How to calculate radiometric dating

Absolute Time. Radiometric Dating: the source of the dates on the Geologic Time Scale. Radiometric Dating Calculating a Radiometric Date. t = (ln (P+D)/P)/l.
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• Radiometric dating
• K-Ar dating calculation (video) | Khan Academy
• 5.7: Calculating Half-Life
• Radioactive Dating
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Pb, we can determine the age of the rock.

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• Radioactive Dating.

This assumes that all of the lead present came from the decay of uranium If there is additional lead present, which is indicated by the presence of other lead isotopes in the sample, it is necessary to make an adjustment. Potassium-argon dating uses a similar method. K decays by positron emission and electron capture to form Ar with a half-life of 1.

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If a rock sample is crushed and the amount of Ar gas that escapes is measured, determination of the Ar K ratio yields the age of the rock. Other methods, such as rubidium-strontium dating Rb decays into Sr with a half-life of As of , the oldest known rocks on earth are the Jack Hills zircons from Australia, found by uranium-lead dating to be almost 4.

An ingenious application of half-life studies established a new science of determining ages of materials by half-life calculations.

After one half-life, a 1. Present day estimates for the age of the Earth's crust from this method is at 4 billion years. Isotopes with shorter half-lives are used to date more recent samples. Chemists and geologists use tritium dating to determine the age of water ocean and fresh. In addition, tritium dating can be useful in determining the age of wines and brandies.

The half-life of an isotope is used to describe the rate at which the isotope will decay and give off radiation. Using the half-life, it is possible to predict the amount of radioactive material that will remain after a given amount of time. Its half-life is approximately years. Skills to Develop Describe what is meant by the term half-life and what factors affect half-life.

Calculate the amount of radioactive material that will remain after an integral number of half-lives. Calculate the age of a material based upon its half-life.

Describe how carbon is used to determine the age of carbon containing objects. Give examples of other isotopes used in radioactive dating. Appreciate the half-life of isotopes involved in nuclear weapons and reactors. Rate of Radioactive Decay During natural radioactive decay, not all atoms of an element are instantaneously changed to atoms of another element.

Solution To determine the number of half-lives n , both time units must be the same. 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.

Radioactive Dating

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. 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.

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.

The creationist "argon escape" theory does not support their young earth model.

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The argon age determination of the mineral can be confirmed by measuring the loss of potassium. In old rocks, there will be less potassium present than was required to form the mineral, because some of it has been transmuted to argon. The decrease in the amount of potassium required to form the original mineral has consistently confirmed the age as determined by the amount of argon formed.

See Carbon 14 Dating in this web site. The nuclide rubidium decays, with a half life of Strontium is a stable element; it does not undergo further radioactive decay. Do not confuse with the highly radioactive isotope, strontium Strontium occurs naturally as a mixture of several nuclides, including the stable isotope strontium If three different strontium-containing minerals form at the same time in the same magma, each strontium containing mineral will have the same ratios of the different strontium nuclides, since all strontium nuclides behave the same chemically.

Note that this does not mean that the ratios are the same everywhere on earth. It merely means that the ratios are the same in the particular magma from which the test sample was later taken. As strontium forms, its ratio to strontium will increase. Strontium is a stable element that does not undergo radioactive change. In addition, it is not formed as the result of a radioactive decay process. The amount of strontium in a given mineral sample will not change. Therefore the relative amounts of rubidium and strontium can be determined by expressing their ratios to strontium It turns out to be a straight line with a slope of The corresponding half lives for each plotted point are marked on the line and identified.

It can be readily seen from the plots that when this procedure is followed with different amounts of Rb87 in different minerals , if the plotted half life points are connected, a straight line going through the origin is produced. These lines are called "isochrons". The steeper the slope of the isochron, the more half lives it represents. When the fraction of rubidium is plotted against the fraction of strontium for a number of different minerals from the same magma an isochron is obtained.

If the points lie on a straight line, this indicates that the data is consistent and probably accurate. An example of this can be found in Strahler, Fig If the strontium isotope was not present in the mineral at the time it was formed from the molten magma, then the geometry of the plotted isochron lines requires that they all intersect the origin, as shown in figure However, if strontium 87 was present in the mineral when it was first formed from molten magma, that amount will be shown by an intercept of the isochron lines on the y-axis, as shown in Fig Thus it is possible to correct for strontium initially present.

The age of the sample can be obtained by choosing the origin at the y intercept. Note that the amounts of rubidium 87 and strontium 87 are given as ratios to an inert isotope, strontium However, in calculating the ratio of Rb87 to Sr87, we can use a simple analytical geometry solution to the plotted data. Again referring to Fig. Since the half-life of Rb87 is