Part 2

Finally, the sample counters are made of specially selected metal tubing that is extremely low in radioactive content, with a fine wire stretched down the middle. (In some recent designs, the anticoincidence ring and sample counter are combined in a single cylindrical housing with a thin foil of metallized plastic between them.) A thin glass filling tube connects the sample counter with the outside world.

The radiocarbon-bearing gas is pumped into the sample counter through the filling tube, and all the counts resulting from its disintegrations are recorded electronically. The age of the sample is calculated from the NET COUNTING RATE (the sample counting rate minus the background); the lower the counting rate the higher the age. The upper limit of the age that can be measured is determined by the STATISTICAL ERROR (that is, by the measure of the instrument accuracy) in the net count. In very old samples this error may be great enough so that the calculated age of the sample may have little or no meaning.

Carbon-14 Results

OBJECTS DATED BY RADIOCARBON

Carbon-14 is by far the most widely used method of measuring geologic time. It has become the mainstay of archeology and geology for studies of events of the past 50,000 years or so, and also has wide applications in climatology, ecology, and geography. It would be difficult to pick out the most significant example of the use of this method, but one important contribution has been in study of the early inhabitants of North America. With the aid of ¹⁴C it has been possible to date human living sites from many points in the western United States. The first appearance of these sites, about 11,500 years ago, apparently coincided with the time when a land bridge was open from Asia to America over what is now the Bering Strait. An ice-free passage extended from this bridge through present-day Alaska and western Canada to the United States. This may have been the route taken by the first immigrants to America—a population of mammoth-hunters, who made the characteristic flint _Clovis_ arrow and spear points.

By about 11,000 years ago, these Clovis people had spread across the area of the United States and into Mexico. It may have been they who killed off the mammoths and then gradually assumed the characteristics of the _Folsom_ culture. The Folsom people were bison-hunters, and long were thought to have been the first population in America. It was with the use of ¹⁴C that it finally was possible to place these two cultures in proper sequence—the Clovis first—and to correlate them with major natural changes, especially the advance and retreat of glaciers across the continent.

THE LONG-LIVED CLOCKS

All other practical age-determination schemes are based on a few long-lived isotopes, with half-lives relatively near the age of the earth (4.5 AEONS). They are:

Table III Isotope Emits Decays to Half-life Uranium-238 8 ALPHA PARTICLES[10] Lead-206 4.51 aeons Uranium-238 Spontaneous fission 2 Fragments 10 million aeons[11] Uranium-235 7 Alpha particles Lead-207 0.713 aeons Thorium-232 6 Alpha particles Lead-208 14.1 aeons Rubidium-87 Beta particle Strontium-87 4.7 aeons Potassium-40 Electron capture Argon-40 1.3 aeons ...... ...... ...... ...... Rhenium-187[12] Beta particle Osmium-187 40 aeons

It is apparent that Table II on page 6, showing the long-lived radioactive nuclides, is much longer than the list of the seven shown here that are actually useful in practice. Some of the nuclides that are theoretically available are useless on a practical basis, because they are so rare in nature. Many others cannot be used for reasons that are fundamental to the whole process of nuclear age determination by “whole hourglass” (that is, parent-daughter) methods. Let’s look at these reasons.

These methods are based on closed systems in which the daughter products of the radioactive decay are locked with the parent material from the beginning of the system, and nothing is added or removed thereafter. To state it in terms of our analogy, the hourglass must be in perfect working order—no leaks or cracks permitted.

There is another fundamental requirement: At the beginning, the bottom part of the hourglass must be empty. If some sand were already in the bottom at the start, we would mistakenly be led to conclude that the time elapsed was longer than it actually was. That necessity places a severe limitation on the type of system we can use.

Consider, for example, the decay of potassium-40 into calcium-40. Measuring this process is perfectly suitable from the point of view of half-life, but the daughter product is identical with the most common isotope of ordinary calcium. And calcium is present everywhere in nature! Even the purest mineral of potassium, sylvite (the salt, potassium chloride), contains so much calcium impurity that the RADIOGENIC daughter calcium, produced by the decay of potassium in geologic time, is negligible in comparison. We can say that the bottom of this potassium-40 hourglass has been stuffed with so much sand from the very beginning that the few grains that fall through the waist are lost in the overall mass. This demonstrates that schemes involving the decay of a relatively rare nuclide into a relatively common one are not usable. Natural geochemical separations of elements are never perfect, anyway.

