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

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Radiometric Dating Timothy G. Standish, Ph. D.

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.”)

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

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

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

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

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

Half-lives 256 14C atoms at time 0

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

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

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

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

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

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

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

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

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

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

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

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 +

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

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

+ 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

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

Carbon-14 A Plant Grows Absorbing CO2

Carbon-14 The Plant Dies

Carbon-14 It Is Burried

Carbon-14 Over Time 14C Decays to 14N

Carbon-14 Over Time 14C Decays to 14N

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

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

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

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

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

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

Potassium Argon Dating
New lava Fossil containing rock Old lava Argon

+ 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

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

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

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

The End