Radioactive Dating

September 2, 2017 | Author: andrew | Category: Radioactive Decay, Atoms, Isotope, Nuclear Fission, Radiocarbon Dating
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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 Earth√Ęs 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

Radioactive Carbon 14 is produced in the upper atmosphere by cosmic rays that bombard the nitrogen and oxygen gas nuclei producing neutrons that collide with nitrogen atoms causing them to transform to atoms of C14. This has been going on for long enough that the ratio of C14 to the other isotopes of carbon, C13 and C12, has reached a steady state. Because carbon dioxide is removed from the atmosphere or from the water and incorporated into living tissue by all organisms, either as carbohydrates, proteins, or shell, all organisms acquire and maintain the normal isotopic ratio for carbon. However, as soon as an organism dies, it ceases to recycle its supply of organic carbon and the C-14 ratio begins to decrease as it decays over time, providing a radiometeric clock. Fission Track Dating Very young minerals and glasses containing Uranium 238 can also be dated using fission tracks. For approximately every 2 million atoms of U238 that decay by emitting an alpha particle, one atom decays by fission, meaning its nucleus flies apart in two halves. Each half moves away from the other in opposite directions, stripping electons off of the atoms they collide with. This leaves a distinct flaw in the mineral or glass that can be made visible by etching. By counting the number of fission tracks in an area of sample an estimate can be made of the number of total decay events which equals the number of daughter atoms produced. The remaining parent isotope of U238 can be measured by standard methods using a mass spectrometer, or the sample can be bombarded by neutrons to drive the remaining Uranium 238 atoms to decay and the total number of fission tracks can be counted. This technique is relatively inexpensive and has been applied to dating pottery samples as young as 700 years. Resetting of Radiometric ages All estimates of the age of a sample of rock made using radiometric techniques can be changed if the rock is reheated by heating during burial or metamorphism. If the isotopic age of a rock is reset by melting or metamorphism then the age estimated will be the age of the heating event and not the original age of the rock. This is not necessarily a bad thing as the age at which a rock experienced metamorphism is often of great interest to geologists. Sometimes some mineral grains in a rock will be reset and others will not. The grains that yield a maximum age record a primary date, whereas the reset grains will yield a metamorphic date. Accuracy of Isotopic Dates Technically, the ages determined by radioisotope analyses are not true ages but estimates of the age of the sample. These isotopic estimates are always reported with some indication of their accuracy, for example 100 +/- 5 million years. The uncertainty term reflects the limitations in the accuracy of the measuring instruments being used and the fact that different samples or isotopic systems from the same rock usually yield slightly different estimates. Geologists strive to obtain the most accuracy they can, but they do not want to mislead anyone into believing that their estimates are more accurate than they really are.

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