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Radiometric Dating

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**Radiometric Dating First Attempted in 1905**

Compare U and Pb content of minerals Very crude but quickly showed ages over a billion years Skepticism about utility from geologists Arthur Holmes and NAS report, 1931 Almost all dating now involves use of mass spectrometer (developed 1940’s)

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Mass Spectroscopy

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Exponential Decay

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Exponential Decay

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Half-Life

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Determining Half Life Decay Constant λ = Fraction of isotope that decays/unit time N= Number of atoms dN/dt = -λN dN/N = -λdt Ln N = -λt + C N = N0 exp(-λt): N0 = original number of Atoms

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**Determining Half Life N = N0 exp(-λt) Solve for N = N0/2**

-Ln(2) = -λt Half life t = Ln(2)/λ = 0.693/λ

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Decay Chains U-238 (4.5 b.y.) Th-234 (24.5 days) Pa-234 (1.14 min.) dU-238 /dt = dTh-234/dt = dPa-234/dt etc. λ(U-238)*N(U-238) = λ(Th-234)*N(Th-234) = λ(Pa-234)*N(Pa-234) etc. Or… N(U-238)/t(U-238) = N(Th-234)/t(Th-234) = N(Pa-234)/t(Pa-234) etc.

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**Ideal Radiometric Dating**

A (parent) B (Daughter) A decays only one way No other sources of B Both A and B stay in place Unfortunately there are no such isotopes in rocks Branching Decay Inherited Daughter Product Diffusion, alteration, metamorphism

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**Potassium-Argon K-40 Half Life 1.3 b.y.**

K-40 Ca-40 (89%) or Ar-40 (11%) Ca-40 is the only stable isotope of Calcium Total decays = 9 x Argon Atoms Argon is a Noble Gas and Doesn’t React Chemically Only way to be in a crystal is by decay Mechanically trapped in lattice

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**Potassium-Argon Ar atoms mechanically trapped in lattice**

Susceptible to loss from alteration or heating One of the first methods developed Least stable method Little used for high-quality dates Minerals must have K Feldspars, Micas, Glauconite, Clays

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**Inherited Argon Mostly affects volcanic rocks**

Usually from trapped or dissolved air in fluid inclusions Only a problem for very young rocks Won’t be an issue in metamorphic rocks Diffuses out quickly in older volcanic rocks 1 m.y. worth of argon is a problem for 100,000 year old rocks but not 500 m.y. old rocks Detect by plotting isochron

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A K-Ar Isochron

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**Rb-Sr Rb substitutes for K, Sr for Ca Rb-87 Sr-87 Half Life 50 b.y.**

Problem: Primordial Sr-87 But there is also Sr-86 If there’s no Rb-87, Sr-87/Sr-86 is constant If there is Rb-87, Sr-87/Sr-86 increases Also Rb-87 decreases Plot on isochron diagram

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Isochron Diagram

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Isochron Diagram

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**What initial Sr-87/Sr-86 means**

Present ratio in mantle = .703 Ratio 4.6 billion years ago = .699 The more Sr-87, the more Rb-87 decayed High initial Sr-87 means old source rocks = remelted continental crust

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**U-Th-Pb Dating U-238 Pb 206; Half-life 4.5 b.y.**

U-235 Pb-207; Half Life 704 m.y. Th-232 Pb-208; Half Life 13.9 b.y. Pb-204: Non-radiogenic Methods Isochron Concordia/Discordia Short-Lived Daughter Products

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Concordia Plot

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Discordia Plot

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**Samarium-Neodymium Sm-147 Nd-143 (Half Life 1.06 b.y.)**

Nd goes into melt more than Sm Mantle: Low Abundance, High Sm/Nd Granite: High Abundance, Low Sm/Nd Nd-144 = 24% of Nd Nd-144 has half life 2.3 x 1015 years Can use isochron methods with Nd-144 or Nd-142 (Stable, 22% of Nd)

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**The CHUR Model: Chondritic Uniform Reservoir (CHUR) line**

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Neodymium Model Ages Terrestrial igneous rocks generally fall on the CHUR line If they don’t, it’s because the suite departed from CHUR evolution at some point Most common separation: from mantle to crust

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Nd-Sm Model Ages

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**Uranium-thorium dating method**

U-234 Th-230 (80,000 years) U-235 Pa-231, (34,300 years) U is soluble, Th and Pa are not Precipitate in sediments

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Fission Track Dating Fission of U-238 causes damage to crystal lattices Etching makes tracks visible Can actually count decays Anneals at 200 C so mostly used on young materials

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**Optically Stimulated Luminescence Dating**

Radioactive trace elements cause lattice damage Create electron traps Excitation by light releases electrons from traps, emitting light Emitted light more energetic than stimulating light (Distinguished from fluorescence) Sunlight resets electrons Measures length of burial time

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Cosmogenic Isotopes Produced by particle interactions with air or surface Materials C-14 Be-10 Cl-36

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**C-14 (Radiocarbon) Dating**

N-14 + electron C-14 Equilibrium between formation and decay About one C atom per trillion is C-14 C-14 in food chain All living things have C-14 After death, C-14 intake stops and existing C-14 decays (5730 years)

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**C-14 (Radiocarbon) Dating**

Half Life: 5730 years Range: Centuries to 100,000 years C-14 can be removed by solution, oxidation or microbial action C-14 can be added from younger sources C-14 production rate by sun variable Calibrate with known ages like tree rings

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**Beryllium-10 Dating Produced by high energy cosmic rays**

Spallation of N and O in atmosphere Half Life 1.51 m.y. Dissolves in rain water Accumulates on surface Also formed by neutron bombardment of C-13 during nuclear explosions Tracer of nuclear testing era

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**Chlorine-36 Dating Forms by spallation of Ar in atmosphere**

Forms by particle reactions with Cl-35 and Ca-40 in surface materials Half life 300,000 years Ground water tracer Also formed by oceanic nuclear tests

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