=Radiocarbon |volume=43 |issue=2A |pages=157–161|doi=10.1017/S0033822200037954 |doi-access=free }}</ref>

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 [[volcano]]es 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; in contrast, 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.<ref>{{Cite journal |last1=Stuiver |first1=Minze |last2=Quay |first2=Paul D. |date=1980 |title=Changes in Atmospheric Carbon-14 Attributed to a Variable Sun |journal=Science |volume=207 |issue=4426 |pages=11–19 |doi=10.1126/science.207.4426.11 |jstor=1683178 |pmid=17730790 |bibcode=1980Sci...207...11S |issn=0036-8075}}</ref>

===Fission track dating method===
{{Main|fission track dating}}
[[File:Apatite Canada.jpg|thumb|[[Apatite]] crystals are widely used in fission track dating.]]
This 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 [[thermal neutrons|slow neutrons]]. This causes induced fission of <sup>235</sup>U, as opposed to the spontaneous fission of <sup>238</sup>U. 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]].<ref>{{Cite book |last1=Fleischer |first1=Robert L. |url=http://www.jstor.org/stable/jj.13167934 |title=Nuclear Tracks in Solids: Principles and Applications |last2=Price |first2=P. Buford |last3=Walker |first3=Robert M. |date=2024-03-29 |publisher=University of California Press |isbn=978-0-520-32023-9 |edition=1 |doi=10.2307/jj.13167934}}</ref>

This scheme has application over a wide range of geologic dates. For dates up to a few million years [[mica]]s, [[tektite]]s (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.<ref>{{cite journal|doi=10.1016/S0899-5362(01)80066-X |title=A titanite fission track profile across the southeastern Archæan Kaapvaal Craton and the Mesoproterozoic Natal Metamorphic Province, South Africa: evidence for differential cryptic Meso- to Neoproterozoic tectonism |date=August 2001 |first=J. |last=Jacobs |author2=R. J. Thomas |journal=Journal of African Earth Sciences |volume=33 |issue=2 |pages=323–333|bibcode = 2001JAfES..33..323J }}</ref> Because the fission tracks are healed by temperatures over about 200&nbsp;°C the technique has limitations as well as benefits. The technique has potential applications for detailing the thermal history of a deposit.<ref name="Naeser-McCulloh1989">{{cite book |last1=Naeser |first1=Nancy |last2=Naeser |first2=Charles |last3=McCulloh |first3=Thane |editor1-last=Naeser |editor1-first=Nancy |editor2-last=McCulloh |editor2-first=Thane |title=Thermal History of Sedimentary Basins |date=1989 |publisher=Springer New York|isbn=978-1-4612-8124-5|pages=157–180|chapter=The Application of Fission-Track Dating to the Depositional and Thermal History of Rocks in Sedimentary Basins|doi=10.1007/978-1-4612-3492-0_10 |chapter-url=https://link.springer.com/chapter/10.1007/978-1-4612-3492-0_10}}</ref>

===Chlorine-36 dating method===
Large amounts of otherwise rare [[chlorine-36|<sup>36</sup>Cl]] (half-life ~300ky) were produced by irradiation of seawater during atmospheric detonations of [[nuclear weapon]]s between 1952 and 1958. The residence time of <sup>36</sup>Cl in the atmosphere is about 1 week. Thus, as an event marker of 1950s water in soil and ground water, <sup>36</sup>Cl is also useful for dating waters less than 50 years before the present. <sup>36</sup>Cl has seen use in other areas of the geological sciences, including dating ice<ref>{{cite journal|last=Willerslev |first=E. |year=2007 |title=Ancient biomolecules from deep ice cores reveal a forested southern Greenland |journal=Science |volume=317 |issue=5834 |pages=111–114 |doi=10.1126/science.1141758|pmid=17615355 |pmc=2694912 |bibcode=2007Sci...317..111W |s2cid=7423309 }}</ref> and sediments.

