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Isochron dating is a common technique of radiometric dating and is applied to date certain events, such as crystallization , metamorphism , shock events, and differentiation of precursor melts, in the history of rocks. Isochron dating can be further separated into mineral isochron dating and whole rock isochron dating ; both techniques are applied frequently to date terrestrial and also extraterrestrial rocks meteorites. The advantage of isochron dating as compared to simple radiometric dating techniques is that no assumptions are needed about the initial amount of the daughter nuclide in the radioactive decay sequence. Indeed, the initial amount of the daughter product can be determined using isochron dating. This technique can be applied if the daughter element has at least one stable isotope other than the daughter isotope into which the parent nuclide decays.

All forms of isochron dating assume that the source of the rock or rocks contained unknown amounts of both radiogenic and non-radiogenic isotopes of the daughter element, along with some amount of the parent nuclide.

Thus, at the moment of crystallization, the ratio of the concentration of the radiogenic isotope of the daughter element to that of the non-radiogenic isotope is some value independent of the concentration of the parent. As time goes on, some amount of the parent decays into the radiogenic isotope of the daughter, increasing the ratio of the concentration of the radiogenic isotope to that of the daughter.

The greater the initial concentration of the parent, the greater the concentration of the radiogenic daughter isotope will be at some particular time.

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Thus, the ratio of the daughter to non-radiogenic isotope will become larger with time, while the ratio of parent to daughter will become smaller. An isochron diagram will only give a valid age if all samples are cogeneticwhich means they have the same initial isotopic composition that is, the rocks are from the same unit, the minerals are from the same rock, etc. The mathematical expression from which the isochron is derived is [4] [5].

Because the isotopes are measured by mass spectrometryratios are used instead of absolute concentrations since mass spectrometers usually measure the former rather than the latter. See the section on isotope ratio mass spectrometry. As such, isochrons are typically defined by the following equation, which normalizes the concentration of parent and radiogenic daughter isotopes to the concentration of a non-radiogenic isotope of the daughter element that is assumed to be constant:.

To perform dating, a rock is crushed to a fine powder, and minerals are separated by various physical and magnetic means. Each mineral has different ratios between parent and daughter concentrations. For each mineral, the ratios are related by the following equation:. The proof of 1 amounts to simple algebraic manipulation. It is useful in this form because it exhibits the relationship between quantities that actually exist at present.

If all data points lie on a straight line, this line is called an isochron. The better the fit of the data points to a line, the more reliable the resulting age estimate.

Since the ratio of the daughter and non-radiogenic isotopes is proportional to the ratio of the parent and non-radiogenic isotopes, the slope of the isochron gets steeper with time.

The change in slope from initial conditions-assuming an initial isochron slope of zero a horizontal isochron at the point of intersection intercept of the isochron with the y-axis-to the current computed slope gives the age of the rock. Whole rock isochron dating uses the same ideas but instead of different minerals obtained from one rock uses different types of rocks that are derived from a common reservoir; e.

It is possible to date the differentiation of the precursor melt which then cooled and crystallized into the different types of rocks. One of the best known isotopic systems for isochron dating is the rubidium-strontium system.

Other systems that are used for isochron dating include samarium-neodymiumand uranium-lead. Some isotopic systems based on short-living extinct radionuclides such as 53 Mn26 AlI60 Fe and others are used for isochron dating of events in the early history of the Solar System. However, methods using extinct radionuclides give only relative ages and have to be calibrated with radiometric dating techniques based on long-living radionuclides like Pb-Pb dating to give absolute ages.

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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. Specifically, a process called radiometric dating allows scientists to determine the ages of objects, including the ages of rocks, ranging from thousands of years old to billions of years old to a marvelous degree of accuracy. This relies on a proven combination of basic mathematics and knowledge of the physical properties of different chemical elements.

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

To understand radiometric dating techniquesyou first have to have an understanding of what is being measured, how the measurement is being made and the theoretical as well as practical limitations of the system of measurement being used.

As an analogy, say you find yourself wondering, "How warm or cold is it outside? You need a device to measure this activity a thermometer, of which various kinds exist.

# Parent daughter ratio radiometric dating

You also need to know when you can or cannot apply a particular type of device to the task at hand; for example, if you want to know how hot it is on the inside of an active wood stove, you probably understand that putting a household thermometer intended to measure body temperature inside the stove is not going to prove helpful.