Similarly, the decay of any of the RARE EARTH elements into other rare earth elements is not particularly helpful, because the rare earths are so similar chemically they tend to travel together when they move in nature.[13] Wherever the parent isotope goes, the daughter tags along.

The Rubidium-Strontium Clock

The decay of rubidium-87 (⁸⁷Rb) into strontium-87 (⁸⁷Sr) is perhaps the most useful scheme for geologic age determination. The same problem shows up here, but at least there is a way out of the wilderness. It is not exactly simple, but a consideration of it is fundamental to understanding the process of nuclear dating. The figure shows patterns from mass spectrometer charts; each peak represents an isotope of strontium, and the height of every peak is proportional to the relative abundance of that isotope. In the figure, A shows the mass-spectrum of a rock or mineral containing COMMON strontium (which is a mixture of several isotopes). The peak of ⁸⁷Sr is small compared to the others. B shows the mass-spectrum of strontium from an old rubidium-rich mineral CRYSTAL, drawn to the same scale, as far as the nonradiogenic isotopes, ⁸⁴Sr, ⁸⁶Sr, and ⁸⁸Sr, are concerned. The ⁸⁷Sr peak in this spectrum is obviously larger than in the common strontium in A. This is because this isotope is radiogenic and has been accumulating from the decay of rubidium since this crystal was formed.

The question we must answer is: How much of this ⁸⁷Sr was formed from ⁸⁷Rb decay and how much originally was present in the crystal as an impurity? If the amount of this ORIGINAL strontium is not too large, the problem can be solved by simple arithmetic.

First, we must find a good sample of common strontium—that is, ordinary strontium, the kind shown at left in the figure. We cannot require that this strontium be entirely uncontaminated by radiogenic strontium, because all strontium is more or less contaminated. What we need is strontium contaminated to _just the same extent_ as the strontium that was taken as an impurity into the closed system when it first formed. In geological specimens such a material is usually available.

Let us take as our closed system a mica crystal in a mass of granite. Mica contains a fair amount of rubidium, and it retains its radiogenic strontium very well. Furthermore, mica crystals are often associated or even intergrown with the slender, rod-shaped crystals of a mineral called apatite—a phosphate of calcium. It is justifiable, on the basis of geological knowledge, to say that the mica and the apatite grew at roughly the same time and thus presumably from the same liquid medium that became granite when it later solidified. Now strontium is geochemically similar to calcium, and some strontium will have gone into the apatite crystal in place of calcium. Apatite contains no alkalis—hence apatite will have virtually no rubidium (which is an alkali) in it to contaminate the ⁸⁷Sr. Consequently, when we find apatite in an old granite, we know the apatite will still contain the kind of common strontium that was taken into the mica crystal when it grew originally.

We can separate the apatite from the granite by standard mineralogical techniques, extract the strontium from the apatite chemically, and analyze it on a mass spectrometer to obtain the isotopic spectrum—the relative amount of each isotope that is present. We can then perform the same isotopic analysis on the strontium extracted from the mica, and subtract the original (apatite) strontium from the total (mica) strontium, to obtain the radiogenic component or daughter product. (See page 32 for details of this method.)

Obviously, there is a certain error associated with every isotopic analysis, so such a calculation is meaningful only when the radiogenic component is large compared with the error in the measurement of isotopic abundance. When one large quantity must be subtracted from another large quantity to obtain a small difference, there is an obvious limit to how much one can trust the result. The absolute accuracy in measuring strontium isotope abundance is a few tenths of 1%, using the best mass spectrometers now available. In practice, one can trust a calculated age for a specimen only when the ⁸⁷Sr is as little as about 5% radiogenic. The results do not mean much when only 1 or 2% is radiogenic.

The Uranium Fission Clock

When a neutron strikes the nucleus of uranium-235 (²³⁵U) or plutonium-239 (²³⁹Pu), it may cause the nucleus to split into two roughly equal fragments, releasing neutrons and energy. This is the well-known process of neutron-induced fission, the method in which nuclear energy is produced in both reactors and bombs.[14] The most common uranium isotope, ²³⁸U, also breaks up by fission, but does so all by itself, without the need for any external neutrons. That process is _spontaneous fission_ and it goes on at random, very much like radioactive decay. It is a relatively rare process and the fission half-life is long—about 10 million aeons (10¹⁶ years). That means that only about one spontaneous fission occurs in uranium-238 for every 2 million alpha decays. That is enough to make a useful clock, however, because ²³⁸U is present almost everywhere. (See Table III on page 19.)

