Science in Christian Perspective




Dating With Radioactivity
Associate Professor of Chemistry
The University of Tennessee,
16, Tennessee

From JASA 9 (September 1957): 5-8.

The fascinating impressiveness of vigorous mathematical analysis, with its atmosphere of precision and elegance, should not blind us to the defects of the premises that condition the whole process.-T. C. Chamberlin, Science, June 30 (1899).

A. Introduction

Human nature has almost always driven man to ask the question: "When?," and therefore the establishing of dates of past events is of great interest. Man has been concerned with the dates of the universe as a whole, this and other galaxies, the solar system, the earth, the moon, and things on the earth. Numerous methods have been applied to attempt answers, and these include: (1u) velocities of galaxial recession, (2u) galaxial cluster densities, (1g) star cluster densities, (2g) separations of binary stars, (3g) distribution of kinetic energy among stars, (4g) distribution of stars among stellar classes, (1s) energetics of solar system, (2s) developmental characteristics of planets. (le) recession of the moon, (2e) cooling of earth's crust, (It) salinity of ocean, (2t) sedimentation, (3t) paleontological index fossils, (4t) orogenic cycles, (5t) non-conformities in strata, (6t) tree rings, and a number of others. The second designation in the parentheses indicates the applicability of the method, (u) universe, (g) galaxy, (s) solar system, (e) earth, (t) things on earth.

With the discovery of radioactivity and the development of nuclear science, another very general and widely applicable chronological method has been made available. An absolute chronology is one that is based on a process which has been active throughout the existence of the entity (universe, galaxy, earth, etc.) and which has produced measurable results at a known unchanging rate. Radioactive decay is the phenomenon which comes the closest to meeting this requirement.

Radioactive decay of a given nuclide (nuclear species) may be described by the relation

P = P'exp(-kt),  (1)

where P is the number of atoms after time t, F is the number of atoms at time 0, and k is known as the decay constant. Suppose that this parent nuclide P decays to a stable daughter nuclide D, then the production of D will be described by

D = P' 11-exp(-kt)l,    (2)

where D is the number of atoms after time t, no atoms of D having been present at time 0. These relations assume that the decay constant has not changed during the decay process. Several direct and indirect evidences indicate that in most applications to dating that this is a warranted assumption.

Among the long-lived elements which are useful for dating are the following, their decay constants, half lives, and modes of disintegration being affixed.

Nuclide             Half life                         Decay Constant
(Z-A)                 (billions of years)        (100 billionths per year)          Mode of Decay
U-235                        0.7                                        97                                   7a,5b.g         Pb-207
K-40                          1.2                                        58                                    b (89 %       Ca-40
                                                                                        EC,g(ll%)    A-40                        
U-238                        4.5                                        15                                    8a,6b,g         Pb-206
Th-232                     13.9                                       5.0                                  6a, 4b,g         Pb-208
Rb-87                        62                                         1.1                                   b                     Sr-87 
La-138                       70                                        0.99                                 EC(94% )   Ba-138
                                                                                                                          b6%)           Ce-139
Lu-176                       75                                        0.93                                  b                   Hf-176  
Sm-147                    100                                        0.69                                  a                   Nd-143

 Since the range of applicability of a radioactive dating method is approximately 10 half lives, these are the most usable because the age of the universe is now considered to be about 6 billion years. In addition to the above nuclides, two relatively short lived ones are of importance for dating: H-3, a beta emitter with a half life of 12.4 years; and C-14, a beta emitter with a half life of 5568 years.

The numerous individual methods for ascertaining dates from nuclear phenomena may be classified under several general headings: (1) parent-daughter methods, (2) parent-parent methods, (3) daughter-daughter methods, (4) parent methods, (5) daughter methods, (6) prodigal daughter methods, and (7) daughter damage methods.

         B. Parent-Daughter Methods

If equation 2 is divided by equation 1, the following results:

D/P=: exp(kt)-l   (3)

This relation is applicable to a calculation of age or time t in a material bearing a parent nuclide and its decay product D provided: (1) the decay constant is known, (2) the determination of the ratio D/P is accurate, (3) if a series is involved equilibrium has been obtained, (4) none of the daughter or any of the intermediates between the parent and the daughter were present at zero time, and (5) no gain or loss of the parent, daughter, and/or any intermediates has occurred. Sometimes when conditions 4 and 5 have been violated, corrections can be made, but more often than not, they are inapplicable. Equation 3 has been applied to igneous rocks containing U-235, K-409 U-238, Th232, and Rb-87. In general, determinations of the nuclides are made mass spectrographically and/or by radioactivity.

