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K–Ar dating


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*Potassium–argon dating* or *K–Ar dating* is a radiometric dating
method used in geochronology and archeology . 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 micas , clay minerals , tephra , and evaporites . In these
materials, the decay product ^40 Ar is able to escape the liquid (molten)
rock, but starts to accumulate when the rock solidifies (recrystallises ).
Time since recrystallization is calculated by measuring the ratio of the
amount of ^40 Ar accumulated to the amount of ^40 K remaining. The long
half-life of ^40 K allows the method to be used to calculate the absolute
age of samples older than a few thousand years.^[1]

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 temperature of iron.
The geomagnetic polarity time scale was calibrated largely using K–Ar
dating.^[2]


Contents

[hide ]

* 1 Decay series 
* 2 Formula 
* 3 Obtaining the data 
* 4 Preconditions 
* 5 Applications 
* 6 Notes 
* 7 References 
* 8 Further reading 


[edit
]
Decay series

Further information: Isotopes of potassium 

Potassium naturally occurs in 3 isotopes – ^39 K (93.2581%), ^40 K
(0.0117%), ^41 K (6.7302%). The radioactive isotope ^40 K decays with a
half-life of 1.248×10^9 yr to ^40 Ca and ^40 Ar . Conversion to stable
^40 Ca occurs via electron emission (beta decay ) in 89.1% of decay
events. Conversion to stable ^40 Ar occurs via positron emission (inverse
beta decay , electron capture ) in the remaining 10.9% of decay
events.^[3]

Argon, being a noble gas , is not a major component of most samples of
geochronological or archeological interest: it does not bind with other
constituents of the material, but normally escapes into the surrounding
region. Specifically, its presence in solid rock cannot be explained by
other mechanisms. When ^40 K decays to ^40 Ar, the gas may be unable to
diffuse out of the host rock. Because argon was able to escape from the
rock while it was in a liquid state (molten), this accumulation provides a
record of how much of the original ^40 K has decayed, and hence the amount
of time that has passed, since the sample solidified.

Calcium is common in the crust, with ^40 Ca being the most abundant
isotope. Despite ^40 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.


[edit ] Formula

The ratio of the amount of ^40 Ar to that of ^40 K is directly related to
the time elapsed since the rock was cool enough to trap the Ar by the
following equation:

t = \frac{t_\frac{1}{2}}{\ln(2)} \ln(\frac{K_f + \frac{Ar_f}{0.109}}{K_f})

* /t/ is time elapsed
* /t_1/2 / is the half life  of ^40 K
* K_f is the amount of ^40 K remaining in the sample
* Ar_f is the amount of ^40 Ar found in the sample.

The scale factor 0.109 corrects for the unmeasured fraction of ^40 K which
decayed into ^40 Ca; the sum of the measured ^40 K and the scaled amount
of ^40 Ar gives the amount of ^40 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.


[edit ] Obtaining the data

To obtain the content ratio of isotopes ^40 Ar to ^39 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 flame photometry or atomic
absorption spectroscopy .

The amount of ^40 K is rarely measured directly. Rather, the more common
^39 K is measured and that quantity is then multiplied by the accepted
ratio of ^40 K/^39 K (i.e., 0.0117%/93.2581%, see above).

The amount of ^36 Ar may also be required to be measured, see /assumptions
/ below.


[edit ] Preconditions

All the following preconditions must be true for computed dates to be
accepted as representing the true age of the rock ^[4]

Great care is needed in collecting a sample for dating to avoid samples
which have been contaminated by absorption of argon from the atmosphere.
The above equation may be corrected for the presence of such contaminating
non-radiogenic ^40 Ar by subtracting from the measured ^40 Ar value the
amount originally present in the air as determined by the ^40 Ar/^36 Ar
ratio. Ordinarily, in air samples ^40 Ar is 295.5 times more plentiful
than ^36 Ar. The amount of the measured ^40 Ar that resulted from ^40 K
decay is then: ^40 Ar_decayed = ^40 Ar_measured − 295.5 × ^36
Ar_measured . Contamination is suspected when the final results are
untenable.

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. Ar–Ar dating is a similar technique which
compares isotopic ratios from the same portion of the sample to avoid this
problem.

Extraneous argon may be incorporated into a rock depending on conditions
during cooling. Commonly, gases are not fully removed from magma at the
time of crystallization, and so not all of the measured argon will have
resulted from /in situ/ decay of ^40 K in the interval since the rock
crystallized or was recrystallized. Examples of incorporation of
extraneous ^40 Ar include chilled basalts and inclusions of older
xenolithic material – such samples should be avoided. The Ar–Ar dating
method was developed to measure the presence of extraneous argon.

The sample must have remained a closed system since it cooled enough to
retain argon, neither admitting nor emitting either of the isotopes of
interest, for example during hydrothermal alteration.^[5] A deficiency of
^40 Ar 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.^[6]


Accuracy depends on the isotopic ratios included in the sample being
normal, since ^40 K is usually not 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.^[7]

Accuracy also requires that the nuclear decay rate be unaffected by
external conditions such as temperature and pressure. Because of the
energy scales involved, this is a very good assumption, though the ^40 K
electron capture partial decay constant may be enhanced at ultrahigh
pressure.^[1]


[edit ] Applications

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 .^[2] Although it finds
the most utility in 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.^[8] It has also been indispensable in other early east
African sites with a history of volcanic activity such as Hadar, Ethiopia
.^[8] The K–Ar method continues to have utility in dating clay mineral
diagenesis .^[9] Clay minerals are less than 2 microns thick and cannot
easily be irradiated for Ar–Ar analysis because Ar recoils from the
crystal lattice.


[edit ] Notes

1. ^ ^/*a*/  ^/*b*/ 
McDougal and Harrison 1999 , p. 10
2. ^ ^/*a*/  ^/*b*/ 
McDougal and Harrison 1999 , p. 9
3. *^ * "ENSDF Decay Data in the MIRD Format for
.
National Nuclear Data Center
.
http://www.nndc.bnl.gov/useroutput/40k_mird.html. Retrieved
2009-09-22. 
4. *^ * McDougal and Harrison & 1999 "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. ,
p. 11
5. *^ * McDougal and Harrison 1999 ,
p. 9–12
6. *^ * McDougal and Harrison 1999 ,
p. 11–12
7. *^ * McDougal and Harrison 1999 , p. 14
8. ^ ^/*a*/  ^/*b*/
Tattersall, 1995
9. *^ * Aronson and Lee, (1986)