Potassium-Argon and Rubidium-Strontium Dating Uranium is not the only isotope that can be used to date rocks; we do see additional methods of radiometric dating based on the decay of different isotopes. Radiocarbon Dating So, we see there are a number of different methods for dating rocks and other non-living things, but what if our sample is organic in nature? Try it risk-free No obligation, cancel anytime.

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Want to learn more? Select a subject to preview related courses: Lesson Summary Let's review. Learning Outcomes As a result of watching this video, you might be able to: Compare radiometric dating, radioactive decay and half-life Understand that uranium-lead dating is one of the most reliable radiometric dating methods Relate the processes of potassium-argon and rubidium-strontium dating Determine how radiocarbon dating works and recognize why it is important.

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Your goal is required. Email Email is required. Email is not a valid email. Email already in use. Cancel before and your credit card will not be charged. Your Cart is Empty. In geochronology the situation is identical. A particular rock or mineral that contains a radioactive isotope or radioisotope is analyzed to determine the number of parent and daughter isotopes present, whereby the time since that mineral or rock formed is calculated.

Of course, one must select geologic materials that contain elements with long half-lives —i. The age calculated is only as good as the existing knowledge of the decay rate and is valid only if this rate is constant over the time that elapsed. Fortunately for geochronology, the study of radioactivity has been the subject of extensive theoretical and laboratory investigation by physicists for almost a century.

The results show that there is no known process that can alter the rate of radioactive decay. By way of explanation it can be noted that since the cause of the process lies deep within the atomic nucleus, external forces such as extreme heat and pressure have no effect. The same is true regarding gravitational, magnetic , and electric fields , as well as the chemical state in which the atom resides. In short, the process of radioactive decay is immutable under all known conditions. Although it is impossible to predict when a particular atom will change, given a sufficient number of atoms, the rate of their decay is found to be constant.

The situation is analogous to the death rate among human populations insured by an insurance company. Even though it is impossible to predict when a given policyholder will die, the company can count on paying off a certain number of beneficiaries every month. The recognition that the rate of decay of any radioactive parent atom is proportional to the number of atoms N of the parent remaining at any time gives rise to the following expression:.

Converting this proportion to an equation incorporates the additional observation that different radioisotopes have different disintegration rates even when the same number of atoms are observed undergoing decay. Solution of this equation by techniques of the calculus yields one form of the fundamental equation for radiometric age determination,. Two alterations are generally made to equation 4 in order to obtain the form most useful for radiometric dating. In the first place, since the unknown term in radiometric dating is obviously t , it is desirable to rearrange equation 4 so that it is explicitly solved for t.

Half-life is defined as the time period that must elapse in order to halve the initial number of radioactive atoms. The half-life and the decay constant are inversely proportional because rapidly decaying radioisotopes have a high decay constant but a short half-life. With t made explicit and half-life introduced, equation 4 is converted to the following form, in which the symbols have the same meaning:.

Alternatively, because the number of daughter atoms is directly observed rather than N , which is the initial number of parent atoms present, another formulation may be more convenient. Since the initial number of parent atoms present at time zero N 0 must be the sum of the parent atoms remaining N and the daughter atoms present D , one can write:. Substituting this in equation 6 gives.

If one chooses to use P to designate the parent atom, the expression assumes its familiar form:. This pair of equations states rigorously what might be assumed from intuition , that minerals formed at successively longer times in the past would have progressively higher daughter-to-parent ratios. This follows because, as each parent atom loses its identity with time, it reappears as a daughter atom.

Equation 8 documents the simplicity of direct isotopic dating. The time of decay is proportional to the natural logarithm represented by ln of the ratio of D to P. In short, one need only measure the ratio of the number of radioactive parent and daughter atoms present, and the time elapsed since the mineral or rock formed can be calculated, provided of course that the decay rate is known. Likewise, the conditions that must be met to make the calculated age precise and meaningful are in themselves simple:. The rock or mineral must have remained closed to the addition or escape of parent and daughter atoms since the time that the rock or mineral system formed.

## Radiometric Dating

It must be possible to correct for other atoms identical to daughter atoms already present when the rock or mineral formed. The measurement of the daughter-to-parent ratio must be accurate because uncertainty in this ratio contributes directly to uncertainty in the age. Different schemes have been developed to deal with the critical assumptions stated above.

In uranium-lead dating , minerals virtually free of initial lead can be isolated and corrections made for the trivial amounts present. In whole-rock isochron methods that make use of the rubidium- strontium or samarium - neodymium decay schemes, a series of rocks or minerals are chosen that can be assumed to have the same age and identical abundances of their initial isotopic ratios. The results are then tested for the internal consistency that can validate the assumptions. In all cases, it is the obligation of the investigator making the determinations to include enough tests to indicate that the absolute age quoted is valid within the limits stated.

In other words, it is the obligation of geochronologists to try to prove themselves wrong by including a series of cross-checks in their measurements before they publish a result. Such checks include dating a series of ancient units with closely spaced but known relative ages and replicate analysis of different parts of the same rock body with samples collected at widely spaced localities.

The importance of internal checks as well as interlaboratory comparisons becomes all the more apparent when one realizes that geochronology laboratories are limited in number. 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.

### Radiometric Dating

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?

## Dating Methods Using Radioactive Isotopes

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. 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.