In the lead methods (U-235, U-238, Th-232), the nuclides Pb-207, 206, and 208 are the products. The lead present at the time of the formation of the earth, called original lead, is composed of four isotopes 204, 206, 207, and 208, the first one not being derived from any long-lived element. Thus the presence of Pb-204 in a uranium or thorium mineral indicates that it originally bore some original lead and that all the lead was not of radiogenic origin. Sometimes a correction can be made, but obviously, much more accurate results are obtained if all the lead is radiogenic. Another possible error in this method is that each of the three decay series contains a gaseous nuclide (Rn-219, Rn-222, Rn-220), which might escape.

In the helium methods (U-235, U-238, Th-232), the measured product is the He-4 which arises from the alpha emission in the various series. This requires equation 3 to be altered by a factor of 7, 8 or 6 corresponding to the alphas emitted in the different series. In rare cases, there is helium other than radiogenic helium present, but in most instances the amount of helium is low, due chiefly to escape by diffusion. Corrections can be applied by virtue of investigations of helium retentivities of minerals, but the degree of success varies over a wide range.

In the argon method (K-40), equation 3 must be adjusted by a factor of 0.11, since that is the percentage of K-40 decaying to the inert gas. Difficulties similar to those in the helium method are encountered.

In the calcium method (K-40) equation 3 must be adjusted by a factor of 0.89. The major difficulty in this method arises from the presence of non-radiogenic Ca-40, which isotope make up 96.97% of the atoms in naturally-occurring calcium. Correction is possible by consideration of the Ca-40/Ca-44 ratio in original calcium.

In the strontium method (Rb-87), a difficulty similar to that in the calcium method is present. However, since Sr-87 makes up only 7.027o' of strontium, it is not quite so serious. Correction can be made from the Sr87/Sr-88 ratio.

Other methods which have not been tested might involve La-138, Lu-176, Sm-147, and the production of xenon from the spontaneous fission of uranium.

        C. Parent-Parent Methods

Consider an element which has two long-lived isotopes (such as U-235, 238). Writing equations similar to equation I one arrives at L=L'exp(-kt) and H=H'exp(-k't). Division of the second relation by the first results in the expression

H/L  =  H'exp(-kt)/ L'exp (-k't)     (4)

The present day ratio U-238/U-235 is about 139 and assuming that it was about 1 at the origin of the elements, the value of t which is obtained runs about 6 billion years.

        D. Daughter-Daughter Methods

When two long-lived isotopes of an element (like U-235, 238) decay to stable daughters (like Pb-207, 206), two equations similar to equation 3 may be written, D/P==exp(kt)-1 and D'/P'=exp(k't)-l. Dividing the second by the first relation, one obtains

UP/DP'  =    exp(k't)-l/exp (kt) -1       (5)

Conditions similar to those in Section B are required. Several errors are frequently recognized in this method, including loss of the two radon isotopes, uncertainty about the presence of original lead, uncertainty about the presence of old radiogenic lead, and re-distribution of elements by geological activity.

        E. Parent Methods

It is interesting to take notice of the nuclides which are radioactive and have half-life values greater than a million years. They may be divided into 3 categories: (1) those which do not occur naturally, including Zr-93, Np-237, Be-10, Pd-107, 1-129, U-236, and Sm146; (2) those which are present in small amounts,

including W-178, U-235, and K-40; and (3) those which are present in sizable amounts, including U-238, Th-232, Lu-196, Re-187, Rb-87, Sm-147, In-115, Nd144, and Bi-209. Those in the first category have half lives less than 100 million years; those in the second have half lives between 500 and 1500 million years; and those in the third have half lives greater than 4000 million years. Thus the age of the elements may be said to be of the order of a billion years.

Secondary neutrons from cosmic rays form C-14 and H-3 in the upper atmosphere by the reactions N14(n,p)C-14 and N-14(n,t)C-12. The newly born C-14 reacts to produce carbon dioxide which mixes with the carbon dioxide of the atmosphere. All living matter comes into equilibrium with this gas, and the specific activity of the carbon in both the atmosphere and the living matter is about 15 disintegrations per minute per gram of carbon. When living matter dies, it is removed from the cycle with atmospheric carbon dioxide and thus the C-14 activity decreases. Hence a measurement of the specific activity will allow an estimate of the time the material has been out of the life cycle. Several assumptions are made in this method: (1) the C-14 was uniform in the entire earth during the last 40,000 years, (2) the samples have remained unaltered since their removal from the life cycle. Difficulties inherent in the radiocarbon method are: (1) the half life is known inadequately, (2) the measurement of low activities is beset with many pitfalls, (3) certain forms of life may take up C-14 selectively, (4) bomb tests since 1945 may affect the results. However, it has been shown that none of these difficulties affects the method to more than a few percent. Calculations are made with equation 1.

Using the ideas, of the C-14 method, some dates have been ascertained with H-3. However, these are of limited value and applicability due to the relatively short half life and the very low rate of production.

        F. Daughter Methods

Most attempts to determine dates by considering all or part of certain nuclides to have arisen from radioactive processes (like He-3, A-40, Xe-129, 131, 132, 134, 136, Pb-207, 206, 208) are burdened with so many difficulties that they are impracticable at the present time.

