| 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.