Radiometric Dating
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)
Mass Spectroscopy
Exponential Decay
Exponential Decay
Half-Life
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
Determining Half Life
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N = N0 exp(-λt)
Solve for N = N0/2
N0/2 = N0 exp(-λt)
½ = exp(-λt)
-Ln(2) = -λt
Half life t = Ln(2)/λ = 0.693/λ
Decay Chains
• U-238 (4.5 b.y.)  Th-234 (24.5 days)  Pa234 (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.
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
Potassium-Argon
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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
Potassium-Argon
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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
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
A K-Ar Isochron
Rb-Sr
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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
Isochron Diagram
Isochron Diagram
What initial Sr-87/Sr-86 means
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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
U-Th-Pb Dating
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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
Concordia Plot
Discordia Plot
Samarium-Neodymium
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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 Nd142 (Stable, 22% of Nd)
The CHUR Model:
Chondritic Uniform Reservoir (CHUR) line
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
Nd-Sm Model Ages
Uranium-thorium dating method
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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
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
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
Cosmogenic Isotopes
• Produced by particle interactions
with air or surface Materials
– C-14
– Be-10
– Cl-36
C-14 (Radiocarbon) Dating
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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 C14 decays (5730 years)
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
Beryllium-10 Dating
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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
Chlorine-36 Dating
• Forms by spallation of Ar in atmosphere
• Forms by particle reactions with Cl-35 and Ca40 in surface materials
• Half life 300,000 years
• Ground water tracer
• Also formed by oceanic nuclear tests