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Geol 02C Historical Geology
J Bret Bennington
Radiometric Dating of the Rock Record
Determining Absolute Ages
Absolute ages are direct measurements of the age of a rock in years, as opposed to a relative age that simply puts rock layers in time order.
Radiometric Dating
Shortly after the discovery in 1895 that certain
radioactive
atoms decay spontaneously through the emission of high energy particles into different non-radioactive atoms, scientists realized that this could provide a method for determining the absolute age of certain rocks. The key to
radiometric dating
is the fact that radioactive elements all have a distinct and unchanging
half life
.
Radioactive decay
Radioactive decay is a stochastic process - it is impossible to predict when exactly a single individual atom will decay, but there is a finite and measurable probability that a certain percentage of a large population of them will decay over a period of time.
Half lives
The half life is defined as the time it take one half of the present radioactive atoms to decay. The radioactive element is called a
radioisotope
or
parent isotope
and the non-radioactive end product of decay is called a
daughter isotope
. Half lives are physical constants that depend only on the type of atom decaying. Half life values appear to be unaffected by temperature, pressure, presence of other atoms, etc. They are a fundamental property of the forces that hold together the atomic nucleus.
How it works
When igneous or metamorphic rocks crystallize during cooling, they may trap within them a supply of radioactive parent atoms, such as Uranium. As time passes and the rock sits within the earth, the radioactive parent atoms decay to non-radioactive daughter atoms (in this case, lead). The rate of the decay process is constant and the more time that passes, the greater is the number of uranium atoms that decay into lead atoms. At any point before most of the uranium atoms are used up, a geologist can take a sample of the rock and count the total number of uranium and lead atoms in the sample. The proportion of daughter lead atoms to parent uranium atoms reveals the number of half lives that have elapsed since the rock crystallized. If the length of the half life is multiplied by the number of elapsed half lives, then the age of the rock is obtained.
By measuring the ratio of parent isotope to daughter isotope in certain rocks,
geochronologists
are able to determine an estimate of the age of the rock in years. Generally, only igneous and metamorphic rocks can be radiometrically dated because sedimentary usually do not contain the radioisotopes needed for dating. Although igneous rocks occur within the stratigraphic record at relatively few times and places, there enough igneous layers such as ash beds and lava flows to tie the geologic time scale to dates in years over much of its duration.
How Radiometric ages are calculated:
A small sample of rock is placed into a mass spectrometer where it is bombarded by neutrons that knock atoms off of the surface of the sample. These atoms are sorted in the mass spectrometer by weight and counted. The information obtained is the total number of remaining parent isotope atoms and the total number of daughter isotope atoms. The equation:
Age = ln (daughter / parent + 1) /
k
k
is the decay constant - the probability that an atom of the parent isotope will decay over any given time. First,
k
must be calculated from the measured half life of the parent isotope:
At t = 1 half life, ratio of parent to daughter is 1:1 T half = ln (1 + 1) /
k
T half = ln 2 /
k
k
= .693 / T half
Now the age can be calculated using the equation at the top. Example: Isotope with a half life of 10,000 years. Measurements with mass spec count 2000 daughter atoms and 400 parent atoms.
k
= .693 / 10,000 = .0000693 Age = ln (2000 / 400 + 1) / .0000693 Age = 1.79 / .0000693 = 25,855 years
Decay series used in modern radiometric dating
Uranium isotopes
For measuring the ages of very old rocks (greater than 100 million years) isotopes with very long half lives are used: Thorium 232 - Lead 208 14 Ga Uranium 238 - Lead 206 4.5 Ga Uranium 235 - Lead 207 .7 Ga These isotopes cannot be used on younger rocks because too little daughter product is produced in under a 100 million years to be accurately measured.
Possible sources of error
It is possible for radiometric methods to yield false dates.
Loss of parent isotope
:
If some parent isotope leaks out of the rock then it will appear as if more parent has decayed than really has. This will increase the apparent age of the sample.
Loss of daughter isotope
: If some daughter isotope leaks out it will appear as if less parent has decayed than really has. This will decrease the apparent age of the sample.
Addition of daughter isotope
: If some daughter isotope was already present when the rock formed or if the sample is contaminated with daughter isotope (for example, lead introduced accidently to the sample) then the age of the sample will be inflated.
How to check the accuracy of radiometric ages
: The best way to check the accuracy of radiometric ages is to use more than one isotope series with different decay rates to obtain independent age estimates for a rock. For example, using both U238-PB206 and U235-Pb207 series. If the ages given by each series are concordant, then it is likely that the system has remained closed, because adding or removing isotopes would alter the age estimates for each isotopic system to a different degree, giving different age estimates for each system.
Daughter-daughter comparisons
Another way of estimating the age of the rock takes advantage of having two isotopic systems with different decay rates. If two daughter isotopes are produced at different rates, then their ratio changes continuously and predictably over time. Thus, measuring the ratio of Lead 207 to Lead 206 can also provide an estimate of the age of a rock. Another way of using daughter lead isotopes is to measure their ratio to Lead 204. Lead 204 is not produced by any known decay series on Earth, meaning that its total amount in the Earthâs crust has not changed, whereas the amounts of the other lead isotopes have been steadily increasing. Thus the ratio of radiogenic lead to Lead 204 has been steadily increasing through time in a predictable way.
Potassium-Argon
For dating rocks between 1 million and 100 million years old an isotope with a shorter half life is needed: Potassium 40 - Argon 40 1.25 Ga Even though this system has a relatively long half life, very small quantities of argon can be measured because it is a gas that can be liberated from the sample by heating. The remaining potassium 40 can then be converted to argon by bombarding the sample with neutrons to artificially drive decay to completion. The newly produced argon 40 can then be measured to obtain the number of potassium parent isotope in the sample.
Carbon 14 dating
For very young
organic
material such as wood, shell, cloth and bone, the ratio of carbon 14 to carbon 12 can be used. Carbon dating is only useful for determining ages between 0 and 80,000 years because the half life of C14 is very short: Carbon 14 - Nitrogen 14 5,730 years

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