Potassium-Argon (K-Ar) Dating
K-Ar Dating In 10,000 K atoms: 9326 39 K 673 41 K 1 40 K
Potassium Decay
Potassium Decay
Potassium Decay
Argon About 1% of atmosphere is argon Three stable isotopes of argon 36 Ar: 0.337% 38 Ar: 0.063% 40 Ar: 99.600% ( 40 Ar/ 36 Ar) atmos = 295.5 Most of the argon in the atmosphere comes from the decay of 40 K in the Earth over geologic time (~4.5 10 9 years = 4.5 Ga) Argon is a noble gas (rare gas) because it does not normally combine chemically with other elements
Why Argon is Neat Argon will readily escape to the atmosphere when melted rock (lava) is erupted at the surface When the lava cools into new rock, it contains potassium, but no argon Argon formed by potassium decay is trapped in the now solid rock We can use the ratio of argon to potassium to date the time since the rock solidified That s the theory, anyway!
Radioactive decay of parent P t = P 0 e λt = P 0 / e λt # of parent atoms at time t (end) # of parent atoms at time 0 (start) Base of natural logs = 2.71828 (see e x key on your calculator)
Radioactive growth of daughter P t = P 0 e λt = P 0 / e λt [P t = present amount of parent; P 0 = original amount of parent; t = age] therefore, P 0 = P t e λt Amount of daughter formed is P 0 P t D t =P 0 P t = P t e λt P t = P t (e λt 1)
Radioactive Growth and Decay
Potassium decay Branching decay needs two lambdas λ β = probability of β - decay to 40 Ca λ ε = probability of electron capture or β + decay to 40 Ar λ T = total lambda = λ β + λ ε = probability of 40 K decay λ β = 4.962 10-10 yr -1 λ ε = 0.581 10-10 yr -1 λ T = 5.543 10-10 yr -1 t ½ = ln 2 / λ T = 1.25 10 9 yr = 1.25 Ga
K-Ar age equation D t = P t (e λt 1) But only a proportion λ ε / λ T of the decaying parent 40 K turns into daughter 40 Ar, so ( 40 Ar*) t = (λ ε / λ T ) ( 40 K) t (e λt 1) [ 40 Ar* = radiogenic 40 Ar, formed in the rock by 40 K decay] Solving the above equation for t (the age), t 40 1 Ar * λ = ln T + 1 λ 40 K λ ε
K-Ar dating Measure amount of K in part of sample (aliquot) gives us 40 K (0.0117% of K) [aliquot implies a representative part of the sample] Measure amount of 40 Ar and 36 Ar in another aliquot, by mass spectrometry Calculate atmospheric 40 Ar = 295.5 36 Ar Subtract atmospheric 40 Ar from measured 40 Ar to get radiogenic 40 Ar* Use 40 Ar*/ 40 K to calculate age
Assumptions of K-Ar dating + The material in question must be a closed system. That is, no radiogenic 40 Ar or K has escaped from the rock/mineral since it formed. + No non-atmospheric 40 Ar was incorporated into the rock/mineral during or after its formation. + A correction must be made for atmospheric 40 Ar ( 40 Ar from the 40 Ar/ 36 Ar ratio = 295.5 subtracted). + The decay constants of 40 K are accurately known. + The quantities of 40 Ar, 36 Ar and potassium in the rock/mineral are accurately determined. (This implies that the aliquots used for K and for Ar analysis have the same K and Ar compositions.)
