Radiometric Dating

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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 1940s)

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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 ? Fraction of isotope that
  decays/unit time
• N Number of atoms
• dN/dt -?N
• dN/N -?dt
• Ln N -?t C
• N N0 exp(-?t) N0 original number of Atoms

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Determining Half Life

• N N0 exp(-?t)
• Solve for N N0/2
• N0/2 N0 exp(-?t)
• ½ exp(-?t)
• -Ln(2) -?t
• Half life t Ln(2)/? 0.693/?

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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.
• ?(U-238)N(U-238) ?(Th-234)N(Th-234)
  ?(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 Doesnt 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
• Wont 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 theres 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 ModelChondritic Uniform Reservoir
(CHUR) line
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Neodymium Model Ages

• Terrestrial igneous rocks generally fall on the
  CHUR line
• If they dont, its 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