Radiometric Dating

1. Radiometric Dating Timothy G. Standish, Ph. D.

2. Dating Fossils • Two methods: • Relative dating - When a previously unknown fossil is found in strata with other fossils of “known age,” the age of the newly discovered fossil can be inferred from the “known age” of the fossils it is associated with. Relative dating is done in terms of the relative appearance of organisms in the fossil record. (“Archaeopteryx appears after Latimeria, but before Australopithecus.”) • Absolute dating - Involves assigning dates in terms of years to fossils. This most frequently involves radiometric dating techniques. (“This Archaeopteryx fossil is 150 million years old.”)

3. Radiometric Dating • Assumptions: • Constant isotope decay rates over time • Initial isotope concentrations can be known • Isotope decay is the only factor that alters relative concentrations of isotopes and their breakdown products • Ensuring that each of these assumptions is met can be very difficult if not impossible

4. Radio Isotope Dating • To be the same, elements must have the same number of protons • Isotopes are elements with the same number of protons, but different numbers of neutrons • e.g., uranium 235 (235U) and 238U each have 92 protons, but 143 and 146 neutrons respectively • Some isotopes are more stable than others • Unstable isotopes tend to decay over time to more stable forms • In this decay process, a proton may be gained or lost changing the element

5. Radioisotope Dating • If you can know the amount of an unstable isotope that was in a sample • And you know the rate at which that isotope decays • And the rate of decay has not changed over time • And you can measure the amount of that isotope presently in the sample • You can figure out how old the sample is

6. 1 1/2 Proportion of isotope left 1/4 1/8 1/16 2 4 5 0 1 3 Half-lives Half-lives • The half-life of an isotope is the time it takes for half of the isotope in a sample to decay • For example, if the half-life of 14C is 5,600 years and a sample today has 1,000 14C atoms, after 5,600 years 500 14C atoms will remain

7. Carbon-14 • Carbon-14 (14C) a rare isotope of carbon, that has 6 protons and 8 neutrons • 14C decays to 14N at a constant rate • Every 5,600 years half the 14C in a sample will emit a beta particle (electron) and decay to 14N • Thus 5,600 years is called the half-life of 14C • Because of 14C’s short half-life, it is not useful for dating million year old fossils, it is only accurate to about 50,000 years

8. Half-lives 256 14C atoms at time 0

9. Half-lives 128 14C and 128 14N atoms after 5,600 years or 1 half-life

10. Half-lives 64 14C and 192 14N atoms after 11,200 years or 2 half-lives

11. Half-lives 32 14C and 224 14N atoms after 16,800 years or 3 half-lives

12. Half-lives 16 14C and 240 14N atoms after 22,400 years or 4 half-lives

13. Half-lives 8 14C and 248 14N atoms after 28,000 years or 5 half-lives

14. Half-lives 4 14C and 252 14N atoms after 33,600 years or 6 half-lives

15. Half-lives 2 14C and 254 14N atoms after 39,200 years or 7 half-lives

16. Carbon-14 • 14C is used to date organic samples like wood, hair, shells (CaCO3) and other plant and animal products • Atmospheric 14C is incorporated into organic molecules by plants during photosynthesis • Animals that eat the plants get 14C from the plants they eat • The current ratio of 14C to 12C in the atmosphere is immeasurably small

17. Carbon-14 • With a relatively short half-life and an earth billions of years old, all C14 should be gone • This would be true if not for production of new 14C in the atmosphere as a result of interactions between the upper atmosphere and neutrons in cosmic radiation • The atmospheric ratio of 14C to 12C represents an equilibrium between production and decay of 14C

18. Cosmic radiation produced neutrons Nitrogen-14 In the upper atmosphere Somewhere Between9,000 and 15,000 m Somewhere between 9,000 and 15,000 m

19. Carbon-14 Somewhere Between9,000 and 15,000 m In the upper atmosphere

20. Neutron from cosmic radiation Neutron Nitrogen Nucleus 15N Nucleus 14C Nucleus N + + N N + N N N + + + N + N N N N N + N N + + + N N + + + N N N N N + + Proton + + + + N N 7 Protons + 7 Neutrons 7 Protons + 8 Neutrons 6 Protons + 8 Neutrons + Nitrogen-14 to Carbon-14 14N 14C

21. 14C Nucleus N + N N N + N + N N + + + N 6 Protons + 8 Neutrons Carbon-14 to Nitrogen-14 14C 14N

