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. 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. 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. The decay process takes time and there is value in being able to express the rate at which a process occurs.

Half-lives can be calculated from measurements on the change in mass of a nuclide and the time it takes to occur.

The only thing we know is that in the time of that substance's half-life, half of the original nuclei will disintegrate. Although chemical changes were sped up or slowed down by changing factors such as temperature, concentration, etc, these factors have no effect on half-life. Each radioactive isotope will have its own unique half-life that is independent of any of these factors. For cobalt, which has a half-life of 5. Image used with permission CC-BY 4. The half-lives of many radioactive isotopes have been determined and they have been found to range from extremely long half-lives of 10 billion years to extremely short half-lives of fractions of a second.

The table below illustrates half-lives for selected elements. In addition, the final elemental product is listed after the decal process. Knowing how an element decays alpha, beta, gamma can allow a person to shield their body appropriately from excess radiation. The quantity of radioactive nuclei at any given time will decrease to half as much in one half-life. Remember, the half-life is the time it takes for half of your sample, no matter how much you have, to remain. The only difference is the length of time it takes for half of a sample to decay. Understand how decay and half life work to enable radiometric dating.

Play a game that tests your ability to match the percentage of the dating element that remains to the age of the object. There are two types of half-life problems we will perform. One format involves calculating a mass amount of the original isotope. Using the equation below, we can determine how much of the original isotope remains after a certain interval of time. The half-life of this isotope is 10 days. For example, carbon has a half-life of 5, years and is used to measure the age of organic material.

The ratio of carbon to carbon in living things remains constant while the organism is alive because fresh carbon is entering the organism whenever it consumes nutrients. When the organism dies, this consumption stops, and no new carbon is added to the organism. As time goes by, the ratio of carbon to carbon in the organism gradually declines, because carbon radioactively decays while carbon is stable.

Analysis of this ratio allows archaeologists to estimate the age of organisms that were alive many thousands of years ago. Along with stable carbon, radioactive carbon is taken in by plants and animals, and remains at a constant level within them while they are alive. So, radiocarbon dating can be used to find the age of things that were once alive, like the Iceman. And this would also include things like trees and plants, which give us paper and cloth.

So, radiocarbon dating is also useful for determining the age of relics, such the Dead Sea Scrolls and the Shroud of Turin. With radiocarbon dating, the amount of the radioactive isotope carbon is measured. Compared to some of the other radioactive isotopes we have discussed, carbon's half-life of 5, years is considerably shorter, as it decays into nitrogen Carbon is continually being created in the atmosphere due to the action of cosmic rays on nitrogen in the air.

Carbon combines with oxygen to create carbon dioxide. Because plants use carbon dioxide for photosynthesis, this isotope ends up inside the plant, and because animals eat plants, they get some as well. When a plant or an animal dies, it stops taking in carbon The existing carbon within the organism starts to decay back into nitrogen, and this starts our clock for radiocarbon dating. A scientist can take a sample of an organic material when it is discovered and evaluate the proportion of carbon left in the relic to determine its age.

Radiometric dating is a method used to date rocks and other objects based on the known decay rate of radioactive isotopes. The decay rate is referring to radioactive decay , which is the process by which an unstable atomic nucleus loses energy by releasing radiation.

## Radiometric dating

Each radioactive isotope decays at its own fixed rate, which is expressed in terms of its half-life or, in other words, the time required for a quantity to fall to half of its starting value. There are different methods of radiometric dating. Uranium-lead dating can be used to find the age of a uranium-containing mineral. Uranium decays to lead, and uranium decays to lead The two uranium isotopes decay at different rates, and this helps make uranium-lead dating one of the most reliable methods because it provides a built-in cross-check. Additional methods of radiometric dating, such as potassium-argon dating and rubidium-strontium dating , exist based on the decay of those isotopes.

Radiocarbon dating is a method used to determine the age of organic material by measuring the radioactivity of its carbon content. With radiocarbon dating, we see that carbon decays to nitrogen and has a half-life of 5, years.

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### Radioactive Dating

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Learn about half-life and how it is used in different dating methods, such as uranium-lead dating and radiocarbon dating, in this video lesson. Try it risk-free for 30 days. An error occurred trying to load this video.

## Calculating Half-Life - Chemistry LibreTexts

Try refreshing the page, or contact customer support. Register to view this lesson Are you a student or a teacher? I am a student I am a teacher. What teachers are saying about Study. Conditions of Fossil Preservation: Are you still watching? Your next lesson will play in 10 seconds. Add to Add to Add to. Want to watch this again later? What is Radioactive Dating? Principles of Radiometric Dating. Relative Dating with Fossils: Index Fossils as Indicators of Time.

Methods of Geological Dating: Numerical and Relative Dating. What is Relative Dating? What is the Age of the Solar System? Absolute Time in Geology. What is Carbon Dating?