The initial ratio has particular importance for studying the chemical evolution of the Earth's mantle and crust, as we discussed in the section on igneous rocks. Since K is one of the 10 most abundant elements in the Earth's crust, the decay of 40 K is important in dating rocks. But this scheme is not used because 40 Ca can be present as both radiogenic and non-radiogenic Ca. Since Ar is a noble gas, it can escape from a magma or liquid easily, and it is thus assumed that no 40 Ar is present initially. Note that this is not always true.

### Radiometric Dating

If a magma cools quickly on the surface of the Earth, some of the Ar may be trapped. If this happens, then the date obtained will be older than the date at which the magma erupted. For example lavas dated by K-Ar that are historic in age, usually show 1 to 2 my old ages due to trapped Ar.

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Such trapped Ar is not problematical when the age of the rock is in hundreds of millions of years. The dating equation used for K-Ar is: Some of the problems associated with K-Ar dating are Excess argon. This is only a problem when dating very young rocks or in dating whole rocks instead of mineral separates. Minerals should not contain any excess Ar because Ar should not enter the crystal structure of a mineral when it crystallizes.

Thus, it always better to date minerals that have high K contents, such as sanidine or biotite.

## Radiometric Dating

If these are not present, Plagioclase or hornblende. If none of these are present, then the only alternative is to date whole rocks. Some 40 Ar could be absorbed onto the sample surface. This can be corrected for. Most minerals will lose Ar on heating above o C - thus metamorphism can cause a loss of Ar or a partial loss of Ar which will reset the atomic clock.

If only partial loss of Ar occurs then the age determined will be in between the age of crystallization and the age of metamorphism. If complete loss of Ar occurs during metamorphism, then the date is that of the metamorphic event. The problem is that there is no way of knowing whether or not partial or complete loss of Ar has occurred. Examples of questions on this material that could be asked on an exam. Prior to the best and most accepted age of the Earth was that proposed by Lord Kelvin based on the amount of time necessary for the Earth to cool to its present temperature from a completely liquid state.

## Radiometric dating - Wikipedia

Principles of Radiometric Dating Radioactive decay is described in terms of the probability that a constituent particle of the nucleus of an atom will escape through the potential Energy barrier which bonds them to the nucleus. Thus, if we start out with 1 gram of the parent isotope, after the passage of 1 half-life there will be 0. Some examples of isotope systems used to date geologic materials. To see how we actually use this information to date rocks, consider the following: To account for this, we first note that there is an isotope of Sr, 86 Sr, that is: If we divide equation 4 through by the amount of 86 Sr, then we get: Note also that equation 5 has the form of a linear equation, i.

How can we use this? In nature, however, each mineral in the rock is likely to have a different amount of 87 Rb. Thus, once the rock has cooled to the point where diffusion of elements does not occur, the 87 Rb in each mineral will decay to 87 Sr, and each mineral will have a different 87 Rb and 87 Sr after passage of time.

The Concordia curve can be calculated by defining the following: The discordia is often interpreted by extrapolating both ends to intersect the Concordia. Pb leakage is the most likely cause of discordant dates, since Pb will be occupying a site in the crystal that has suffered radiation damage as a result of U decay. U would have been stable in the crystallographic site, but the site is now occupied by by Pb. An event like metamorphism could heat the crystal to the point where Pb will become mobile.

Another possible scenario involves U leakage, again possibly as a result of a metamorphic event. U leakage would cause discordant points to plot above the cocordia. The Age of the Earth A minimum age of the Earth can be obtained from the oldest known rocks on the Earth. So far, the oldest rock found is a tonalitic Gneiss metamorphic rock rock from the Northwest Territories, Canada, with an age of 3.

This gives us only a minimum age of the Earth. Is it likely that we will find a rock formed on the Earth that will give us the true age of the Earth? From the Pb-Pb isochron equation 11 we can make some arguments about meteorites. First, it appears that meteorites have come from somewhere in the solar system, and thus may have been formed at the same time the solar system and thus the Earth formed.

