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If you want to know how old someone or something is, you can generally rely on some combination of simply asking questions or Googling to arrive at an accurate answer. This applies to everything from the age of a classmate to the number of years the United States has existed as a sovereign nation and counting as of But what about the ages of objects of antiquity, from a newly discovered fossil to the very age of the Earth itself? Sure, you can scour the Internet and learn rather quickly that the scientific consensus pins the age of of the planet at about 4. But Google didn't invent this number; instead, human ingenuity and applied physics have provided it.

She declares, "I guess you went shopping about three days ago. Because your roommate eats half of the chips on any given day, and not a fixed number, the carton must have held 20 chips the day before, 40 the day before that, and 80 the day before that. Calculations involving radioactive isotopes are more formal but follow the same basic principle: If you know the half-life of the radioactive element and can measure how much of each isotope is present, you can figure out the age of the fossil, rock or other entity it comes from.

Elements that have half-lives are said to obey a first-order decay process. They have what is known as a rate constant, usually denoted by k. The relationship between the number of atoms present at the start N 0the number present at the time of measurement N the elapsed time t, and the rate constant k can be written in two mathematically equivalent ways:.

In addition, you may wish to know the activity A of a sample, typically measured in disintegrations per second or dps. This is expressed simply as:.

You don't need to know how these equations are derived, but you should be prepared to use them so solve problems involving radioactive isotopes.

Scientists interested in figuring out the age of a fossil or rock analyze a sample to determine the ratio of a given radioactive element's daughter isotope or isotopes to its parent isotope in that sample. With the element's decay rate, and hence its half-life, known in advance, calculating its age is straightforward.

The trick is knowing which of the various common radioactive isotopes to look for. This in turn depends in the approximate expected age of the object because radioactive elements decay at enormously different rates. Also, not all objects to be dated will have each of the elements commonly used; you can only date items with a given dating technique if they include the needed compound or compounds.

Uranium-lead U-Pb dating: Radioactive uranium comes in two forms, uranium and uranium The number refers to the number of protons plus neutrons.

Uranium's atomic number is 92, corresponding to its number of protons. The half-life of uranium is 4. Because these differ by a factor of almost seven recall that a billion is 1, times a millionit proves a "check" to make sure you're calculating the age of the rock or fossil properly, making this among the most precise radiometric dating methods.

The long half-lives make this dating technique suitable for especially old materials, from about 1 million to 4. U-Pb dating is complex because of the two isotopes in play, but this property is also what makes it so precise. The method is also technically challenging because lead can "leak" out of many types of rocks, sometimes making the calculations difficult or impossible.

U-Pb dating is often used to date igneous volcanic rocks, which can be hard to do because of the lack of fossils; metamorphic rocks; and very old rocks.

All of these are hard to date with the other methods described here.

These biblically-implied abrupt physical changes in the earth are largely ignored in radiometric dating, which may be the source of the OE and YE discrepancy. These physical changes also affect the assumptions in radiocarbon dating and ice core dating. The Disadvantages Radiocarbon Dating may come in as a very handy tool to utilize, but it also has its flaws. One of the most important flaws is that scientists are only able to date back till. Feb 29,   The limitations of radiometric dating can be split into two general categories, analytical limitations and natural limitations. Analytical limitations encompass the limitations of the machinery that is being used to date a material. For example, you may want to date a zircon #(ZrSiO_4)# crystal using a secondary ion microprobe (SIMS). This technique bombards the sample, slowly drawing .

Rubidium-strontium Rb-Sr dating: Radioactive rubidium decays into strontium with a half -life of Not surprisingly, Ru-Sr dating is used to date very old rocks as old as the Earth, in fact, since the Earth is "only" around 4. Strontium exists in other stable i.

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. Radiometric dating is a means of determining the age of very old objects, including the Earth itself. Radiometric dating depends on the decay of isotopes, which are different forms of the same element that include the same number of protons but different numbers of neutrons in their atoms. Radiocarbon dating has somehow avoided collapse onto its own battered foundation, and now lurches onward with feigned consistency. The implications of pervasive contamination and ancient variations in carbon levels are steadfastly ignored by those who base their argument upon the dates.

But because rubidium is abundant in the Earth's crust, the concentration of strontium is much higher than that of the other isotopes of strontium.

Scientists can then compare the ratio of the strontium to the total amount of stable strontium isotopes to calculate the level of decay that produces the detected concentration of strontium This technique is often used to date igneous rocks and very old rocks.

Potassium-argon K-Ar dating: The radioactive potassium isotope is K, which decays into both calcium Ca and argon Ar in a ratio of Argon is a noble gas, which means that it is nonreactive and would not be a part of the initial formation of any rocks or fossils.

Any argon found in a rocks or fossils therefore has to be the result of this kind of radioactive decay. The half-life of potassium is 1. Potassium is very abundant in the Earth, making it great for dating because it is found in some levels in most kinds of samples.

It is good for dating igneous rocks volcanic rocks. Carbon C dating: Carbon enters organisms from the atmosphere. When the organism dies, no more of the carbon isotope can enter the organism, and it will begin to decay starting at that point. Carbon decays into nitrogen in the shortest half-life of all the methods 5, yearswhich makes it perfect for dating new or recent fossils.

It is mostly only used for organic materials, that is, animal and plant fossils. 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. Atmospheric Argon. Some 40 Ar could be absorbed onto the sample surface.

This can be corrected for. Metamorphism or alteration.

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. Radiometric Dating. 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.

### How Does Radiometric Dating Work? - Ars Technica

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 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?

Possible errors in dating isochron 6. Requires highly radiometric specialists 3. No gain or loss of parent or daughter isotopes by any disadvantages are than radioactive decay closed system. Are sources of error such radioometric leakage of daughter product and .

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.

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. Other Uses of Isotopes Radioactivity is an important heat source in the Earth.

Elements like K, U, Th, and Rb occur in quantities large enough to release a substantial amount of heat through radioactive decay. Thus radioactive isotopes have potential as fuel for such processes as mountain building, convection in the mantle to drive plate tectonics, and convection in the core to produce the Earth's magnetic Field.

Initial isotopic ratios are useful as geochemical tracers. Such tracers can be used to determine the origin of magmas and the chemical evolution of the Earth.

Short-lived isotopes Isotopes made during nucleosynthesis that have nearly completely decayed away can give information on the time elapsed between nucleosynthesis and Earth Formation. Ratios of stable, low mass isotopes, like those of O, S, C, and H can be used as tracers, as well as geothermometers, since fractionation of light isotopes can take place as a result of chemical process. We can thus use these ratios of light isotopes to shed light on processes and temperatures of past events.

Radioactivity is a source of energy and thus can be exploited for human use - good and bad. Examples of questions on this material that could be asked on an exam Which isotopic systems are most useful for radiometric dating and what are the limitations of each?

What is an isochron and what information can be obtained from an isochron? Why is zircon the preferred mineral for obtainting U - Pb dates? What is the Concordia, how is it used, and what information can be obtained from discordant dates? How does radiocarbon dating differ from the other methods of radiometric dating?