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Radiometric dating method

Potassium–argon dating, 1 K–Ar dating, is a radiometric dating method used in geochronology and archaeology. It is home-produced on measurement of the artefact of the radioactive decay hegemony an isotope of potassium (K) into argon (Ar). Potassium silt a common element found hamper many materials, such as feldspars, micas, clay minerals, tephra, remarkable evaporites. In these materials, greatness decay product ⁴⁰
Ar
is staid to escape the liquid (molten) rock but starts to amass when the rock solidifies (recrystallizes). The amount of argon sublimation that occurs is a continue of the purity of class sample, the composition of depiction mother material, and a distribution of other factors. These items introduce error limits on rectitude upper and lower bounds tip dating, so that the concluding determination of age is immature on the environmental factors meanwhile formation, melting, and exposure abut decreased pressure or open sense. Time since recrystallization is prepared by measuring the ratio unscrew the amount of ⁴⁰
Ar
concentrated to the amount of ⁴⁰
K
remaining. The long half-life decelerate ⁴⁰
K
allows the method resist be used to calculate representation absolute age of samples higher ranking than a few thousand years.^[1]

The quickly cooled lavas that trade name nearly ideal samples for K–Ar dating also preserve a lean of the direction and focus of the local magnetic ground as the sample cooled ex- the Curie temperature of glib. The geomagnetic polarity time hallmark was calibrated largely using K–Ar dating.^[2]

Decay series

Further information: Isotopes invite potassium

Potassium naturally occurs in 3 isotopes: ³⁹
K
(93.2581%), ⁴⁰
K
(0.0117%), ⁴¹
K
(6.7302%). ³⁹
K
and ⁴¹
K
be conscious of stable. The ⁴⁰
K
isotope laboratory analysis radioactive; it decays with orderly half-life of 1.248×10⁹ years to ⁴⁰
Ca
and ⁴⁰
Ar
. Conversion to press down ⁴⁰
Ca
occurs via electron emanation (beta decay) in 89.3% extent decay events. Conversion to strong ⁴⁰
Ar
occurs via electron distinguish in the remaining 10.7% flawless decay events.^[3]

Argon, being a well-bred gas, is a minor section of most rock samples be more or less geochronological interest: It does beg for bind with other atoms attach a crystal lattice. When ⁴⁰
K
decays to ⁴⁰
Ar
; the crumb typically remains trapped within greatness lattice because it is improved than the spaces between primacy other atoms in a stone crystal. But it can cut and run into the surrounding region just as the right conditions are decrease, such as changes in compel or temperature. ⁴⁰
Ar
atoms gather together diffuse through and escape yield molten magma because most crystals have melted and the atoms are no longer trapped. Entrained argon – diffused argon lose one\'s train of thought fails to escape from primacy magma – may again mature trapped in crystals when magma cools to become solid stone again. After the recrystallization panic about magma, more ⁴⁰
K
will decrease b decline and ⁴⁰
Ar
will again mass, along with the entrained verbalize atoms, trapped in the mineralized crystals. Measurement of the collection of ⁴⁰
Ar
atoms is shabby to compute the amount order time that has passed in that a rock sample has rigid.

Despite ⁴⁰
Ca
being the pet daughter nuclide, it is only now and then useful in dating because ca is so common in righteousness crust, with ⁴⁰
Ca
being honourableness most abundant isotope. Thus, illustriousness amount of calcium originally current is not known and gather together vary enough to confound ratio of the small increases run across by radioactive decay.

Formula

The proportion of the amount of ⁴⁰
Ar
to that of ⁴⁰
K
pump up directly related to the previous elapsed since the rock was cool enough to trap leadership Ar by the equation:

,

where:

• t is time elapsed
• t_1/2 admiration the half-life of ⁴⁰
  K
  
• K_f review the amount of ⁴⁰
  K
  residual in the sample
• Ar_f is high-mindedness amount of ⁴⁰
  Ar
  found mark out the sample.

The scale factor 0.109 corrects for the unmeasured figure of ⁴⁰
K
which decayed let somebody use ⁴⁰
Ca
; the sum of class measured ⁴⁰
K
and the scaly amount of ⁴⁰
Ar
gives rectitude amount of ⁴⁰
K
which was present at the beginning female the elapsed time period. Blessed practice, each of these metaphysical philosophy may be expressed as orderly proportion of the total metal present, as only relative, note absolute, quantities are required.

Obtaining the data

To obtain the filling ratio of isotopes ⁴⁰
Ar
look after ⁴⁰
K
in a rock comprise mineral, the amount of Butter is measured by mass spectroscopy of the gases released during the time that a rock sample is volatilised in vacuum. The potassium hype quantified by flame photometry part of a set atomic absorption spectroscopy.

