dating for anthropologynsl/lectures/phys10262/art-chap3-7.pdf · dating for anthropology...
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Dating for Anthropology
Radiocarbon dating is limited to the analysis of archaeological samples because of its relatively short half life T1/2 = 5730 y. For dating samples with older history - geological samples for exploring earth history, paleonthological samples for studying the origin and evolution of life, or anthropological samples forexploring the origin and early development of mankind – other methods are typically used involving longer-lived radionuclides.
Most frequently used radionuclide methods are: • potassium-argon method: >10 000 y• uranium series method: >10 000 – 1 000 000 y
3.7. Potassium-Argon Dating40K has unusual decay mode• e--capture to 1.excited state in 40Ar (11%)• β--decay to 40Ca (89%)
40K is very long-livedT1/2=1.28·109 y
40K is in body material and in rock content, 40Ar is noble gas with no chemical reactivity40Ca cannot be distinguished from natural Ca content
22401821
4019 AreK K ⇒+ −
40Ar/40K time-relation
build-up of 40Ar/40K abundance ratio in material
)e(.)K(N)Ar(N
y.)e()K(N.)Ar(N
t
t
1110
1045 :decayK for 1110
40
40
110-40
4040
−⋅=
⋅=
−⋅⋅=
⋅
−
⋅
λ
λ
λ
T1/2=1.28·109 y
anthropological time range
time-determination
teKNArN t ⋅⋅≈−⋅= −⋅ 11
40
40
1082.5)1(11.0)()( λ
chemical or physical analysis of this ratiogives age of sample.
minerals (bone material) contain ~2-10% of Kwith ~0.021% of 40K
40Ar must be releasedand can be counted bymass spectrometry
Problem: zero-point40K is in mineral material since the original formation• for rock material dating back to geological formation
since 40Ar remains trapped• for volcanic material dating back to last activity
since 40Ar is released in melting process
• for organic material dating back to mineralizationsince organic material is porous and releases 40Ar
Zero-point in 40Ar counting
lava sample
40Ar build-up by 40K decay
40Ar depletion by melting
Possibly reflected in two step 40Ar release yielding two different dates, one for the second melting and one for the first melting period of rock.
Volcanic dating
Potassium Argon method is often applied to material embedded in volcanic layers. dating the material above and below the sample gives age range information.
Release and analysis of 40ArTo count 40Ar nuclei the argon must be released from rock sample!
Typical analysis techniques require • melting the sample • catching the released gas• ionizing the argon gas• selecting the gas atoms by mass spectrometry
error sources:loss of 40Ar due to diffusion → simulates low ageinfusion of atmospheric 40Ar → simulates large age(measurement of 36Ar content in sample)
Efficiency of 40Ar countingSuppose you have a 10g sample which is 3.2 Million years old,
that sample contains ~ <1g K ⇒ ~0.00021g 40K
How many 40Ar atoms have been generated by decay?
atomsArArNeArN
eKNKNKNArN
atomsKg
gg
atomsKg
yy
tt
40151840
102.31028.12ln
1840
400
40400
40
401823
4023
1047.5)99827.01(1016.3)()1(1016.3)(
)1()()()()(
1016.340
00021.010023.600021.0
10023.640
69
⋅=−⋅⋅=
−⋅⋅=
−⋅=−=
⋅=⋅⋅
≡
⋅≡
⋅⋅⋅
−
⋅−λ
Number of 40K basically constant (within uncertainties)
Laser Heating TechniqueRelease by laser heating . Released 40Ar atoms can Also be counted using mass spectrometer techniques.
Main advantage of laser heating is the high spatial resolution ~μm!
Dating the Ashes by counting Atoms
40Ar/40K Method
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅= 1
)()(09.9ln1
40
40
ArNArNt
λ40Ar is easily released, 40K must be detected by
measuring characteristic γ-activity with Eγ=1.461 MeV
Age is determined by ratio of 40Ar and 40K abundance in sample.