===Luminescence dating methods===
{{Main|Luminescence dating}}

Luminescence dating methods are not radiometric dating methods in that they do not rely on abundances of isotopes to calculate age. Instead, they are a consequence of [[background radiation]] on certain minerals. Over time, [[ionizing radiation]] is absorbed by mineral grains in sediments and archaeological materials such as [[quartz]] and [[potassium feldspar]]. The radiation causes charge to remain within the grains in structurally unstable "electron traps". Exposure to sunlight or heat releases these charges, effectively "bleaching" the sample and resetting the clock to zero. The trapped charge accumulates over time at a rate determined by the amount of background radiation at the location where the sample was buried. Stimulating these mineral grains using either light ([[optically stimulated luminescence]] or infrared stimulated luminescence dating) or heat ([[thermoluminescence dating]]) causes a luminescence signal to be emitted as the stored unstable electron energy is released, the intensity of which varies depending on the amount of radiation absorbed during burial and specific properties of the mineral.<ref>{{Cite journal |last1=Roberts |first1=Richard G. |last2=Jacobs |first2=Zenobia |last3=Li |first3=Bo |last4=Jankowski |first4=Nathan R. |last5=Cunningham |first5=Alastair C. |last6=Rosenfeld |first6=Anatoly B. |date=2015-04-01 |title=Optical dating in archaeology: thirty years in retrospect and grand challenges for the future |url=https://linkinghub.elsevier.com/retrieve/pii/S0305440315000667 |journal=Journal of Archaeological Science |series=Scoping the Future of Archaeological Science: Papers in Honour of Richard Klein |volume=56 |pages=41–60 |doi=10.1016/j.jas.2015.02.028 |bibcode=2015JArSc..56...41R |issn=0305-4403|url-access=subscription }}</ref>

These methods can be used to date the age of a sediment layer, as layers deposited on top would prevent the grains from being "bleached" and reset by sunlight. Pottery shards can be dated to the last time they experienced significant heat, generally when they were fired in a kiln.<ref>{{Cite journal |last1=Roberts |first1=Richard G. |last2=Jacobs |first2=Zenobia |last3=Li |first3=Bo |last4=Jankowski |first4=Nathan R. |last5=Cunningham |first5=Alastair C. |last6=Rosenfeld |first6=Anatoly B. |date=2015-04-01 |title=Optical dating in archaeology: thirty years in retrospect and grand challenges for the future |url=https://linkinghub.elsevier.com/retrieve/pii/S0305440315000667 |journal=Journal of Archaeological Science |series=Scoping the Future of Archaeological Science: Papers in Honour of Richard Klein |volume=56 |pages=41–60 |doi=10.1016/j.jas.2015.02.028 |bibcode=2015JArSc..56...41R |issn=0305-4403|url-access=subscription }}</ref>

===Other methods===
Other methods include:{{Citation needed|date=October 2022}}
* [[Argon–argon dating|Argon–argon]] (Ar–Ar)
* [[Iodine–xenon dating|Iodine–xenon]] (I–Xe)
* [[Lanthanum–barium dating|Lanthanum–barium]] (La–Ba)
* [[Lead–lead dating|Lead–lead]] (Pb–Pb)
* [[Lutetium–hafnium dating|Lutetium–hafnium]] (Lu–Hf)
* [[Hafnium–tungsten dating]] (Hf-W)
* [[K–Ca dating|Potassium–calcium]] (K–Ca)
* [[Rhenium–osmium dating|Rhenium–osmium]] (Re–Os)
* [[Uranium–uranium dating|Uranium–uranium]] (U–U)
* [[Krypton–krypton dating|Krypton–krypton]] (Kr–Kr)
* [[Beryllium#Isotopes and nucleosynthesis|Beryllium]] (<sup>10</sup>Be–<sup>9</sup>Be)<ref>Application of the authigenic 10 Be/ 9 Be dating method to Late
Miocene–Pliocene sequences in the northern Danube Basin;Michal Šujan – Global and Planetary Change 137 (2016) 35–53; [https://www.researchgate.net/profile/Michal_Sujan/publication/287807148_Application_of_the_authigenic_10Be9Be_dating_method_to_Late_Miocene-Pliocene_sequences_in_the_northern_Danube_Basin_Pannonian_Basin_System_Confirmation_of_heterochronous_evolution_of_sedimentary_envir/links/5684144b08ae1e63f1f1c4c8/Application-of-the-authigenic-10Be-9Be-dating-method-to-Late-Miocene-Pliocene-sequences-in-the-northern-Danube-Basin-Pannonian-Basin-System-Confirmation-of-heterochronous-evolution-of-sedimentary-envi.pdf pdf]</ref>