Characteristics of K-Ar dating 1.3 Ga half-life of 40 K makes it suitable for ages up to that of the Earth 4.55 Ga but only works well down to ~50,000 yrs K-Ar dating works on rocks and their minerals not bone, pottery, materials of archaeological interest Must therefore find datable rocks, ideally above and below remains of interest The most suitable materials are volcanic rocks, including basalt, and minerals with reasonably high potassium contents The gold standard mineral for K-Ar dating of younger rocks is sanidine, a potassium feldspar mineral in some volcanics
Dateable layers
Characteristics of K-Ar dating 1.3 Ga half-life of 40 K makes it suitable for ages up to that of the Earth 4.55 Ga but only works well down to ~50,000 yrs K-Ar dating works on rocks and their minerals not bone, pottery, materials of archaeological interest Must therefore find datable rocks, ideally above and below remains of interest The most suitable materials are volcanic rocks, including basalt, and minerals with reasonably high potassium contents The gold standard mineral for K-Ar dating of younger rocks is sanidine, a potassium feldspar mineral in some volcanics
A thin section of a rock of basaltic composition, in ordinary light
The same thin section, in polarized light Long, thin crystals of plagioclase feldspar (suitable for K-Ar or Ar-Ar dating pyroxene
Characteristics of K-Ar dating 1.3 Ga half-life of 40 K makes it suitable for ages up to that of the Earth 4.55 Ga but only works well down to ~50,000 yrs K-Ar dating works on rocks and their minerals not bone, pottery, materials of archaeological interest Must therefore find datable rocks, ideally above and below remains of interest The most suitable materials are volcanic rocks, including basalt, and minerals with reasonably high potassium contents The gold standard mineral for K-Ar dating of younger rocks is sanidine, a potassium feldspar mineral in some volcanics
Problems with K-Ar dating Complex and separate procedures to measure amounts of K and Ar Measurements of K and Ar subject to errors on order of a percent error in ratio is even larger K and Ar must be measured on different parts of sample inhomogeneity errors No way of knowing if age is correct, or sample has lost or gained K or Ar
Ar-Ar Dating Nuclear reactor + Mass spectrometer + High-powered laser = 40 Ar- 39 Ar geochronology
Ar-Ar ( 40 Ar- 39 Ar) Dating A nuclear reactor is an intense source of neutrons from uranium fission A common type of reaction when atoms are bombarded with neutrons is the so-called (n, p) reaction, in which a neutron enters the nucleus and a proton leave This is equivalent to a positron decay A A 1; N N + 1; M M In this way, the most abundant K isotope, 39 K, can be turned into the radioactive isotope 39 Ar
Ar-Ar ( 40 Ar- 39 Ar) Dating
Ar-Ar Method 39 K 1 0 n Neutron in (from reactor): 39 K + 1 n 40 K
Ar-Ar Method 1 1 p 40 K Proton out: 40 K 39 Ar + 1 p (this happens almost instantaneously after the neutron arrives)
Ar-Ar Method 39 Ar 39 K + 1 n 39 Ar + 1 p, or for short, 39 K (n, p) 39 Ar
Ar-Ar ( 40 Ar- 39 Ar) Dating To measure how much 39 K has been converted to 39 Ar, we irradiate samples of known age along with the unknowns The 39 Ar becomes a proxy for the K in the sample 39 Ar 39 K 40 K [ 40 K = (0.0117 / 93.26) 39 K] In a mass spectrometer, we measure the ratio of 40 Ar to 39 Ar, which can be done very accurately We can then use the 40 Ar/ 39 Ar ratio in place of the 40 Ar/ 40 K ratio in a modified age equation
Modified 40 Ar- 39 Ar age equation t 40 1 Ar * = ln 1 + J λ 39 Ar T Here J is a constant for a particular irradiation 1. Measure 40 Ar*/ 39 Ar in known-age standards, and solve for J 2. Then measure 40 Ar*/ 39 Ar in the unknown samples and solve for the age
Advantages of 40 Ar- 39 Ar dating K and Ar are now measured on a single sample no inhomogeneity problem Measurement of 40 Ar/ 39 Ar ratio is much more accurate than separate K and Ar Can use the method of step heating, which can give a check on the accuracy of ages, even when the sample has gained or lost argon! Provides additional information on calcium and chlorine in the sample
Step heating Argon is held in many kinds of microscopic sites in the sample These sites will commonly differ in how tightly they hold onto their argon how retentive they are Argon is released from the sample in the lab by heating The most retentive sites in the sample will release argon at the highest temperatures A series of heating steps, and analyses of the gas at each step, will result in a series of ages, corresponding to a release of argon at progressively higher temperatures A plot of the ages obtained in progressive step heating of the sample, versus the amount of 39 Ar released, is called an age spectrum
Age spectrum with no argon loss
More complex age spectra, showing argon loss
Dating an older woman (Australopithecus afarensis) http://www.bbc.co.uk/sn/prehistoric_life/tv_radio/wwcavemen/images/wwc_article_pop2.jpg
Africa is the ancestral home of the human species Lucy s home
The African Rift Valley is home to many fossils of our ancestors Lucy s home
Typical rift volcano in the Afar Triangle
Sanidine crystal from the preceding volcano
Lucy with her discoverer, Don Johanson
Lucy is ~3.18 Ma old
~3.5 Ma old footprints in volcanic ash Laetoli Footprints
Laetoli Footprints
McMaster Nuclear Reactor
Sample Loading
Sample Loading
Laser Heating of the Sample
Laser Heating of the Sample
Laser Heating of the Sample
Laser Heating of the Sample
Gas Extraction and Cleanup
Mass Spectrometry
Mass Spectrometry
Ion Detection
Data Reduction