©1998 timothy g. standish timothy g. standish, ph. d. radiometric dating

©1998 Timothy G. Standish

Timothy G. Standish, Ph. D.

Radiometric Radiometric DatingDating


Dating FossilsDating 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 DatingRadiometric DatingAssumptions:1 Constant isotope decay rates over time2 Initial isotope concentrations can be known3 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 DatingRadio 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 DatingRadio 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-livesHalf-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

Pro

port

ion

of is

otop

e le

ft

1/41/8

1/16

1

1/2

30 4 52Half-lives

1


Carbon-14Carbon-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-livesHalf-lives

256 14C atoms at time 0



128 14C and

128 14N atoms

after 5,600 years or

1 half-life



64 14C and

192 14N atoms


2 half-lives



32 14C and

224 14N atoms


3 half-lives



16 14C and

240 14N atoms


4 half-lives



8 14C and

248 14N atoms


5 half-lives



4 14C and

252 14N atoms


6 half-lives



2 14C and

254 14N atoms


7 half-lives


Carbon-14Carbon-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-14Carbon-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 BetweenSomewhere Between9,000 and 15,000 m9,000 and 15,000 m

Nitrogen-14 In the upper atmosphere

Somewhere between 9,000 and 15,000 m

Cosmic radiation produced neutrons


Carbon-14

In the upper atmosphere

Somewhere BetweenSomewhere Between9,000 and 15,000 m9,000 and 15,000 m


Nitrogen-14 to Carbon-14Nitrogen-14 to Carbon-14

14C14NProton

Neutron

N +N+N

+N +N

+N

+N

+

Nitrogen Nucleus

7 Protons +7 Neutrons

14CNucleus


N +N+N

+N +N

+

N

+NN

15N Nucleus


N

Neutron from cosmic

radiation

N +N+N

+N +N

++N

+ N

+


Carbon-14 to Nitrogen-14Carbon-14 to Nitrogen-14

14CNucleus


N+ N+N

+N+N

+

N

+NN

14N14C


1s orbital

N+ N+N

+N+N

+

N

+NN

Carbon-14 to Nitrogen-14Carbon-14 to Nitrogen-1414N14C

2sp hybrid orbitals


+N+ N

+N+N+N

+

N

+NN

14CNucleus


Carbon-14 to Nitrogen-14Carbon-14 to Nitrogen-14

14N Nucleus


14N14C

N+ N+N

+N+N

++NN +

Ne-


Carbon-14Carbon-14Sometime in the Ancient PastSometime in the Ancient Past

CO2 fixation

Plant absorbs both C12 and C14 in the ratio they exist in the atmosphere


Carbon-14Carbon-14A Plant Grows Absorbing COA Plant Grows Absorbing CO22


Carbon-14Carbon-14The Plant DiesThe Plant Dies


Carbon-14Carbon-14It Is BurriedIt Is Burried


Carbon-14Carbon-14Over Time Over Time 1414C Decays to C Decays to 1414NN


Carbon-14Carbon-14ExampleExample

= 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(1.2 x 105/2.0 x 105)/-1.238 x 10-4

t = 4,126 years

t=ln(N0/Nt)/

Assuming present 14C = Ancient 14C concentration

In our ancient sample of plant material 2 x 105 14C atoms are found per gram of C

In a recently collected sample of plant material 1.2 x 105 14C atoms are found per gram of C

Standard exponential decay formula


Other Isotopic Dating MethodsOther 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:

Uranium-235 Lead-207 0.7 x 109

emission (8)Uranium-238 Lead-206 4.5 x 109

Thorium-232 Lead-208 14.0 x 109

Rubidium-87 Strontium-87 48.6 x 109

e- capturePotassium-40 Argon-40 8.4 x 109

MethodIsotope Product Half life


Potassium Argon DatingPotassium 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


Ar

Potassium Argon DatingPotassium 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

Old lavaFossil baringrockVolcano




contain no argon

Volcano




contain no argon

New layer of argon free volcanic rock over fossil baring

rockVolcano


Potassium Argon DatingPotassium Argon Dating

Fossil containing rock

Old lava

New lava

Potassium

Argon


40KNucleus


N+ N+N

+N

+N

+

+NN

+N+ N

+N+N+N

++NN +

N

N+N

+N+N

N +

N

+

Potassium-40 to Argon-40Potassium-40 to Argon-40

40Ar Nucleus


40Ar40K

N+e-

N+ N+N

+N

+N

+

+NN

+N+ N

+N+N+N

++NN

N

N+ +N

+N+

N

N

N +

N

e-


40KNucleus


N+ N+N

+N

+N

+

+NN

+N+ N

+N+N+N

++NN +

N

N+N

+N+N

N +

N

+

Potassium-40 to Calcium-40Potassium-40 to Calcium-40

40Ca Nucleus


40Ca40K

e-+N

e-

+

N+ N+N

+N

+N

+

+NN

+N+ N

+N+

+N

++NN

N

N+N

+N+N

N +

N

++


Potassium Argon DatingPotassium Argon Dating

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

OlderOlder

OldestOldest

OldOld

Many years laterMany years later

PotassiumArgon


When the Data SpeaksWhen 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

©1998 timothy g. standish timothy g. standish, ph. d. radiometric dating

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