==Dating with decay products of short-lived extinct radionuclides==
Absolute radiometric dating requires a measurable fraction of parent nucleus to remain in the sample rock. For rocks dating back to the beginning of the [[Solar System]], this requires extremely long-lived parent isotopes, making measurement of such rocks' exact ages imprecise. To be able to distinguish the relative ages of rocks from such old material, and to get a better time resolution than that available from long-lived isotopes, short-lived isotopes that are no longer present in the rock can be used.<ref>Imke de Pater and Jack J. Lissauer: ''Planetary Sciences'', page 321. Cambridge University Press, 2001. {{ISBN|0-521-48219-4}}</ref>

At the beginning of the solar system, there were several relatively short-lived radionuclides like <sup>26</sup>Al, <sup>60</sup>Fe, <sup>53</sup>Mn, and <sup>129</sup>I present within the solar nebula. These radionuclides—possibly produced by the explosion of a supernova—are [[Extinct radionuclide|extinct]] today, but their decay products can be detected in very old material, such as that which constitutes [[meteorite]]s. By measuring the decay products of extinct radionuclides with a [[mass spectrometer]] and using isochronplots, it is possible to determine relative ages of 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. Thus both the approximate age and a high time resolution can be obtained. Generally a shorter half-life leads to a higher time resolution at the expense of timescale.{{Citation needed|date=October 2022}}

===The <sup>129</sup>I – <sup>129</sup>Xe chronometer===
{{See also|Iodine-129#Meteorite age dating}}
{{SimpleNuclide|I|129}} beta-decays to {{SimpleNuclide|Xe|129}} with a half-life of {{val|16.14|0.12|u=million years}}.{{NUBASE2020|ref}} The iodine-xenon chronometer<ref name=IXe>{{cite journal|last=Gilmour|first=J. D. |author2=O. V Pravdivtseva |author3=A. Busfield |author4=C. M. Hohenberg|title=The I-Xe Chronometer and the Early Solar System|journal=Meteoritics and Planetary Science|year=2006|volume=41|issue=1 |pages=19–31|doi=10.1111/j.1945-5100.2006.tb00190.x|bibcode = 2006M&PS...41...19G |doi-access=free}}</ref> is an isochron technique. Samples are exposed to neutrons in a nuclear reactor. This converts the only stable isotope of iodine ({{SimpleNuclide|I|127}}) into {{SimpleNuclide|Xe|128}} via neutron capture followed by beta decay (of {{SimpleNuclide|I|128}}). After irradiation, samples are heated in a series of steps and the xenon [[isotopic signature]] of the gas evolved in each step is analysed. When a consistent {{SimpleNuclide|Xe|129}}/{{SimpleNuclide|Xe|128}} ratio is observed across several consecutive temperature steps, it can be interpreted as corresponding to a time at which the sample stopped losing xenon.{{Citation needed|date=October 2022}}

Samples of a meteorite called Shallowater are usually included in the irradiation to monitor the conversion efficiency from {{SimpleNuclide|I|127}} to {{SimpleNuclide|Xe|128}}. The difference between the measured {{SimpleNuclide|Xe|129}}/{{SimpleNuclide|Xe|128}} ratios of the sample and Shallowater then corresponds to the different ratios of {{SimpleNuclide|I|129}}/{{SimpleNuclide|I|127}} when they each stopped losing xenon. This in turn corresponds to a difference in age of closure in the early solar system.{{Citation needed|date=October 2022}}

