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| '''Potassium–argon dating''', abbreviated '''K–Ar dating''', is a [[radiometric dating]] method used in [[geochronology]] and [[archaeology]]. It is based on measurement of the product of the [[radioactive]] decay of an [[isotope]] of [[potassium]] (K) into [[argon]] (Ar). Potassium is a common element found in many materials, such as [[mica]]s, [[clay minerals]], [[tephra]], and [[evaporites]]. In these materials, the decay product <sup>40</sup>Ar is able to escape the liquid (molten) rock, but starts to accumulate when the rock solidifies ([[Recrystallization (geology)|recrystallizes]]). Time since recrystallization is calculated by measuring the ratio of the amount of <sup>40</sup>Ar accumulated to the amount of <sup>40</sup>K remaining. The long [[half-life]] of <sup>40</sup>K allows the method to be used to calculate the [[absolute dating|absolute age]] of samples older than a few thousand years.<ref name=McD-H_10>{{harvnb|McDougall|Harrison|1999|p=10}}</ref>
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| The quickly cooled lavas that make nearly ideal samples for K–Ar dating also preserve a record of the direction and intensity of the local magnetic field as the sample cooled past the [[Curie point|Curie temperature]] of iron. The [[geomagnetic polarity time scale]] was calibrated largely using K–Ar dating.<ref name=McD-H_9>{{harvnb|McDougall|Harrison|1999|p=9}}</ref>
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| ==Decay series==
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| {{Further2|[[Isotopes of potassium]]}}
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| Potassium naturally occurs in 3 isotopes – <sup>39</sup>K (93.2581%), <sup>40</sup>K (0.0117%), <sup>41</sup>K (6.7302%). The radioactive isotope <sup>40</sup>K decays with a [[half-life]] of {{val|1.248|e=9|u=years}} to [[Calcium-40|<sup>40</sup>Ca]] and [[Argon-40|<sup>40</sup>Ar]]. Conversion to stable <sup>40</sup>Ca occurs via electron emission ([[beta decay]]) in 89.1% of decay events. Conversion to stable <sup>40</sup>Ar occurs via positron emission ([[inverse beta decay]]) in the remaining 10.9% of decay events.<ref>
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| {{cite web
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| |date=June 1993
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| |title=ENSDF Decay Data in the MIRD Format for <sup>40</sup>K
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| |url=http://www.orau.org/ptp/PTP%20Library/library/DOE/bnl/nuclidedata/MIRK40.htm
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| |publisher=[[National Nuclear Data Center]]
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| |accessdate=20 September 2013
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| }}</ref>
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| Argon, being a [[noble gas]], is a minor component of most rock samples of [[geochronology|geochronological]] interest: it does not bind with other atoms in a crystal lattice. When <sup>40</sup>K decays to <sup>40</sup>Ar (Argon), the atom typically remains trapped within the lattice because it is larger than the spaces between the other atoms in a mineral crystal. But it can escape into the surrounding region when the right conditions are met, such as change in pressure and/or temperature. <sup>40</sup>Ar atoms are able to diffuse through and escape from molten magma because most crystals have melted and the atoms are no longer trapped. Entrained argon—diffused argon that fails to escape from the magma—may again become trapped in crystals when magma cools to become solid rock again. After the recrystallization of magma, more <sup>40</sup>K will decay and <sup>40</sup>Ar will again accumulate, along with the entrained argon atoms, trapped in the mineral crystals. Measurement of the quantity of <sup>40</sup>Ar atoms is used to compute the amount of time that has passed since a rock sample has solidified.
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| Calcium is common in the crust, with <sup>40</sup>Ca being the most abundant isotope. Despite <sup>40</sup>Ca being the favored daughter nuclide, its usefulness in dating is limited since a great many decay events are required for a small change in relative abundance, and also the amount of calcium originally present may not be known.
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| ==Formula==
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| The ratio of the amount of <sup>40</sup>Ar to that of <sup>40</sup>K is directly related to the time elapsed since the rock was cool enough to trap the Ar by the following equation:
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| <math> t = \frac{t_\frac{1}{2}}{\ln(2)} \ln\left(\frac{K_f + \frac{Ar_f}{0.109}}{K_f}\right)</math>
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| * ''t'' is time elapsed
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| * ''t<sub>1/2</sub>'' is the [[half-life]] of <sup>40</sup>K
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| * K<sub>f</sub> is the amount of <sup>40</sup>K remaining in the sample
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| * Ar<sub>f</sub> is the amount of <sup>40</sup>Ar found in the sample.
