Nuclear Clocks / Revised :: THE LONG-LIVED CLOCKS

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.

Drawings of mass-spectrometer charts showing the isotopic spectra of two kinds of strontium: (A) common strontium and (B) strontium from an old mineral rich in rubidium. (See page 32 for photo of a mass spectrometer.)

Rubidium-87 and strontium-87 fall on the same spot in the mass spectrum. Therefore, rubidium must be separated chemically from strontium before the strontium can be analyzed in a mass spectrometer. It is done with ion-exchange columns. Four of them are shown in this photograph. The author of this booklet is adding a sample, dissolved in a few drops of hydrochloric acid, to the second column.

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.

A sample of granite being made ready for crushing and mineral separation.

The Uranium Fission Clock

When a neutron strikes the nucleus of uranium-235 (²³5U) or plutonium-239 (²³?Pu), 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).

Tracks of uranium fission from a fossil antelope bone fragment from Hopefield, Cape Province, South Africa.

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, ?_f, is known, as are the rate it decays by alpha decay, ?_a, 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 =

?_a

ln (1 +

nN_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:

?_a×582×10?²4

?_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.

An atomic absorption spectrophotometer is used to measure the amount of potassium in samples of mica dissolved in acid.

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.

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