Formula radiometric dating

Radiometric dating is a means of determining the "age" of a mineral specimen by in a mineral, it would be a simple matter to calculate its age by the formula.
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The half-life of a radioactive isotope describes the amount of time that it takes half of the isotope in a sample to decay. In the case of radiocarbon dating, the half-life of carbon 14 is 5, years.

Radiometric Dating

This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50, years ago. After 5, years, the amount of carbon 14 left in the body is half of the original amount. If the amount of carbon 14 is halved every 5, years, it will not take very long to reach an amount that is too small to analyze. When finding the age of an organic organism we need to consider the half-life of carbon 14 as well as the rate of decay, which is —0.

Carbon 14 Dating - Math Central

How old is the fossil? We can use a formula for carbon 14 dating to find the answer. So, the fossil is 8, years old, meaning the living organism died 8, years ago. 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. Therefore the relative amounts of rubidium and strontium can be determined by expressing their ratios to strontium 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 minerals , if 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 If the strontium isotope was not present in the mineral at the time it was formed from the molten magma, then the geometry of the plotted isochron lines requires that they all intersect the origin, as shown in figure 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.

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

Radiometric Dating: Methods, Uses & the Significance of Half-Life

Since the half-life of Rb87 is 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. Of course, test procedures, like anything else, can be screwed up. Mistakes can be made at the time a procedure is first being developed.

Creationists seize upon any isolated reports of improperly run tests and try to categorize them as representing general shortcomings of the test procedure. This like saying if my watch isn't running, then all watches are useless for keeping time. Creationists also attack radioactive dating with the argument that half-lives were different in the past than they are at present.

There is no more reason to believe that than to believe that at some time in the past iron did not rust and wood did not burn. Furthermore, astronomical data show that radioactive half-lives in elements in stars billions of light years away is the same as presently measured. On pages and of The Genesis Flood, creationist authors Whitcomb and Morris present an argument to try to convince the reader that ages of mineral specimens determined by radioactivity measurements are much greater than the "true" i.

The mathematical procedures employed are totally inconsistent with reality. Henry Morris has a PhD in Hydraulic Engineering, so it would seem that he would know better than to author such nonsense. Apparently, he did know better, because he qualifies the exposition in a footnote stating:.

Radioactive Dating

This discussion is not meant to be an exact exposition of radiogenic age computation; the relation is mathematically more complicated than the direct proportion assumed for the illustration. Nevertheless, the principles described are substantially applicable to the actual relationship. Morris states that the production rate of an element formed by radioactive decay is constant with time. This is not true, although for a short period of time compared to the length of the half life the change in production rate may be very small.

Radioactive elements decay by half-lives. At the end of the first half life, only half of the radioactive element remains, and therefore the production rate of the element formed by radioactive decay will be only half of what it was at the beginning. The authors state on p.

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If these elements existed also as the result of direct creation, it is reasonable to assume that they existed in these same proportions. Say, then, that their initial amounts are represented by quantities of A and cA respectively.


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Morris makes a number of unsupported assumptions: This is not correct; radioactive elements decay by half lives, as explained in the first paragraphs of this post. There is absolutely no evidence to support this assumption, and a great deal of evidence that electromagnetic radiation does not affect the rate of decay of terrestrial radioactive elements. He sums it up with the equations: He then calculates an "age" for the first element by dividing its quantity by its decay rate, R; and an "age" for the second element by dividing its quantity by its decay rate, cR.

It's obvious from the above two equations that the result shows the same age for both elements, which is: