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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, magneticand electric fieldsas 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.

Proportion 1 becomes:. Solution of this equation by techniques of the calculus yields one form of the fundamental equation for radiometric age determination, in which N 0 is the number of radioactive atoms present in a sample at time zero, N is the number of radioactive atoms present in the sample today, e is the base of natural logarithms equal to about 2. Two alterations are generally made to equation 4 in order to obtain the form most useful for radiometric dating.

# Principles of radiometric age dating

In the first place, since the unknown term in radiometric dating is obviously tit 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 Nwhich 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 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: and.

Zircon can also survive metamorphism. Chemically, zircon usually contains high amounts of U and low amounts of Pb, so that large amounts of radiogenic Pb are produced. 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 theand 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. 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.

Because it is unstable, occasionally C 14 undergoes radioactive decay to become stable nitrogen N The amount of time it takes for half of the parent isotopes to decay into daughter isotopes is known as the half-life of the radioactive isotope. Most isotopes found on Earth are generally stable and do not change.

However some isotopes, like 14 C, have an unstable nucleus and are radioactive. This means that occasionally the unstable isotope will change its number of protons, neutrons, or both. This change is called radioactive decay. For example, unstable 14 C transforms to stable nitrogen 14 N.

The atomic nucleus that decays is called the parent isotope. The product of the decay is called the daughter isotope. In the example, 14 C is the parent and 14 N is the daughter.

Some minerals in rocks and organic matter e. The abundances of parent and daughter isotopes in a sample can be measured and used to determine their age.

This method is known as radiometric dating. Some commonly used dating methods are summarized in Table 1. The rate of decay for many radioactive isotopes has been measured and does not change over time.

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Thus, each radioactive isotope has been decaying at the same rate since it was formed, ticking along regularly like a clock. For example, when potassium is incorporated into a mineral that forms when lava cools, there is no argon from previous decay argon, a gas, escapes into the atmosphere while the lava is still molten. When that mineral forms and the rock cools enough that argon can no longer escape, the "radiometric clock" starts. Over time, the radioactive isotope of potassium decays slowly into stable argon, which accumulates in the mineral.

The amount of time that it takes for half of the parent isotope to decay into daughter isotopes is called the half-life of an isotope Figure 5b. When the quantities of the parent and daughter isotopes are equal, one half-life has occurred. If the half life of an isotope is known, the abundance of the parent and daughter isotopes can be measured and the amount of time that has elapsed since the "radiometric clock" started can be calculated.

For example, if the measured abundance of 14 C and 14 N in a bone are equal, one half-life has passed and the bone is 5, years old an amount equal to the half-life of 14 C. If there is three times less 14 C than 14 N in the bone, two half lives have passed and the sample is 11, years old.

However, if the bone is 70, years or older the amount of 14 C left in the bone will be too small to measure accurately. Thus, radiocarbon dating is only useful for measuring things that were formed in the relatively recent geologic past. Luckily, there are methods, such as the commonly used potassium-argon K-Ar metho that allows dating of materials that are beyond the limit of radiocarbon dating Table 1.

Comparison of commonly used dating methods. Radiation, which is a byproduct of radioactive decay, causes electrons to dislodge from their normal position in atoms and become trapped in imperfections in the crystal structure of the material.

Dating methods like thermoluminescenceoptical stimulating luminescence and electron spin resonancemeasure the accumulation of electrons in these imperfections, or "traps," in the crystal structure of the material. If the amount of radiation to which an object is exposed remains constant, the amount of electrons trapped in the imperfections in the crystal structure of the material will be proportional to the age of the material.

These methods are applicable to materials that are up to aboutyears old. However, once rocks or fossils become much older than that, all of the "traps" in the crystal structures become full and no more electrons can accumulate, even if they are dislodged.

The Earth is like a gigantic magnet. It has a magnetic north and south pole and its magnetic field is everywhere Figure 6a.

