# Theme, will radiometric dating calculations agree

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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. 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.

On the other end of the spectrum we have Uranium with a half-life of about years.

Radioactive decay is an exponential process, meaning that the quantity of matter decreases at a rate proportional to its current value.

The most intuitive mathematical description of the rate of decay is half-life, which our half-life calculator can calculate.

This is the equation for the relation between half-life, mean lifetime and the decay constant:. As you can see, conversion between these three is fairly trivial mathematically, and our decay calculator will handle it for you. This is what is commonly referred to as "carbon dating". Let us say that you have a sample that you want to carbon date. Plugging the numbers in the formula above, you will get that the organism was decaying for about 7, years, which result can easily be verified in our calculator.

The formula for calculating the time elapsed from the beginning of the decay process to the current moment, or a chosen moment in the future, relative to the beginning of the decay is calculated using the formula:.

This is the equation used in our half-life calculator as well.

This equation is used in the decay calculator when solving for half-life time. The applications of half-life calculation and exponential decay are many, as it has uses in electrostatics, chemical reaction rates, geophysics, archeology, fluid dynamics, heat transfer, optics, luminescence, pharmacology and toxicology, thermoelectricity, vibrations and, of course - radioactivity.

There are even applications in finances and routing protocols in computer science. Strontium is a stable element; it does not undergo further radioactive decay. Do not confuse with the highly radioactive isotope, strontium Strontium occurs naturally as a mixture of several nuclides, including the stable isotope strontium If three different strontium-containing minerals form at the same time in the same magma, each strontium containing mineral will have the same ratios of the different strontium nuclides, since all strontium nuclides behave the same chemically.

Note that this does not mean that the ratios are the same everywhere on earth. It merely means that the ratios are the same in the particular magma from which the test sample was later taken. As strontium forms, its ratio to strontium will increase. Strontium is a stable element that does not undergo radioactive change. In addition, it is not formed as the result of a radioactive decay process. The amount of strontium in a given mineral sample will not change.

It turns out to be a straight line with a slope of The corresponding half lives for each plotted point are marked on the line and identified. It can be readily seen from the plots that when this procedure is followed with different amounts of Rb87 in different mineralsif the plotted half life points are connected, a straight line going through the origin is produced.

These lines are called "isochrons". The steeper the slope of the isochron, the more half lives it represents. When the fraction of rubidium is plotted against the fraction of strontium for a number of different minerals from the same magma an isochron is obtained. If the points lie on a straight line, this indicates that the data is consistent and probably accurate. An example of this can be found in Strahler, Fig However, if strontium 87 was present in the mineral when it was first formed from molten magma, that amount will be shown by an intercept of the isochron lines on the y-axis, as shown in Fig Thus it is possible to correct for strontium initially present.

Comparing figures The age of the sample can be obtained by choosing the origin at the y intercept.

## Age of the Earth

In Fig Note that the amounts of rubidium 87 and strontium 87 are given as ratios to an inert isotope, strontium However, in calculating the ratio of Rb87 to Sr87, we can use a simple analytical geometry solution to the plotted data. Again referring to Fig. Since the half-life of Rb87 is Therefore: log. When properly carried out, radioactive dating test procedures have shown consistent and close agreement among the various methods.

If the same result is obtained sample after sample, using different test procedures based on different decay sequences, and carried out by different laboratories, that is a pretty good indication that the age determinations are accurate.

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. Calculations involving radioactive isotopes are.

Of course, test procedures, like anything else, can be screwed up. After Henri Becquerel 's initial discovery inMarie and Pierre Curie discovered the radioactive elements polonium and radium in ; and inPierre Curie and Albert Laborde announced that radium produces enough heat to melt its own weight in ice in less than an hour.

Geologists quickly realized that this upset the assumptions underlying most calculations of the age of Earth. These had assumed that the original heat of the Earth and Sun had dissipated steadily into space, but radioactive decay meant that this heat had been continually replenished. George Darwin and John Joly were the first to point this out, in Radioactivity, which had overthrown the old calculations, yielded a bonus by providing a basis for new calculations, in the form of radiometric dating.

