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

• 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) 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.

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• 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

• 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• 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

• 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

• 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• 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)

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

• 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

• 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)

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• 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 Ca-

40 in surface materials• Half life 300,000 years• Ground water tracer• Also formed by oceanic nuclear tests