## Half life radioactive dating

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. The formula for the fraction remaining is one-half raised to the power given by the number of years divided by the half-life in other words raised to a power equal to the number of half-lives.

To determine the fraction still remaining, we must know both the amount now present and also the amount present when the mineral was formed.

Contrary to creationist claims, it is possible to make that determination, as the following will explain: By way of background, all atoms of a given element have the same number of protons in the nucleus; however, the number of neutrons in the nucleus can vary. An atom with the same number of protons in the nucleus but a different number of neutrons is called an isotope.

For example, uranium is an isotope of uranium, because it has 3 more neutrons in the nucleus. It has the same number of protons, otherwise it wouldn't be uranium. The number of protons in the nucleus of an atom is called its atomic number.

The sum of protons plus neutrons is the mass number. We designate a specific group of atoms by using the term "nuclide. The element potassium symbol K has three nuclides, K39, K40, and K Only K40 is radioactive; the other two are stable. K40 can decay in two different ways: The ratio of calcium formed to argon formed is fixed and known.

Therefore the amount of argon formed provides a direct measurement of the amount of potassium present in the specimen when it was originally formed. Because argon is an inert gas, it is not possible that it might have been in the mineral when it was first formed from molten magma. Any argon present in a mineral containing potassium must have been formed as the result of radioactive decay. F, the fraction of K40 remaining, is equal to the amount of potassium in the sample, divided by the sum of potassium in the sample plus the calculated amount of potassium required to produce the amount of argon found.

The age can then be calculated from equation 1. In spite of the fact that it is a gas, the argon is trapped in the mineral and can't escape. Creationists claim that argon escape renders age determinations invalid. However, any escaping argon gas would lead to a determined age younger, not older, than actual. The creationist "argon escape" theory does not support their young earth model. The argon age determination of the mineral can be confirmed by measuring the loss of potassium.

In old rocks, there will be less potassium present than was required to form the mineral, because some of it has been transmuted to argon. The decrease in the amount of potassium required to form the original mineral has consistently confirmed the age as determined by the amount of argon formed. See Carbon 14 Dating in this web site. The nuclide rubidium decays, with a half life of 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.

Therefore the relative amounts of rubidium and strontium can be determined by expressing their ratios to strontium These curves are illustrated in Fig 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. 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: 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. 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.

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: Of course, the mathematics are completely wrong. The correct relation can obtained by rearranging the equation given at the beginning of this post: For a half life of years, the following table shows the fraction remaining for various time periods: In all his mathematics, R is taken as a constant value. We may therefore set R as equal to the initial rate in the above table: Click on the web site of Dr.

Roger Wiens of Cal Tech for a detailed analysis of the accuracy of radioactive dating.