Imagine an atom of ²³⁸U in some mineral. When the atom suddenly fissions, it breaks in two with considerable energy, and the two fission fragments rip like cannon balls through the surrounding crystalline structure in opposite directions, creating havoc along the way. They travel a distance something like 10 microns (4 millionths of an inch) before they are finally slowed down and stopped by all their collisions with other atoms. Each fragment’s path remains behind as an intensely damaged tube through the crystal.

The process was known for a long time before anyone was able to find these fission tracks (the damaged tubes) in the crystals. Finally, about 1960, three young physicists, R. L. Fleischer, P. B. Price, and R. M. Walker, working at the General Electric Research Laboratory, fell upon the idea of etching freshly broken surfaces of crystals with acid. They reasoned that a region so intensely disturbed by the passage of a fission fragment should be etched more easily and deeply than the undisturbed surrounding crystal. That idea turned out to be correct, and fission tracks have now been found in almost every common mineral (since almost all minerals contain small amounts of uranium).

The fission clock method works this way: A cleavage face or a polished surface of a crystal or glass fragment is etched with a suitable solvent. Different acids work best for different materials, and a suitable procedure must be developed especially for each substance. The etching brings out the fission tracks so they can be seen (usually as little conical pits) and counted under a microscope.

After this, the sample is exposed to a known amount of slow neutrons[15] in a nuclear reactor. New fissions are produced, but this time only in ²³⁵U (which is present in all natural uranium in the proportion of 1 atom of ²³⁵U to 137.7 atoms of ²³⁸U), because slow neutrons do not produce fissions in ²³⁸U. After the neutron irradiation, the same surface is etched again, and the new tracks counted. The old tracks, having been etched twice, now appear larger and thus can be distinguished from the new ones that were caused by ²³⁵U fission.

The rate at which ²³⁸U decays by fission, λ_{f}, is known, as are the rate it decays by alpha decay, λ_{α}, and the total number of slow neutrons, _n_, to which the sample was exposed in the reactor. The age of the crystal or glass can then be calculated:

t = (1)/(λ_{α}) ln (1 + (_n_N_{s})/(N_{i}) × constant)

where

ln = the natural logarithm (log to the base _e_),

N_{s} = the number of atoms in the sample.

N_{i} = the number of atoms of ²³⁵U in the irradiated sample,

and the constant has the value:

½ (λ_{α} × 582 × 10⁻²⁴)/(λ_{f} × 137.7) = 4.25 × 10⁻¹⁸

Fission-track dating is a brand new technique, still only partly developed. It has enormous range and is applicable to numerous minerals; these advantages imply that it is likely to become very useful.

Plumbology

The most complicated and therefore probably the most interesting decay scheme of all is the decay of uranium to lead, discovered well over half a century ago and still intensively studied. There are several reasons for the interest.

First, uranium and lead are geochemically separated to a high degree, not only on the small scale of an ore deposit but also on the scale of the earth as a whole. Second, natural uranium has two isotopes with half-lives that are neither too long nor too short to be useful (the greater half-life almost exactly equaling the age of the earth), and these half-lives differ from each other by a factor of about 6.3. That leads to very important consequences, as we shall see. Third, uranium and lead are both common, and techniques are available for extracting them in measurable quantities from almost any natural material.

As a consequence of these happy circumstances, the study of uranium and lead has contributed a great deal to understanding the earth’s history and the processes that go on inside it. F. G. Houtermans, one of the great pioneers in this study, jokingly called the method PLUMBOLOGY, and it seems a useful name.

THE AGE OF THE EARTH

The greatest achievement of the “plumbologists” has been the calculation of the age of the earth, first proposed by Houtermans, a German physicist, and independently by Arthur Holmes, a British geologist, in 1946 and finally perfected by C. C. Patterson in 1953. It is actually a rather simple calculation, although the way to discovering it was far from easy. Before we look at it in detail, however, let’s consider some basic assumptions and explain what is meant by “the age of the earth”.

From studying the mechanics of the solar system, scientists have become reasonably certain that the earth and the other planets and their satellites all were formed in a common process in a relatively short period of time, geologically speaking. Perhaps it took a dozen million years or so, but compared to the time that has elapsed since, that is a twinkling. At some time soon afterwards, the earth became molten, or at any rate fluid enough to allow much of its iron to settle toward the center to form the earth’s core. Similar cores presumably formed in other planets. As the iron went down, it took some lead with it, and as the silica went up, uranium followed it toward the surface, because of the chemical affinity between these kinds of elements. In the present earth, we have found, almost all the uranium is concentrated in the top layer, or crust, which is only about 25 miles thick under the continents and even thinner under the oceans.

