Other minerals that also show these properties, but are less commonly used in radiometric dating are Apatite and sphene. Discordant dates will not fall on the Concordia curve. Sometimes, however, numerous discordant dates from the same rock will plot along a line representing a chord on the Concordia diagram. Such a chord is called a discordia. We can also define what are called Pb-Pb Isochrons by combining the two isochron equations 7 and 8.

Since we know that the , and assuming that the Pb and Pb dates are the same, then equation 11 is the equation for a family of lines that have a slope. The answer is about 6 billion years. This argument tells when the elements were formed that make up the Earth, but does not really give us the age of the Earth.

It does, however, give a maximum age of the Earth. Is this the age of the Earth? Lunar rocks also lie on the Geochron, at least suggesting that the moon formed at the same time as meteorites. Modern Oceanic Pb - i. Pb separated from continents and thus from average crust also plots on the Geochron, and thus suggests that the Earth formed at the same time as the meteorites and moon.

Thus, our best estimate of the age of the Earth is 4.

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. 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.

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. If these are not present, Plagioclase or hornblende.

If none of these are present, then the only alternative is to date whole rocks.

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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.

## Example -- Exponential Decay

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.

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.

Radiocarbon dating can be used on samples of bone, cloth, wood and plant fibers. The half-life of a radioactive isotope describes the amount of time that it takes half of the isotope in a sample to decay. In the case of radiocarbon dating, the half-life of carbon 14 is 5, years. This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50, years ago. After 5, years, the amount of carbon 14 left in the body is half of the original amount.

If the amount of carbon 14 is halved every 5, years, it will not take very long to reach an amount that is too small to analyze. When finding the age of an organic organism we need to consider the half-life of carbon 14 as well as the rate of decay, which is —0. How old is the fossil? We can use a formula for carbon 14 dating to find the answer.