8-3 The abundances of radioactive elements reveal the solar system’s age
Our solar system, which formed 9 billion years after the Big Bang, is a relative newcomer to the universe
The heavy elements can tell us even more about the solar system: They also help us determine its age. The particular heavy elements that provide us with this information are radioactive. Their atomic nuclei are unstable because they contain too many protons or too many neutrons. A radioactive nucleus therefore ejects particles until it becomes stable. In doing so, a nucleus may change from one element to another. Physicists refer to this transmutation as radioactive decay. For example, a radioactive form of the element rubidium (atomic number 37) decays into the element strontium (atomic number 38) when one of the neutrons in the rubidium nucleus decays into a proton and an electron (which is ejected from the nucleus).
Experiment shows that each type of radioactive nucleus decays at its own characteristic rate, which can be measured in the laboratory. Furthermore, the older a solid rock is, the less of its original radioactive nuclei remains. This behavior is the key to a technique called radioactive dating, which is used to determine how many years ago a rock cooled and solidified, or simply, to determine the “ages” of rocks. For example, if a rock contained a certain amount of radioactive rubidium when it first solidified, over time more and more of the atoms of rubidium within the rock will decay into strontium atoms. The ratio of the number of strontium atoms the rock contains to the number of rubidium atoms it contains then gives a measure of the age of the rock. Box 8-1 describes radioactive dating in more detail.
Dating the Solar System
A Meteorite Although it resembles an ordinary Earth rock, this is actually a meteorite that fell from space. The proof of its extraterrestrial origin is the meteorite’s composition and its surface. Searing heat melted the surface as the rock slammed into our atmosphere. Meteorites are the oldest objects in the solar system.
Scientists have applied techniques of radioactive dating to rocks taken from all over Earth. The results show that most rocks are tens or hundreds of millions of years old, but that some rocks are as much as 4 billion (4 × 109) years old. These results confirm that geologic processes—for example, lava flows—have produced new surface material over Earth’s history, as we concluded from the small number of impact craters found on Earth (see Section 7-6). They also show that Earth must be at least 4 × 109 years old.
Radioactive dating has also been applied to rock samples brought back from the Moon by the Apollo astronauts. The oldest Apollo specimen, collected from one of the most heavily cratered and hence most ancient regions of the Moon, is 4.5 × 109 years old. But the oldest rocks found anywhere in the solar system are meteorites, bits of interplanetary debris that survive passing through Earth’s atmosphere and land on our planet’s surface (Figure 8-5). Radioactive dating of meteorites reveals that they are all nearly the same age, about 4.54 billion years old. The absence of any younger or older meteorites indicates that these are all remnants of objects that formed around the same time when rocky material in the early solar system—which was initially hot—first cooled and solidified. We conclude that the age of the oldest meteorites, about 4.54 × 109 years, is the age of the solar system itself. Note that this almost inconceivably long span of time is only about one-third of the current age of the universe, 13.7 × 109 years.
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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 ¼ [0.25] 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.
| Original Radioactive Isotope | Final Stable Isotope | Half-Life (Years) | Range of Ages that Can Be Determined (Years) |
|---|---|---|---|
| Rubidium (87Rb) | Strontium (87Sr) | 47.0 billion | 10 million–4.54 billion |
| Uranium (238U) | Lead (206Pb) | 4.5 billion | 10 million–4.54 billion |
| Potassium (40K) | Argon (40Ar) | 1.3 billion | 50,000–4.54 billion |
| Carbon (14C) | Nitrogen (14N) | 5730 | 100–70,000 |
Thus, by studying the abundances of radioactive elements, we are led to a remarkable insight: Some 4.54 billion years ago, a collection of hydrogen, helium, and a much smaller amount of heavy elements came together to form the Sun and all of the objects that orbit around it. All of those heavy elements, including the carbon atoms in your body and the oxygen atoms that you breathe, were created and cast off by stars that lived and died long before our solar system formed, during the first 9 billion years of the universe’s existence. We are literally made of old star dust, and our solar system is relatively young.
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CONCEPT CHECK 8-4
What is meant by the “age” of a rock? Is it the age of the rock’s atoms?