22. 14C 14N 2sp hybrid orbitals 1s orbital N + N N N + N + N N + + + N Carbon-14 to Nitrogen-14

23. 14C 14N N + e- 14C Nucleus N + + N N + N + N + N N N + + N N + + N N + N N + + + N 6 Protons + 8 Neutrons Carbon-14 to Nitrogen-14 14N Nucleus 7 Protons + 7 Neutrons

24. CO2 fixation Carbon-14Sometime in the Ancient Past Plant absorbs both C12 and C14 in the ratio they exist in the atmosphere

25. Carbon-14A Plant Grows Absorbing CO2

26. Carbon-14The Plant Dies

27. Carbon-14It Is Buried

28. Carbon-14Over Time 14C Decays to 14N

29. Carbon-14Over Time 14C Decays to 14N

30. Standard exponential decay formula Carbon-14Example • In our ancient sample of plant material 2 x 10514C atoms are found per gram of C • In a recently collected sample of plant material 1.2 x 10514C atoms are found per gram of C l = The radioactive decay constant for 14C which is -1.238 x 10-4 N0 = Amount of 14C at time 0 Nt = amount of 14C at present t=ln(N0/Nt)/l t=ln(1.2 x 105/2.0 x 105)/-1.238 x 10-4 t = 4,126 years • Assuming present 14C = Ancient 14C concentration

31. Isotope Product Half life Method Potassium-40 Argon-40 8.4 x 109 e- capture Uranium-238 Lead-206 4.5 x 109 a emission (8) Uranium-235 Lead-207 0.7 x 109 Rubidium-87 Strontium-87 48.6 x 109 Thorium-232 Lead-208 14.0 x 109 Other Isotopic Dating Methods • 14Cdating is not useful for dating geological strata so other methods have been developed using isotopes with much longer half lives • Examples include:

32. Potassium Argon Dating • Potassium is abundant in rocks • 40K decays to 40Ar and 40Ca in a specific ratio, 11.2 40Ar to 88.8 40Ca • As calcium is abundant in rocks, 40Ca is not an easy isotope to use in dating • In theory, all 40Ar should be released as argon gas when igneous rock is formed • Thus, during creation of new igneous rock, the potassium argon clock is set to zero . . . at least in theory

33. Ar Old lava Fossil baring rock Potassium Argon Dating • As lava comes out of volcanoes, gasses, including argon, are released • Thus when lava cools to form rock it should contain no argon Volcano

34. Potassium Argon Dating • As lava comes out of volcanoes, gasses, including argon, are released • Thus when lava cools to form rock it should contain no argon Volcano

35. New layer of argon free volcanic rock over fossil bearing rock Potassium Argon Dating • As lava comes out of volcanoes, gasses, including argon, are released • Thus when lava cools to form rock it should contain no argon Volcano

36. Potassium Fossil containing rock Old lava New lava Argon Potassium Argon Dating

37. + N e- 40K Nucleus + + N N + + N N + + N + + N + N N N N N + + N N + + N N N N + + + + + + N N N N + + N N + + N N + + + + N N N N + + N N N N + + + + N N + + N N N N N N e- + + N N 19 Protons + 21 Neutrons Potassium-40 to Argon-40 40K 40Ar 40Ar Nucleus 18 Protons + 22 Neutrons

38. N + e- 40K Nucleus + + N N + + N + + + + + + N + N N N N N + + N N + + N N N N + + + + + + N N N N + + N N + + N N + + + + N N N N + + N N N N + + + + N N + + N N N N N N e- + + N N 19 Protons + 21 Neutrons Potassium-40 to Calcium-40 40K 40Ca 40Ca Nucleus 20 Protons + 20 Neutrons

39. Potassium Argon Potassium-Argon Dating Many years later • Fossils found in strata above the old lava must be younger than it is • Fossils in strata under the new lava must be older than it is • Thus potassium-argon dating can give ages between which fossils must have formed Old Older Oldest

40. When the Data Speaks “For example, researchers have calculated that 'mitochondrial Eve'--the woman whose mtDNA was ancestral to that in all living people--lived 100,000 to 200,000 years ago in Africa. Using the new clock, she would be a mere 6,000 years old. No one thinks that's the case, but at what point should models switch from one mtDNA time zone to the other?” Gibbons, A. 1998. Calibrating the mitochondrial clock. Science 279:28-29

41. The End