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| The scale factor 0.109 corrects for the unmeasured fraction of <sup>40</sup>K which decayed into <sup>40</sup>Ca; the sum of the measured <sup>40</sup>K and the scaled amount of <sup>40</sup>Ar gives the amount of <sup>40</sup>K which was present at the beginning of the elapsed time period. In practice, each of these values may be expressed as a proportion of the total potassium present, as only relative, not absolute, quantities are required.
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| ==Obtaining the data==
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| To obtain the content ratio of isotopes <sup>40</sup>Ar to <sup>40</sup>K in a rock or mineral, the amount of Ar is measured by [[mass spectrometry]] of the gases released when a rock sample is melted in vacuum. The potassium is quantified by [[Emission spectrometry|flame photometry]] or [[atomic absorption spectroscopy]].
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| The amount of <sup>40</sup>K is rarely measured directly. Rather, the more common <sup>39</sup>K is measured and that quantity is then multiplied by the accepted ratio of <sup>40</sup>K/<sup>39</sup>K (i.e., 0.0117%/93.2581%, see above).
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| The amount of <sup>36</sup>Ar may also be required to be measured.
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| == Assumptions ==
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| According to {{harvtxt|McDougall|Harrison|1999|p=11}} the following assumptions must be true for computed dates to be accepted as representing the true age of the rock:<ref>{{harvnb|McDougall|Harrison|1999|p=11}}: "As with all isotopic dating methods, there are a number of assumptions that must be fulfilled for a K–Ar age to relate to events in the geological history of the region being studied."</ref>
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| * The parent nuclide, {{SimpleNuclide|Potassium|40}}, decays at a rate independent of its physical state and is not affected by differences in pressure or temperature. This is a well founded major assumption, common to all dating methods based on radioactive decay. Although changes in the electron capture partial decay constant for {{SimpleNuclide|Potassium|40}} possibly may occur at high pressures, theoretical calculations indicate that for pressures experienced within a body of the size of the Earth the effects are negligibly small.<ref name=McD-H_10 />
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| * The {{SimpleNuclide|Potassium|40}}/{{SimpleNuclide|Potassium|39}} ratio in nature is constant so the {{SimpleNuclide|Potassium|40}} is rarely measured directly, but is assumed to be 0.0117% of the total potassium. Unless some other process is active at the time of cooling, this is a very good assumption for terrestrial samples.<ref>{{harvnb|McDougall|Harrison|1999|p=14}}</ref>
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| * The radiogenic argon measured in a sample was produced by in situ decay of {{SimpleNuclide|Potassium|40}} in the interval since the rock crystallized or was recrystallized. Violations of this assumption are not uncommon. Well-known examples of incorporation of extraneous {{SimpleNuclide|Argon|40}} include chilled glassy deep-sea basalts that have not completely outgassed preexisting {{SimpleNuclide|Argon|40}}*,<ref>{{SimpleNuclide|Argon|40}}* means radiogenic argon</ref> and the physical contamination of a magma by inclusion of older xenolitic material. The Ar–Ar dating method was developed to measure the presence of extraneous argon.
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| * Great care is needed to avoid contamination of samples by absorption of nonradiogenic {{SimpleNuclide|Argon|40}} from the atmosphere. The equation may be corrected by subtracting from the {{SimpleNuclide|Argon|40}}<sub>measured</sub> value the amount present in the air where {{SimpleNuclide|Argon|40}} is 295.5 times more plentiful than {{SimpleNuclide|Argon|36}}. {{SimpleNuclide|Argon|40}}<sub>decayed</sub> = {{SimpleNuclide|Argon|40}}<sub>measured</sub> − 295.5 × {{SimpleNuclide|Argon|36}}<sub>measured</sub>.
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| * The sample must have remained a closed system since the event being dated. Thus, there should have been no loss or gain of {{SimpleNuclide|Potassium|40}} or {{SimpleNuclide|Argon|40}}*, other than by radioactive decay of {{SimpleNuclide|Potassium|40}}. Departures from this assumption are quite common, particularly in areas of complex geological history, but such departures can provide useful information that is of value in elucidating thermal histories. A deficiency of {{SimpleNuclide|Argon|40}} in a sample of a known age can indicate a full or partial melt in the thermal history of the area. Reliability in the dating of a geological feature is increased by sampling disparate areas which have been subjected to slightly different thermal histories.<ref>{{harvnb|McDougall|Harrison|1999|pp=9–12}}</ref>
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| Both flame photometry and mass spectrometry are destructive tests, so particular care is needed to ensure that the aliquots used are truly representative of the sample. [[Argon–argon dating|Ar–Ar dating]] is a similar technique which compares isotopic ratios from the same portion of the sample to avoid this problem.
