Radiometric dating

by Frank Steiger
Copyright © 1996

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." If a half life is equal to one year, then one half of the radioactive element will have decayed in the first year after the mineral was formed; one half of the remainder will decay in the next year (leaving one-fourth remaining), and so forth. 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).

If we knew the fraction of a radioactive element still remaining in a mineral, it would be a simple matter to calculate its age by the formula

                   log F = N/Hlog(1/2)       (1)

                where: F = fraction remaining
                       N = number of years
                   and H = half life.
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 238 is an isotope of uranium 235, 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." A nuclide refers to a group of atoms with specified atomic number and mass number.


The element potassium (symbol K) has three nuclides, K39, K40, and K41. Only K40 is radioactive; the other two are stable. K40 can decay in two different ways. It can break down into either calcium or argon. 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 40 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 40 must have been formed as the result of radioactive decay. F, the fraction of K 40 remaining, is equal to the amount of potassium 40 in the sample, divided by the sum of potassium 40 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.


The nuclide rubidium-87 decays, with a half-life of 48.8 billion years, to strontium-87. Strontium-87 is a stable element; it does not undergo further radioactive decay. (Do not confuse with the highly radioactive isotope, strontium-90.) Strontium occurs naturally as a mixture of several nuclides, including the stable isotope strontium-86. 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 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-87 forms, its ratio to strontium-86 will increase. We express the amounts of rubidium-87 and strontium-87 as ratios to an unchanging content of strontium-86.

Because of radioactivity, the fraction of rubidium-87 decreases from an initial value of 1.00, approaching zero with increasing number of half lives. At the same time, the fraction of strontium-87 increases from zero and approaches 1.00 with increasing number of half-lives. The two curves cross each other at half life = 1.00. At this point the fraction of Rb87 = Sr87 = 0.500; at half life = 2.00, Rb87 = 0.25 and Sr87 =0.75, and so on. These curves are illustrated in Fig 17.2 of p. 131, of Strahler, "Science and Earth History."

Points are taken from these curves and a plot of fraction Sr-87 (as ordinate) vs. Rb-87 (as abscissa) is made. It turns out to be a straight line with a slope of -1.00. The corresponding half lives for each plotted point are marked on the line and identified. It can readily be 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-87 is plotted against the fraction of strontium-87 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 17.5, page 133. If the strontium-87 isotope was not present in the mineral at the time is 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 17.3. 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 17.5. Thus it is possible to correct for strontium-87 initially present.

Comparing figures 17.2 and 17.3, it is obvious that the steeper the slope, the greater the number of half-lives, and the older the sample. The age of the sample can be obtained by choosing the origin at the y intercept. In Fig 17.5 the isochron line has a slope of approximately 0.005/0.105 = 0.048 and intersects the Sr87 axis at 0.699 = y intercept. Note that the amounts of rubidium 87 and strontium 87 are given as ratios to an inert isotope, strontium 86. However, in calculating the ratio of Rb87 to Sr87, we can use a simple analytical geometry solution to the plotted data.

Referring to Fig. 17.3, the slope of the strontium-87/rubidium-87 line is -1, and y = 1-x. Therefore, with the origin placed at the y intercept, the intersection of the Rb/Sr line and the isochron line can be obtained by solving the equation 1-x = 0.048x, giving the result x = 0.954, which is the rubidium-87/strontium-86 ratio (strontium 86, not strontium 87) corresponding the given isochron line. (The corresponding strontium-87/strontium-86 ratio is 1.0000- 0.954 = 0.046) Thus the fraction of Rb87 decayed is 0.954.

Since the half-life of Rb87 is 48.8 billion years, we can substitute in the half-life equation: 0.954 = (1.2) raised to the power (age/48.8), where age = age in billions of years. Therefore:

               log(.954) = (age/48.8)(log 1/2)
             and:    age = 3.3 billion years
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. Samples can be contaminated and/or improperly prepared. 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.

Whitcomb and Morris of the Institute for Creation Research attack the mathematics of radioactive dating on pp 358 and 359 of "The Genesis Flood." Their calculations are based on assuming a straight line relationship for radioactive decay instead of decaying by half-lives, and therefore are completely meaningless. The authors were evidently aware that they were presenting bogus mathematics, since they describe the calculation as being "somewhat simplified," referring to a footnote: "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."

Of course, this is total nonsense!

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