Ernest Rutherford and Frederick Soddy jointly had continued their work on radioactive materials and concluded that radioactivity was due to a spontaneous transmutation of atomic elements. In radioactive decay, an element breaks down into another, lighter element, releasing alpha, beta, or gamma radiation in the process. They also determined that a particular isotope of a radioactive element decays into another element at a distinctive rate. This rate is given in terms of a " half-life ", or the amount of time it takes half of a mass of that radioactive material to break down into its "decay product".

Some radioactive materials have short half-lives; some have long half-lives. Uranium and thorium have long half-lives, and so persist in Earth's crust, but radioactive elements with short half-lives have generally disappeared.

This suggested that it might be possible to measure the age of Earth by determining the relative proportions of radioactive materials in geological samples. In reality, radioactive elements do not always decay into nonradioactive "stable" elements directly, instead, decaying into other radioactive elements that have their own half-lives and so on, until they reach a stable element.

These " decay chains ", such as the uranium-radium and thorium series, were known within a few years of the discovery of radioactivity and provided a basis for constructing techniques of radiometric dating.

The pioneers of radioactivity were chemist Bertram B. Boltwood and the energetic Rutherford. Boltwood had conducted studies of radioactive materials as a consultant, and when Rutherford lectured at Yale in[28] Boltwood was inspired to describe the relationships between elements in various decay series. Late inRutherford took the first step toward radiometric dating by suggesting that the alpha particles released by radioactive decay could be trapped in a rocky material as helium atoms.

At the time, Rutherford was only guessing at the relationship between alpha particles and helium atoms, but he would prove the connection four years later. Soddy and Sir William Ramsay had just determined the rate at which radium produces alpha particles, and Rutherford proposed that he could determine the age of a rock sample by measuring its concentration of helium. He dated a rock in his possession to an age of 40 million years by this technique.

Rutherford wrote.

I came into the room, which was half dark, and presently spotted Lord Kelvin in the audience and realized that I was in trouble at the last part of my speech dealing with the age of the Earth, where my views conflicted with his.

To my relief, Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye, and cock a baleful glance at me!

Then a sudden inspiration came, and I said, "Lord Kelvin had limited the age of the Earth, provided no new source was discovered. That prophetic utterance refers to what we are now considering tonight, radium! Rutherford assumed that the rate of decay of radium as determined by Ramsay and Soddy was accurate, and that helium did not escape from the sample over time.

Rutherford's scheme was inaccurate, but it was a useful first step. Boltwood focused on the end products of decay series. Inhe suggested that lead was the final stable product of the decay of radium. It was already known that radium was an intermediate product of the decay of uranium.

Rutherford joined in, outlining a decay process in which radium emitted five alpha particles through various intermediate products to end up with lead, and speculated that the radium-lead decay chain could be used to date rock samples. Boltwood did the legwork, and by the end of had provided dates for 26 separate rock samples, ranging from 92 to million years.

He did not publish these results, which was fortunate because they were flawed by measurement errors and poor estimates of the half-life of radium. Boltwood refined his work and finally published the results in Boltwood's paper pointed out that samples taken from comparable layers of strata had similar lead-to-uranium ratios, and that samples from older layers had a higher proportion of lead, except where there was evidence that lead had leached out of the sample.

His studies were flawed by the fact that the decay series of thorium was not understood, which led to incorrect results for samples that contained both uranium and thorium.

However, his calculations were far more accurate than any that had been performed to that time. Refinements in the technique would later give ages for Boltwood's 26 samples of million to 2.

Although Boltwood published his paper in a prominent geological journal, the geological community had little interest in radioactivity. Rutherford remained mildly curious about the issue of the age of Earth but did little work on it. Robert Strutt tinkered with Rutherford's helium method until and then ceased.