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| ==Applications==
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| Due to the long [[half-life]], the technique is most applicable for dating minerals and rocks more than 100,000 years old. For shorter timescales, it is likely that not enough Argon 40 will have had time to accumulate in order to be accurately measurable. K–Ar dating was instrumental in the development of the [[geomagnetic polarity time scale]].<ref name=McD-H_9 /> Although it finds the most utility in [[geology|geological]] applications, it plays an important role in [[archaeology]]. One archeological application has been in bracketing the age of archeological deposits at [[Olduvai Gorge]] by dating [[lava]] flows above and below the deposits.<ref name="Tattersall_1995">{{harvnb|Tattersall|1995}}</ref> It has also been indispensable in other early east [[Africa]]n sites with a history of [[volcanic]] activity such as [[Hadar, Ethiopia]].<ref name="Tattersall_1995" /> The K–Ar method continues to have utility in dating clay mineral [[diagenesis]].<ref>{{harvnb|Aronson|Lee|1986}}</ref> Clay minerals are less than 2 micrometres thick and cannot easily be irradiated for [[Argon–argon dating|Ar–Ar]] analysis because Ar recoils from the crystal lattice.
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| ==Notes==
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| {{Reflist}}
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| ==References==
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| *{{cite book
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| |last1=McDougall |first1=I. |author1-link=Ian McDougall (geologist)
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| |last2=Harrison |first2=T. M.
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| |year=1999
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| |title=Geochronology and thermochronology by the <sup>40</sup>Ar/<sup>39</sup>Ar method
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| |publisher=[[Oxford University Press]]
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| |isbn=0-19-510920-1
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| |ref=harv
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| }}
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| *{{Cite book
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| |last=Tattersall |first=I.
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| |year=1995
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| |title=The Fossil Trail: How We Know What We Think We Know About Human Evolution
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| |publisher=[[Oxford University Press]]
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| |isbn=0-19-506101-2
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| |ref=harv
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| }}
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| ==Further reading==
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| *{{cite web
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| |author=
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| |date=
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| |title=K/Ar and <sup>40</sup>K/<sup>39</sup>K methodology
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| |url=http://www.ees.nmt.edu/Geol/labs/Argon_Lab/Methods/Methods.html
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| |archiveurl=http://web.archive.org/web/20060417234339/http://www.ees.nmt.edu/Geol/labs/Argon_Lab/Methods/Methods.html
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| |archivedate=2006-04-17
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| |publisher=[[New Mexico Geochronology Research Laboratory]]
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| }}
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| *{{cite web
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| |last1=Michaels |first1=G. H.
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| |last2=Fagan |first2=B. M.
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| |date=15 December 2005
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| |title=Chronological Methods 9: Potassium–Argon Dating
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| |publisher=[[University of California]]
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| |url=http://id-archserve.ucsb.edu/anth3/courseware/Chronology/09_Potassium_Argon_Dating.html
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| |archiveurl=http://web.archive.org/web/20100810084507/http://id-archserve.ucsb.edu/anth3/courseware/Chronology/09_Potassium_Argon_Dating.html
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| |archivedate=2010-08-10
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| }}
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| *{{cite journal
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| |last1=Aronson |first1=J. L.
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| |last2=Lee |first2=M.
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| |year=1986
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| |title=K/Ar systematics of bentonite and shale in a contact metamorphic zone
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| |journal=[[Clays and Clay Minerals]]
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| |volume=34 |issue=4 |pages=483–487
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| |bibcode=1986CCM....34..483A
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| |doi=10.1346/CCMN.1986.0340415
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| |ref=harv
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| }}
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| *{{cite journal
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| |last1=Moran |first1=T. J.
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| |year=2009
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| |title=Teaching Radioisotope Dating Using the Geology of the Hawaiian Islands
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| |journal=[[Journal of Geoscience Education]]
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| |url=http://mast.unco.edu/JGE-PDFs/MAR/p101-105MAR2009Moran.pdf
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| |volume=57 |issue=2 |pages=101–105
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| |bibcode=2009JGeEd..57..101M
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| |doi=10.5408/1.3544237
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| }}
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| {{Use dmy dates|date=May 2011}}
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| {{DEFAULTSORT:K-Ar dating}}
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| [[Category:Radiometric dating]]
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