        G. Prodigal Daughter Methods

In the decay of U-235, U-238, and Th-232 into stable lead there are numerous intermediate nuclides. In order for equation 2 to be applicable, equilibrium must have been established in the series being used. About 1 million years are required for the U-238 series, about 100 thousand for the U-235 one, and about 100 for the Th-232 one.

One of the intermediate nuclides in the U-238 series is Th-230 which has a half life of about 80,000 years and decays to Ra-226 which exhibits a half life of about 1600 years. It is known that in sea waters Th-230 is removed from solution (and thus from the U-238 to Pb-206 chain) by adsorption upon iron and manganese hydroxides which fall to the bottom as sediments.

Thus one should be able to measure the ages of sediments by the amount of Th-230, or by the amount of Ra-226 after equilibrium has been established. Several suppositions are inherent here: (1) the rate of Th-230 deposition has been constant per unit time and bottom surface, (2) the Th-230 has remained in place along with its daughter Ra-226, and (3) the deposition of other members of the series has been negligible.

        H. Daughter Damage Methods

The major portion of the energy carried by the radioactive emissions is expended in crystals by ionization and dislocation of the constituent atoms. Numerous changes are produced in the crystals, and if the changes can be measured along with the rates of change, then the time elapsed since the initiation of the damaging process can be estimated. The value of such estimates is, of course, determined by the constancy of the rate of damage.

Alpha particles discolor a number of minerals, and in fewer cases, beta particles do so. When the radioactive substance is homogeneous with respect to the mineral, the coloration is evenly distributed. When the radioactive substance is a small piece of material included in a crystal, a spherical pleochroic halo is formed around the included substance. These haloes contain various rings which are accounted for by the ranges of the alpha particles involved. Theoretically the age of the mineral may be calculated from the intensity of the coloration and the amount of radioactive substance present.

In some minerals, the structural arrangement of the constituent entities will suffer dislocations causing the material to become more amorphous in character. The degree of this may be determined by X-ray diffraction, changes in specific gravity, and alterations in the refractive indexes. Another way is by differential thermal analysis in which the mineral returns to the crystalline state at a given temperature with an evolution of heat, this heat probably corresponding to the amount of energy produced by bombardment with the emissions.

Electrons released from atoms by the action of radioactive emissions on crystals become trapped and stored in the structure. This results in an increase in the potential energy of the crystal. By slowly heating the material, the displaced electrons will fall back into position releasing energy in the form of light. By using known standards and by making radioactivity determinations, the results may be coupled with the amount of light energy to permit estimates of mineral ages.

In minerals containing U02 (or Th02), when a uranium atom disintegrates, two oxygen atoms are liberated. These may react with U02 to give U03- If the content of U02 and U03 in a mineral is known, the number of disintegrated uranium atoms may be calculated, which leads to a method for dating the substance. This method assumes a number of things which are somewhat open to question.

In uraninites and thorianites, a shrinkage of the unit cell occurs as a result of the smaller lead atom taking the place of the uranium or thorium atom. In addition, more shrinkage is produced by the oxidation of U(IV) to U(VI) by the oxygen atoms liberated in the decay of uranium. The shrinkage may be measured by X-ray methods.

Almost all of these damage methods are beset with so many sources of error that they are accurate in only very few, if any, cases.

        I. Conclusion

It can be seen that nuclear science which had its discovery couched in the field of geology (Becquerel and uranium minerals, 1896) has begun to pay back the debt by making sizable and important contributions to its parent.

Almost since the beginnings of science as we know it today, men have attempted to develop suitable methods for the measurement of ages. Many approaches have been proposed, but only relatively few have had any degree of success. Nuclear science has now made a contribution which may be said to he a major one, in fact, the most reliable results come from its hand. In short, nuclear geology has come of age. But it has just barely passed 21, and thus the field stands wide open for development after development, which are certain to come to pass.


(1) F. Faul, editor, Nuclear Geology, Wiley and Sons, Inc., New York, 1954.

(2) K. Rankama, Isotope Geology, McGraw-Hill Book Co., Inc., New York, 1954.

(3) F. Zeuner, Dating the Past, Methuen and Co., Ltd., London, 1952.

(4) W. F. Libby, Radiocarbon Dating, University of Chicago Press, Chicago, 1952.

(5) T. P. Kohman and N. Saito, "Radioactivity in Geology and Cosmology," Ann. Rev. Nuclear Sci. 4, 401 (1954).

(6) R. A. Alpher and R. C. Herman, "The Origin and Abundance Distribution of the Elements," Ann. Rev. Nuclear Sci. 2, 1 (1953).

(7) Report of the Committee on the Measurement of Geologic Time, National Academy of Sciences, National Research Council, Washington, issued annually, 1924 to present.