===The <sup>26</sup>Al – <sup>26</sup>Mg chronometer===
Another example of short-lived extinct radionuclide dating is the {{SimpleNuclide|Aluminium|26|link=yes}} – {{SimpleNuclide|Mg|26}} chronometer, which can be used to estimate the relative ages of [[chondrule]]s. {{SimpleNuclide|Al|26}} decays to {{SimpleNuclide|Mg|26}} with a [[half-life]] of 720 000 years. The dating is simply a question of finding the deviation from the [[natural abundance]] of {{SimpleNuclide|Mg|26}} (the product of {{SimpleNuclide|Al|26}} decay) in comparison with the ratio of the stable isotopes {{SimpleNuclide|Al|27}}/{{SimpleNuclide|Mg|24}}.<ref>{{Cite journal |journal=Press Abstracts from the Nineteenth Lunar and Planetary Science Conference |last1=Hutcheon |first1=I. D. |last2=Hutchison |first2=R. |last3=Wasserburg |first3=G. J. |date=1988-03-01 |title=Evidence of In-situ Decay of 26Al in a Semarkona Chondrule |url=https://ui.adsabs.harvard.edu/abs/1988LPICo.650...14H |volume=650 |page=14|bibcode=1988LPICo.650...14H }}</ref>

The excess of {{SimpleNuclide|Mg|26}} (often designated {{SimpleNuclide|Mg|26}}*) is found by comparing the {{SimpleNuclide|Mg|26}}/{{SimpleNuclide|Mg|27}} ratio to that of other Solar System materials.<ref>Alexander N. Krot(2002) Dating the Earliest Solids in our Solar System, Hawaiʻi Institute of Geophysics and Planetology http://www.psrd.hawaii.edu/Sept02/isotopicAges.html.</ref>

The {{SimpleNuclide|Al|26}} – {{SimpleNuclide|Mg|26}} chronometer gives an estimate of the time period for formation of primitive meteorites of only a few million years (1.4 million years for Chondrule formation).<ref>Imke de Pater and Jack J. Lissauer: ''Planetary Sciences'', page 322. Cambridge University Press, 2001. {{ISBN|0-521-48219-4}}</ref>

===A terminology issue===
In a July 2022 paper in the journal ''[[Applied Geochemistry]]'', the authors proposed that the terms "parent isotope" and "daughter isotope" be avoided in favor of the more descriptive "precursor isotope" and "product isotope", analogous to "precursor ion" and "product ion" in [[mass spectrometry]].<ref>{{cite journal |last1=Pourret |first1=Olivier |last2=Johannesson |first2=Karen |title=Radiogenic isotope: Not just about words |journal=Applied Geochemistry |date=July 2022 |volume=142 |article-number=105348 |doi=10.1016/j.apgeochem.2022.105348 |bibcode=2022ApGC..14205348P |s2cid=248907159 |doi-access=free }}</ref>

==See also==
{{Portal|Earth sciences|Geophysics|Physics}}
* [[Hadean zircon]]
* [[Isotope geochemistry]]
* [[Paleopedological record]]
* [[Radioactivity]]
* [[Radiohalo]]
* [[Sensitive high-resolution ion microprobe]] (SHRIMP)

==References==
{{Reflist|30em}}

==Further reading==
* {{cite journal|last1=Gunten|first1=Hans R. von|title=Radioactivity: A Tool to Explore the Past|journal=Radiochimica Acta|volume=70–71|issue=s1|year=1995|pages=305–413|doi=10.1524/ract.1995.7071.special-issue.305|s2cid=100441969|url=http://doc.rero.ch/record/292801/files/ract.1995.7071.special-issue.305.pdf}}
* {{cite book|title=Radioactivity Radionuclides Radiation |chapter=Archaeology and Dating| first1=Joseph |last1=Magill |first2=Jean |last2=Galy |publisher=Springer Berlin Heidelberg |year=2005|pages=105–115|doi=10.1007/3-540-26881-2_6 |isbn=978-3-540-26881-9|bibcode=2005rrr..book.....M}}
* {{cite book|isbn=978-0-521-86228-8 |title=Isotope Geology|last1=Allègre|first1=Claude J|date=2008-12-04|publisher=Cambridge University Press }}
* {{cite book|isbn=978-0-231-12440-9 |title=Geochemistry: Pathways and Processes |edition=2|last1=McSween |first1=Harry Y |last2=Richardson |first2=Steven Mcafee |last3=Uhle |first3=Maria E |last4=Uhle |first4=Professor Maria |year=2003 |publisher=Columbia University Press }}
* {{cite book|isbn=978-0-521-87862-3 |title= Cosmochemistry|last1= Harry y. Mcsween|first1= Jr|last2= Huss|first2= Gary R|date= 2010-04-29|publisher= Cambridge University Press}}

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