)(11.0)( 4040 KNKA ⋅⋅= λγ
Sensitivity is limited by characteristic activity
Example: 40K countingminerals (bone material) contain ~2-10% of Kwith ~0.021% of 40K
You have 10 g of sample material⇒ <1g K ⇒ ~0.00021g 40K
;/6)(101
/109.11016.31028.12ln11.0)(
1016.340
00021.010023.600021.0
10023.640
40
7
8189
40
401823
4023
sKAsywith
yy
KA
atomsKg
gg
atomsKg
γ
π
γ
γ
γ
=
⋅≈
⋅=⋅⋅⋅
⋅=
⋅=⋅⋅
≡
⋅≡
Typical detection efficiency is ~1% ⇒ Nγ=0.06 γ/sTo achieve significant statistics of 10% (100±10)You need to count for t = 100/0.06=1666 s ≈ 1/2 h
Problems of 40K activity counting
• Significant 40K background in laboratory environment (concrete)Count rate ~ 1 event/s ⇒ heavy shielding required
• Good statistics requires long counting time and >10g sample size
• Uncertainties due to different counting methods for 40K and 40Ar (different efficiencies in producing 40Ar ionsand detecting 40K γ-radiation.)
Development of alternative method using identical techniques ⇒ 39Ar/40Ar counting
39Ar/40Ar MethodMethod has advantage of parallel counting of 39Ar and 40Ar atomsin mass analyzer ⇒ identical efficiencies, reduced uncertainties!
Problem of generating 39Ar and relating it to 40K
Fixed ratio of stable 39K and radioactive 40K isotopes
39K93.2581
40K0.0117
41K6.7302 Z=19
Conversion of 39K into 39Ar by neutron activation:
39K(n,p)39Ar
Standard Reactor TechniquesConventional TRIGA reactorNeutron flux of Fn ~ 1014 n s-1 cm2
http://geology.cr.usgs.gov/facilities/gstr/
Conversion rate 39K⇒39Ar
;1055.1)(10544.11010)(
10
10110544.1)(1
)()(
1939
22211422739
2114
227),(
223939
39),(
39
39
39
−
−−−
−−
−
⋅=
⋅⋅⋅=
≈
=≈
⋅=⇒
⋅⋅=
sArYcmsncmArY
cmsnF
cmmbKNKofg
KNFArY
n
pnK
npnK
σ
σ
Full conversion would take quite a long time, a 1 hour generation of measurable 39Ar content is sufficient
to produce the measurable amount of N(39Ar)=5.5·1012!
39Ar/40Ar Method
Advantages:Parallel release of 39Ar and 40Ar by heatingParallel separation of 39Ar and 40Ar in mass spectrometerParallel counting in identical detector systems
Neutron flux dependent parameters are typically determined byusing well known 39K standard sample ⇒ relative measurement
)()(
1)()(ln1
40
39
),(
39
40
39KNKNtFJ
JArNArNt
irrpnKnn
n
⋅⋅⋅=
⎟⎟⎠
⎞⎜⎜⎝
⎛−⋅⋅=
σ
λ Jn determined with astandard sample thatis exposed to parallel treatment
Hornblende (mineral) from the McClure Mountains, Colorado (a.k.a. MMhb-1).
Example 1: The cradle of mankind
Ex Africa Semper Aliquid Novi (Always something new out of Africa) Pliny the Elder
The Olduvai GorgeOlduvai Gorge is an archaeological site located in the eastern Serengeti Plains in northern Tanzania. The gorge is a very steep sided ravine roughly 30 miles long and 295 ft. deep. Exposed deposits show rich fossil fauna, many hominid remains belong to the one of the oldest stone tool technologies, called Olduwan. The time span of the objects recovered date from 2,100,000 to 15,000 years ago.
fossil samples from Olduvai site
post-cranial remainsof homo erectus: 0.5 million years
Australopithecus boisei1.8 million years
mineralized fossil
Danakil Rift Valley
Hadar, Ethiopia
Lucy
australopethicus afarensis3.5 Million years
The Discovery of Lucy
Chronology of Evolution
Documentation
Footprints of our Ancestors?
The Age of the Moment!3,500,000 years ago, our very remote ancient ancestors walked through a landscape very like that which we see today. On one particular day the volcano Sadiman puffed out a lot of gray ash, which covered the plains. A rain shower dampened and settled the ashes, so that the local animals left their crisp, clear tracks when they walked. Through this desolated grey landscape, traveled three hominids walking on two legs. A large, medium sized and small individual walked together. Some days later, a fresh ash fall buried the tracks, until they were excavated in 1978. How do we know the age of the footprints?