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.
Internal structure of the earth. The central core is probably an alloy of iron and nickel, surrounded by a mantle of less dense silicate material, with a thin crust of still lighter silicates.
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.