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. Radio Isotope 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. 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 C atoms will remain
Proportion of isotope left
1/4
1/8
1/16 1
1/2 3 4 5 2
Half-lives 1

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

19. Somewhere Between 9,000 and 15,000 m
Carbon-14
In the upper atmosphere

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

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

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

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

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

25. Carbon-14 A Plant Grows Absorbing CO2

26. Carbon-14 The Plant Dies

27. Carbon-14 It Is Burried

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

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

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

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

32. Potassium Argon Dating
Potassium is abundant in rocks
40K decays to 40Ar and 40Ca in a specific ratio, Ar to Ca
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. 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 Ar
Fossil baring
rock
Volcano
Old lava

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. 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
New layer of argon free volcanic rock over fossil baring
rock
Volcano

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

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

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

39. 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
Potassium
Argon

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 Calibrating the mitochondrial clock. Science 279:28-29

41. The
End