However, Strutt's student Arthur Holmes became interested in radiometric dating and continued to work on it after everyone else had given up. Holmes focused on lead dating, because he regarded the helium method as umariechloepujol.comomising. He performed measurements on rock samples and concluded in that the oldest a sample from Ceylon was about 1. For example, he assumed that the samples had contained only uranium and no lead when they were formed.

More important research was published in It showed that elements generally exist in multiple variants with different masses, or " isotopes ". In the s, isotopes would be shown to have nuclei with differing numbers of the neutral particles known as " neutrons ". In that same year, other research was published establishing the rules for radioactive decay, allowing more precise identification of decay series. Many geologists felt these new discoveries made radiometric dating so complicated as to be worthless.

His work was generally ignored until the s, though in Joseph Barrella professor of geology at Yale, redrew geological history as it was understood at the time to conform to Holmes's findings in radiometric dating. Barrell's research determined that the layers of strata had not all been laid down at the same rate, and so current rates of geological change could not be used to provide accurate timelines of the history of Earth.

Holmes' persistence finally began to pay off inwhen the speakers at the yearly meeting of the British Association for the Advancement of Science came to a rough consensus that Earth was a few billion years old, and that radiometric dating was credible.

Holmes published The Age of the Earth, an Introduction to Geological Ideas in in which he presented a range of 1. No great push to embrace radiometric dating followed, however, and the die-hards in the geological community stubbornly resisted.

Radiometric dating is a means of determining the "age" of a mineral specimen by determining the relative amounts present of certain radioactive elements. By "age" we mean the elapsed time from when the mineral specimen was formed. Radioactive elements "decay" (that is, change into other elements) by "half lives.". Radiometric dating calculations. Setting the principles of information. Useful for this article on faulty. Useful for rocks. Other pieces of the beginning of a material from cosmic rays. Geologists often in such cases so little carbon is a man in organic . For those needing portability, Rad Pro for Desktop works with Windows /10 tablets. Will not work with Surface tablets running Windows RT. Calculated ActivityOriginal Activity Decay Calculations Calculation Date and/or TimeOriginal Date and/or Time Isotope Not Listed? Useful for calculating today's activity for any radioactive isotope.

They had never cared for attempts by physicists to intrude in their domain, and had successfully ignored them so far. Holmes, being one of the few people on Earth who was trained in radiometric dating techniques, was a committee member, and in fact wrote most of the final report. Thus, Arthur Holmes' report concluded that radioactive dating was the only reliable means of pinning down geological time scales.

Questions of bias were deflected by the great and exacting detail of the report. It described the methods used, the care with which measurements were made, and their error bars and limitations.

Radiometric dating continues to be the predominant way scientists date geologic timescales.

Techniques for radioactive dating have been tested and fine-tuned on an ongoing basis since the s. Forty or so different dating techniques have been utilized to date, working on a wide variety of materials. Dates for the same sample using these different techniques are in very close agreement on the age of the material. Possible contamination problems do exist, but they have been studied and dealt with by careful investigation, leading to sample preparation procedures being minimized to limit the chance of contamination.

An age of 4. The quoted age of Earth is derived, in part, from the Canyon Diablo meteorite for several important reasons and is built upon a modern understanding of cosmochemistry built up over decades of research.

Most geological samples from Earth are unable to give a direct date of the formation of Earth from the solar nebula because Earth has undergone differentiation into the core, mantle, and crust, and this has then undergone a long history of mixing and unmixing of these sample reservoirs by plate tectonicsweathering and hydrothermal circulation.

All of these processes may adversely affect isotopic dating mechanisms because the sample cannot always be assumed to have remained as a closed system, by which it is meant that either the parent or daughter nuclide a species of atom characterised by the number of neutrons and protons an atom contains or an intermediate daughter nuclide may have been partially removed from the sample, which will skew the resulting isotopic date.

To mitigate this effect it is usual to date several minerals in the same sample, to provide an isochron. Alternatively, more than one dating system may be used on a sample to check the date.

## Doudal

1. Mikazshura

I hope, you will come to the correct decision.

06.05.2020
2. Kazrat

At you a uneasy choice

08.05.2020