The time of this early and relatively rapid separation of uranium and lead on a worldwide scale is the event that plumbologists can determine, and the period since then is what they mean by “the age of the earth”. When Houtermans first wrote about it, he called it “the age of uranium”.

How is this done? We have said that one of the isotopes of uranium, ²³⁵U, decays faster—about 6.3 times faster—than the other, ²³⁸U. They decay into two different isotopes of lead. Therefore, if we can determine the isotopic composition of average ordinary lead in the earth’s crust today, and if we can somehow obtain a sample of the kind of lead that is locked in the earth’s core, we can calculate how long it took to change the PRIMORDIAL lead (like that in the core) into present-day lead in the crust by the gradual addition of radiogenic lead—lead that has resulted from the decay of uranium. Now, someone might logically ask, “Isn’t it necessary to know also the actual amount of uranium involved in the process, and isn’t this difficult to determine?” It turns out to be a remarkable aspect of the Holmes-Houtermans calculation that the uranium-concentration terms cancel out in the equations and only the _ratio_ of the isotopes and their decay constants need be considered. These are all known accurately.

Next, we must decide just what is average present-day lead? It isn’t enough to go to a lead mine and get a sample, because, unfortunately, leads from different mines have widely varied isotopic composition—that is, a different mixture of four natural isotopes, ²⁰⁴Pb, ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb—as a result of their geologic histories. No, lead samples from a mine won’t do. However, geologists have been able to separate lead from recent marine sediments, obtained from the ocean bottom, far from land. These are of uniform composition, and are good samples of what the world’s rivers bring into the ocean. Other useful samples can be found in plateau basalts, which are enormous bodies of dark volcanic rock that make up the bedrock in many parts of the world. The lead from these basalts is isotopically very much like the lead in the oceans.

Very well, but how about the lead from the core? Where can we hope to find a sample of it? It turns out to be easier than you might think. Astronomers believe it highly probable that most meteorites are fragments of a former planet that broke up for reasons that are not entirely clear. It is pretty definite, however, that this protoplanet (or these protoplanets, for there may have been more than one) had an iron core, and this core (or these cores) is the source of the iron meteorites sailing around in space. A large meteorite hit the earth not too long ago (geologically speaking) and caused the Meteor Crater near Canyon Diablo in Arizona.

Many fragments of the meteorite iron have been found around the crater, and it is reasonable to assume that this is the kind of iron we would expect to find in the core of the earth. Like the core iron, it is mixed with a little lead, which can be isolated and analyzed in a mass spectrometer for its isotopic composition. This lead is found to be much less contaminated with radiogenic lead, and hence is much more primitive than the oldest leads found on earth. Thus, meteorites presumably are as close as we can get to true primordial lead—the lead of the time when the earth (and the protoplanet) first formed.

Once these measurements were available, it was easy to write the Houtermans equation for present-day and primordial leads in this way:

((²⁰⁶Pb)/(²⁰⁴Pb)) present - ((²⁰⁶Pb)/(²⁰⁴Pb)) primordial ------------------------ -------------------------- ((²⁰⁷Pb)/(²⁰⁴Pb)) present - ((²⁰⁷Pb)/(²⁰⁴Pb)) primordial

= 137.7 ((e^{λ}238^{t} - 1))/((e^{λ}235^{t} - 1))

The present ratio of ²³⁸U to ²³⁵U is 137.7.

e = the base of natural logarithms

λ = the DECAY CONSTANT of each isotope of uranium

t = the age of the earth.

Substituting the best experimental lead isotope ratios into the equation and solving for t, Patterson was able to calculate that the earth is 4550 million years (4.55 aeons) old. Subsequent calculations based on other procedures generally have confirmed that result.

Analytical Techniques

Each method of nuclear age determination involves a different sequence of sample preparation. Wood, peat, charcoal, bones, or shells are cleaned for carbon-14 dating in order to remove every trace of possible contamination by modern carbon as well as extraneous old carbon. Rocks are crushed and ground, minerals are separated according to what is needed in any particular study, and the desired elements are extracted and separated by chemical procedures. Often there may be several different ways of doing the same thing; different laboratories use different procedures. In every case, however, long and complicated procedures must be followed before results are obtained from which an age can be calculated. There is no such thing as a black box into which you can throw a rock and read its age on a dial!