TOOLS OF THE ASTRONOMER’S TRADE

Radioactive Dating

How old are the rocks found on Earth and other planets? Are rocks found at different locations the same age or different ages? How old are meteorites? Questions like these are important to scientists who wish to reconstruct the history of our solar system. The age of a rock is how long ago it solidified, but simply looking at a rock cannot tell us whether it was formed a million years, or a billion years ago. Fortunately, most rocks contain trace amounts of radioactive elements such as uranium. By measuring the relative abundances of various radioactive isotopes and their decay products within a rock, scientists can determine the rock’s age.

As we saw in Box 5-5, every atom of a particular element has the same number of protons in its nucleus. However, different isotopes of the same element have different numbers of neutrons in their nuclei. For example, the common isotopes of uranium are ²³⁵U and ²³⁸U. Each isotope of uranium has 92 protons in its nucleus (correspondingly, uranium is element 92 in the periodic table; see Box 5-5). However, a ²³⁵U nucleus contains 143 neutrons, whereas a ²³⁸U nucleus has 146 neutrons.

A radioactive nucleus with too many protons or too many neutrons is unstable; to become stable, it decays by ejecting particles until it becomes stable. If the number of protons (the atomic number) changes in this process, the nucleus changes from one element to another.

Some radioactive isotopes decay rapidly, while others decay slowly. Physicists find it convenient to talk about the decay rate in terms of an isotope’s half-life. The half-life of an isotope is the time interval in which one-half of the nuclei decay. For example, the half-life of ²³⁸U is 4.5 billion (4.5 × 10⁹) years. Uranium’s half-life means that if you start out with 1 kg of ²³⁸U, after 4.5 billion years, you will have only ½ kg of ²³⁸U remaining; the other ½ kg will have turned into other elements. If you wait another half-life, so that a total of 9.0 billion years has elapsed, only 4¼ kg of ²³⁸U—one-half of one-half of the original amount—will remain. Several isotopes useful for determining the ages of rocks are listed in the accompanying table.

To see how geologists date rocks, consider the slow conversion of radioactive rubidium (⁸⁷Rb) into strontium (⁸⁷Sr). (The periodic table in Box 5-5 shows that the atomic numbers for these elements are 37 for rubidium and 38 for strontium, so in the decay a neutron is transformed into a proton. In this process an electron is ejected from the nucleus.) Over the years, the amount of ⁸⁷Rb in a rock decreases, while the amount of ⁸⁷Sr increases. Because the ⁸⁷Sr appears in the rock due to radioactive decay, this isotope is called radiogenic. Dating the rock is not simply a matter of measuring its ratio of rubidium to strontium, however, because the rock already had some strontium in it when it was formed. Geologists must therefore determine how much fresh strontium came from the decay of rubidium after the rock’s formation.

To make this determination, geologists use as a reference another isotope of strontium whose concentration has remained constant. In this case, they use ⁸⁶Sr, which is stable and is not created by radioactive decay; it is said to be nonradiogenic. Dating a rock thus entails comparing the ratio of radiogenic and nonradiogenic strontium (⁸⁷Sr/⁸⁶Sr) in the rock to the ratio of radioactive rubidium to nonradiogenic strontium (⁸⁷Rb/⁸⁶Sr). Because the half-life for converting ⁸⁷Rb into ⁸⁷Sr is known, the rock’s age can then be calculated from these ratios (see the table).

Radioactive isotopes decay with the same half-life no matter where in the universe they are found. Hence, scientists have used the same techniques to determine the ages of rocks from the Moon and of meteorites.