More Precisely 7-2

MORE PRECISELY 7-2 Radioactive Dating

In Chapter 4 we saw that atoms are made up of electrons and nuclei, and that nuclei are composed of protons and neutrons.

(Sec. 4.2) The number of protons in a nucleus determines which element it represents. However, the number of neutrons can vary. In fact, most elements can exist in several isotopic forms, all containing the same number of protons but different numbers of neutrons in their nuclei. The particular nuclei we have encountered so far—the most common forms of hydrogen, helium, carbon, iron—are all stable. For example, left alone, a carbon-12 nucleus, consisting of six protons and six neutrons, will remain unchanged forever. It will not break up into smaller pieces, nor will it turn into anything else.

Not all nuclei are stable, however. Many nuclei—for example, carbon-14 (containing 6 protons and 8 neutrons), thorium-232 (90 protons, 142 neutrons), uranium-235 (92 protons, 143 neutrons), uranium-238 (92 protons, 146 neutrons), and plutonium-241 (94 protons, 147 neutrons)—are inherently unstable. Left alone, they will eventually break up into lighter "daughter" nuclei, in the process emitting some elementary particles and releasing some energy. The change happens spontaneously, without any external influence. This instability is known as radioactivity. The energy released by the disintegration of the radioactive elements just listed is the basis for nuclear fission reactors (and nuclear bombs).

Unstable heavy nuclei achieve greater stability by disintegrating into lighter nuclei, but they do not do so immediately. Each type of "parent" nucleus takes a characteristic amount of time to decay. The half-life is the name given to the time required for half of a sample of parent nuclei to disintegrate. Notice that this is really a statement of probability. We cannot say which nuclei will decay in any given half-life interval, only that half of them are expected to do so. Thus, if we start with a billion radioactive nuclei embedded in a sample of rock, a half-billion nuclei will remain after one half-life, a quarter-billion after two half-lives, and so on.

Every radioactive isotope has its own half-life, and most of them are now well known from studies conducted since

the 1950s. For example, the half-life of uranium-235 is 713 million years, and that of uranium-238 is 4.5 billion years. Some radioactive elements decay much more rapidly, others much more slowly, but these two types of uranium are particularly important to geologists because their half-lives are comparable to the age of the solar system. The accompanying figure illustrates the half-lives and decay reactions for four unstable heavy nuclei.

The decay of unstable radioactive nuclei into more stable daughter nuclei provides us with a useful tool for measuring the ages of any rocks we can get our hands on. The first step is to measure the amount of stable nuclei of a given kind (for example, lead-206, which results from the decay of uranium-238). This amount is then compared with the amount of remaining unstable parent nuclei (in this case, uranium-238) from which the daughter nuclei descended. Knowing the rate (or half-life) at which the disintegration occurs, the age of the rock then follows directly. For example, if half of the parent nuclei of some element have decayed, so that the number of daughter nuclei equals the number of parents, the age of the rock must be equal to the half-life of the radioactive nucleus studied. Similarly, if only a quarter of the parent nuclei remain (three times as many daughters as parents), the rock's age is twice the half-life of that element, and so on. In practice, ages can be determined by these means to within an accuracy of a few percentage points. The most ancient rocks on Earth are dated at 3.9 billion years old. These rare specimens have been found in Greenland and Labrador.

The radioactive-dating technique rests on the assumption that the rock has remained solid while the radioactive decays have been going on. If the rock melts, there is no reason to expect the daughter nuclei to remain in the same locations their parents had occupied, and the whole method fails. Thus, radioactive dating indicates the time that has elapsed since the last time the rock in question solidified. Hence this 3.9 billion year value represents only a portion—a lower limit—of the true age of our planet. It does not measure the duration of Earth's molten existence.