## Radiometric dating

If all of the meteorites formed at the same time and have been closed to U and Pb since their formation, then we can use the Pb-Pb isochron to date all meteorites. First, however, we need to know the initial ratios of the Pb isotopes. We recognize two major types of meteorites: Fe- meteorites and stony or chondritic meteorites The Fe meteorites contain the mineral troilite FeS that has no U.

Since the mineral troilite contains no U, all of the Pb present in the troilite is the Pb originally present, and none of it has been produced by U decay. We can then determine the Pb ratios in other meteorites and see if they fall on a Pb-Pb isochron that passes through the initial ratios determined from troilite in Fe-meteorites. The slope of this isochron, known as the Geochron, gives an age of 4. K-Ar Dating 40 K is the radioactive isotope of K, and makes up 0. Thus the ratio of 14 C to 14 N in the Earth's atmosphere is constant.

Living organisms continually exchange Carbon and Nitrogen with the atmosphere by breathing, feeding, and photosynthesis. When an organism dies, the 14 C decays back to 14 N, with a half-life of 5, years. Measuring the amount of 14 C in this dead material thus enables the determination of the time elapsed since the organism died. Radiocarbon dates are obtained from such things as bones, teeth, charcoal, fossilized wood, and shells.

Because of the short half-life of 14 C, it is only used to date materials younger than about 70, years. The original atom is referred to as the parent and the following decay products are referred to as the daughter. Carbon is a very special element. In combination with hydrogen it forms a component of all organic compounds and is therefore fundamental to life. Libby of the University of Chicago predicted the existence of carbon before it was actually detected and formulated a hypothesis that radiocarbon might exist in living matter.

Willard Libby and his colleague Ernest Anderson showed that methane collected from sewage works had measurable radiocarbon activity whereas methane produced from petroleum did not. Perseverance over three years of secret research to develop the radiocarbon method came into fruition and in Libby received the Nobel Prize for chemistry for turning his vision into an invaluable tool.

Carbon has three naturally occurring isotopes , with atoms of the same atomic number but different atomic weights. They are 12 C, 13 C and 14 C.

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C being the symbol for carbon and the isotopes having atomic weights 12, 13 and The three isotopes don't occur equally either, The radiocarbon dating method is based on the rate of decay of the radioactive or unstable 14 C which is formed in the upper atmosphere through the effect of cosmic ray neutrons upon nitrogen The reaction is as follows: After formation the three carbon isotopes combine with oxygen to form carbon dioxide. The carbon dioxide mixes throughout the atmosphere, dissolves in the oceans, and via photosynthesis enters the food chain to become part of all plants and animals.

In principle the uptake rate of 14 C by animals is in equilibrium with the atmosphere. As soon as a plant or animal dies, they stop the metabolic function of carbon uptake and with no replenishment of radioactive carbon, the amount of 14 C in their tissues starts to reduce as the 14 C atoms decay. Libby and his colleagues first discovered that this decay occurs at a constant rate. They found that after years, half the 14 C in the original sample will have decayed and after another years, half of that remaining material will have decayed, and so on.

This became known as the Libby half-life. After 10 half-lives, there is a very small amount of radioactive carbon present in a sample. At about 50 to 60 years, the limit of the technique is reached beyond this time, other radiometric techniques must be used for dating. By measuring the 14 C concentration or residual radioactivity of a sample whose age is not known, it is possible to obtain the number of decay events per gram of Carbon. By comparing this with modern levels of activity wood corrected for decay to AD and using the measured half-life it becomes possible to calculate a date for the death of the sample.

As a result of atomic bomb usage, 14 C was added to the atmosphere artificially. This affects the 14 C ages of objects younger than Any material which is composed of carbon may be dated. Herein lies the true advantage of the radiocarbon method. Potassium-Argon K-Ar dating is the most widely applied technique of radiometric dating. Potassium is a component in many common minerals and can be used to determine the ages of igneous and metamorphic rocks.

The Potassium-Argon dating method is the measurement of the accumulation of Argon in a mineral.

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It is based on the occurrence of a small fixed amount of the radioisotope 40 K in natural potassium that decays to the stable Argon isotope 40 Ar with a half-life of about 1, million years. In contrast to a method such as Radiocarbon dating, which measures the disappearance of a substance, K-Ar dating measures the accumulation of Argon in a substance from the decomposition of potassium.