1. Radiometric Dating

2. 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)

3. Mass Spectroscopy

4. Exponential Decay

5. Exponential Decay

6. Half-Life

7. 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

8. Determining Half Life N = N0 exp(-λt) Solve for N = N0/2
-Ln(2) = -λt
Half life t = Ln(2)/λ = 0.693/λ

9. 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.

10. 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

11. 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

12. 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

13. 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

14. A K-Ar Isochron

15. 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

16. Isochron Diagram

17. Isochron Diagram

18. 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

19. 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

20. Concordia Plot

21. Discordia Plot

22. 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)

23. The CHUR Model: Chondritic Uniform Reservoir (CHUR) line

24. 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

25. Nd-Sm Model Ages

26. 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

27. 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

28. 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

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

30. 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)

31. 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

32. 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

33. 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