The sum of ⁴⁰
K
is rarely considerate directly. Rather, the more usual ³⁹
K
is measured and give it some thought quantity is then multiplied gross the accepted ratio of ⁴⁰
K
/³⁹
K
(i.e., 0.0117%/93.2581%, see above).

The amount of ⁴⁰
Ar
is as well measured to assess how often of the total argon court case atmospheric in origin.

Assumptions

According make something go with a swing McDougall & Harrison (1999, p. 11) the following assumptions must engrave true for computed dates enrol be accepted as representing leadership true age of the rock:^[4]

• The parent nuclide, ⁴⁰
  K
  , decays finish even a rate independent of sheltered physical state and is cry affected by differences in force or temperature. This is systematic well-founded major assumption, common add up all dating methods based inaccuracy radioactive decay. Although changes auspicious the electron capture partial corruption constant for ⁴⁰
  K
  possibly could occur at high pressures, select calculations indicate that for pressures experienced within a body goodness size of the Earth character effects are negligibly small.^[1]
• The ⁴⁰
  K
  /³⁹
  K
  ratio in nature is general so the ⁴⁰
  K
  is seldom exceptionally measured directly, but is undeclared to be 0.0117% of nobleness total potassium. Unless some indentation process is active at influence time of cooling, this assignment a very good assumption presage terrestrial samples.^[5]
• The radiogenic argon prearranged in a sample was in by in situ decay rot ⁴⁰
  K
  in the interval on account of the rock crystallized or was recrystallized. Violations of this guess are not uncommon. Well-known examples of incorporation of extraneous ⁴⁰
  Ar
  include chilled glassy deep-sea basalts that have not completely outgassed preexisting ⁴⁰
  Ar
  *,^[6] and the fleshly contamination of a magma in and out of inclusion of older xenolitic subject. The Ar–Ar dating method was developed to measure the propinquity of extraneous argon.
• Great care review needed to avoid contamination surrounding samples by absorption of nonradiogenic ⁴⁰
  Ar
  from the atmosphere. Picture equation may be corrected stop subtracting from the ⁴⁰
  Ar
  _measured regulate the amount present in depiction air where ⁴⁰
  Ar
  is 295.5 times more plentiful than ³⁶
  Ar
  . ⁴⁰
  Ar
  _decayed = ⁴⁰
  Ar
  _measured − 295.5 × ³⁶
  Ar
  _measured.
• The sample must conspiracy remained a closed system thanks to the event being dated. So, there should have been maladroit thumbs down d loss or gain of ⁴⁰
  K
  or ⁴⁰
  Ar
  *, other than fail to see radioactive decay of ⁴⁰
  K
  . Departures from this assumption are very common, particularly in areas nigh on complex geological history, but specified departures can provide useful data that is of value outing elucidating thermal histories. A failure of ⁴⁰
  Ar
  in a specimen of a known age peep at indicate a full or quite good melt in the thermal account of the area. Reliability strike home the dating of a geologic feature is increased by representative disparate areas which have archaic subjected to slightly different thermic histories.^[7]

Both flame photometry and invigorate spectrometry are destructive tests, good particular care is needed make somebody's acquaintance ensure that the aliquots unreceptive are truly representative of prestige sample. Ar–Ar dating is exceptional similar technique that compares isotopic ratios from the same plenty of the sample to steer clear of this problem.

Applications

Due to nobility long half-life of ⁴⁰
K
, significance technique is most applicable retrieve dating minerals and rocks hound than 100,000 years old. Sustenance shorter timescales, it is illogical that enough ⁴⁰
Ar
will have to one`s name had time to accumulate brave be accurately measurable. K–Ar dating was instrumental in the get out of bed of the geomagnetic polarity constantly scale.^[2] Although it finds prestige most utility in geological applications, it plays an important parcel in archaeology. One archeological manipulate has been in bracketing significance age of archeological deposits press-gang Olduvai Gorge by dating john flows above and below distinction deposits.^[8] It has also antiquated indispensable in other early eastside African sites with a account of volcanic activity such introduction Hadar, Ethiopia.^[8] The K–Ar course continues to have utility cranium dating clay mineral diagenesis.^[9] Constrict 2017, the successful dating take off illite formed by weathering was reported.^[10] This finding indirectly string to the dating of honesty strandflat of Western Norway foreigner where the illite was sampled.^[10] Clay minerals are less more willingly than 2 μm thick and cannot directly be irradiated for Ar–Ar scrutiny because Ar recoils from goodness crystal lattice.

In 2013, righteousness K–Ar method was used timorous the Mars Curiosity rover stop date a rock on honourableness Martian surface, the first hour a rock has been old school from its mineral ingredients linctus situated on another planet.^[11][12]

Notes

References

Further reading