Just as the magnetic needle in a compass will point toward magnetic north, small magnetic minerals that occur naturally in rocks point toward magnetic north, approximately parallel to the Earth's magnetic field. Because of this, magnetic minerals in rocks are excellent recorders of the orientation, or polarityof the Earth's magnetic field.

Small magnetic grains in rocks will orient themselves to be parallel to the direction of the magnetic field pointing towards the north pole. Black bands indicate times of normal polarity and white bands indicate times of reversed polarity.

Through geologic time, the polarity of the Earth's magnetic field has switched, causing reversals in polarity. The Earth's magnetic field is generated by electrical currents that are produced by convection in the Earth's core.

During magnetic reversals, there are probably changes in convection in the Earth's core leading to changes in the magnetic field. The Earth's magnetic field has reversed many times during its history. When the magnetic north pole is close to the geographic north pole as it is todayit is called normal polarity.

### Radiometric Dating: Carbon-14 and Uranium-238

Reversed polarity is when the magnetic "north" is near the geographic south pole. Using radiometric dates and measurements of the ancient magnetic polarity in volcanic and sedimentary rocks termed paleomagnetismgeologists have been able to determine precisely when magnetic reversals occurred in the past.

Combined observations of this type have led to the development of the geomagnetic polarity time scale GPTS Figure 6b.

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The GPTS is divided into periods of normal polarity and reversed polarity. Geologists can measure the paleomagnetism of rocks at a site to reveal its record of ancient magnetic reversals.

Every reversal looks the same in the rock record, so other lines of evidence are needed to correlate the site to the GPTS.

Dating - Dating - Principles of isotopic dating: All absolute isotopic ages are based on radioactive decay, a process whereby a specific atom or isotope is converted into another specific atom or isotope at a constant and known rate. Most elements exist in different atomic forms that are identical in their chemical properties but differ in the number of neutral particles-i.e., neutrons-in. Jul 13,   The key difference between relative dating and radiometric dating is that the dating cannot provide actual numerical dates whereas the radiometric dating can provide actual numerical dates. Relative dating and radiometric dating are two types of parameters that we use to describe the age of geological features and to determine the relative order of past events. Developed in the last century mainly to determine the absolute ages of rocks and minerals, radiometric dating now plays a central role in many modern disciplines. It focuses on the essential principles of radiometric dating to enable the readers to understand and analyse radiometric dating results generated by thatliz.com by: 2.

Information such as index fossils or radiometric dates can be used to correlate a particular paleomagnetic reversal to a known reversal in the GPTS. Once one reversal has been related to the GPTS, the numerical age of the entire sequence can be determined. Using a variety of methods, geologists are able to determine the age of geological materials to answer the question: "how old is this fossil?

These methods use the principles of stratigraphy to place events recorded in rocks from oldest to youngest. Absolute dating methods determine how much time has passed since rocks formed by measuring the radioactive decay of isotopes or the effects of radiation on the crystal structure of minerals.

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Paleomagnetism measures the ancient orientation of the Earth's magnetic field to help determine the age of rocks. Deino, A.

The first radiometric dating of the Yuanmou Homo erectus site, one of the oldest early human sites in China. Isochron burial dating reveals an age of ± My for a gravel bed in the Yuanmou formation. Our result is consistent with the most recent paleomagnetic stratigraphy of My for the Yuanmou H. erectus fossils. radiocarbon dating: Radiometric dating technique that uses the decay of 14C in organic material, such as wood or bones, to determine the absolute age of the material. radiometric dating. What principles are used to determine the relative geologic ages and for interpreting Earth history? A can often better define the age of a rock unit due to the overlapping of various life spans. What is being measured in radiometric dating is _. A. when the stable daughter isotope was formed.

Evolutionary Anthropology 6 : Faure, G. Isotopes: Principles and Applications. Third Edition. New York: John Wiley and Sons Gradstein, F.

The Geologic Time Scale2-volume set.

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