Be aware also that for many centuries, most human "knowledge" of the age of rocks, formations such as the Grand Canyon, and everything else around you was predicated on the Genesis account of the Bible, which posits that the entire cosmos is perhaps 10, years old.

Modern geological methods have at times proven thorny in the face of such popular but quaint and scientifically unsupported notions. Radiometric dating takes advantage of the fact that the composition of certain minerals rocks, fossils and other highly durable objects changes over time. Specifically, the relative amounts of their constituent elements shift in a mathematically predictable way thanks to a phenomenon called radioactive decay.

This in turn relies on knowledge of isotopessome of which are "radioactive" that is, they spontaneously emit subatomic particles at a known rate. Isotopes are different versions of the same element e. Some things in nature disappear at a more or less constant rate, regardless of how much there is to start with and how much remains.

Radiometric Dating - Mathematical Method. Mathematical calculation of radiometric dating involves the use of a simple equation. The age of a mineral is determined from the number of parent and daughter isotopes it contains. The greater the number of daughter isotopes, the older the mineral. Ages can be determined using the equation. The ratio of the daughter isotope, neodymium, to another neodymium isotope, neodymium, is plotted against the ratio of the parent, samarium, to neodymium If different minerals from the same rock plot along a line, the slope is determined, and the age is given by the same equation as above. Radiometric dating is a means of determining the age of very old objects, including the Earth itself. 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.

For example, certain drugs, including ethyl alcohol, are metabolized by the body at a fixed number of grams per hour or whatever units are most convenient. If someone has the equivalent of five drinks in his system, the body takes five times as long to clear the alcohol as it would if he had one drink in his system.

The slope of the isochron, (?) or ?, represents the ratio of daughter to parent as used in standard radiometric dating and can be derived to calculate the age of the sample at time t. The y-intercept of the isochron line yields the initial radiogenic daughter ratio, D 0 D r e f {\displaystyle {\frac {\mathrm {D_{0}} }{\mathrm {D} _{ref}}}}. The half-life is the amount of time it takes for one half of the initial amount of the parent, radioactive isotope, to decay to the daughter isotope. Thus, if we start out with 1 gram of the parent isotope, after the passage of 1 half-life there will be gram of the parent isotope left.

Many substances, however, both biological and chemical, conform to a different mechanism: In a given time period, half of the substance will disappear in a fixed time no matter how much is present to start with. Such substances are said to have a half-life. Radioactive isotopes obey this principle, and they have wildly different decay rates.

The utility of this lies in being able to calculate with ease how much of a given element was present at the time it was formed based on how much is present at the time of measurement.

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This is because when radioactive elements first come into being, they are presumed to consist entirely of a single isotope. As radioactive decay occurs over time, more and more of this most common isotope "decays" i.

Imagine that you enjoy a certain kind of ice cream flavored with chocolate chips. You have a sneaky, but not especially clever, roommate who doesn't like the ice cream itself, but cannot resist picking out eating the chips - and in an effort to avoid detection, he replaces each one he consumes with a raisin.

He is afraid to do this with all of the chocolate chips, so instead, each day, he swipes half of the number of remaining chocolate chips and puts raisins in their place, never quite completing his diabolical transformation of your dessert, but getting closer and closer.

Say a second friend who is aware of this arrangement visits and notices that your carton of ice cream contains 70 raisins and 10 chocolate chips.

She declares, "I guess you went shopping about three days ago.

Radiometric Dating: the source of the dates on the Geologic Time Scale. Radiometric Dating. Actually a simple technique. Only two measurements are needed: 1. The parent:daughter ratio measured with a mass spectrometer. 2. The decay constant measured by a scintillometer. Basis of the Technique. Radioactive elements "decay.". Radiometric Dating. The duration of a half-life is unique for each radioactive isotope. Some examples: the half-life for the decay of potassium 40 atoms into argon 40 atoms is about billion years, the half-life for the decay of uranium into lead is about billion years, and the half-life for the decay of carbon 14 into Nitrogen. Match each of these pairs of parent-daughter isotopes used in radiometric dating to its half-life. 40K -> 39Ar: billion years 14C -> 14N: 5, years The parent-daughter elements are 14C > 14N. the ratio of carbon to carbon isotopes can indicate the relative amounts of .

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.

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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.