Skip to main content
Physics LibreTexts

5.4 Ages Using Radioactivity

In the late 1800s, the crucial discovery of radioactivity made possible even more accurate estimates of the Earth's age. The process is worth discussing in detail because it allows us to date not only Earth, but also rock samples from other worlds, such as lunar rocks and meteorites. Such dating sheds light on the age of our whole Solar System and even the universe itself.

The discovery of radioactivity happened by accident. In 1896 French physicist Antoine Becquerel left some photographic plates in a drawer with some uranium-bearing minerals. Later he opened the drawer and found the plates fogged. Being a good scientist, he did not dismiss the event, but investigated further. He found that the uranium emitted "rays," which, like X-rays (discovered the previous year), could pass through cardboard. The new "rays" turned out to be not electromagnetic radiation, like ultraviolet light or X-rays, but rather energetic particles emitted by unstable atoms. It might seem that serendipity plays no part in the scientific method, yet a number of important discoveries happened by accident. Examples include X-rays by Roentgen and penicillin by Fleming. The perceptive scientist will pursue unexpected phenomena. Often, they will find a flaw in the equipment. Occasionally, they will make an important discovery. A lesser scientist than Bequerel might have seen the fogged photographs, shrugged, and carried on with his work. Louis Pasteur put it this way: "Fortune favors the prepared mind."

Here is how radioactivity works. A radioactive atom is an unstable atom that spontaneously changes (usually into a more stable form) by emitting one or more particles from its nucleus. The original atom thus becomes either a new element (change in the number of protons in the nucleus) or a new form of the same element, called an isotope (change in the number of neutrons in the nucleus). The original atom is called the parent isotope and the new atom is called the daughter isotope.

The time required for half of the atoms of any original radioactive parent isotope to decay into daughter isotopes is called the half-life of the radioactive element. If a billion atoms of a parent isotope were present in a certain mineral specimen, a half billion would be left after one half-life, a quarter billion after the second half-life, and so on. Sometimes the result of the decay is another radioactive element, so the decay continues. But in every case the final product of the decay (or chain of decays) is a stable element.

The list that follows has some examples of the half-lives of unstable elements. The number after the name of the element is the atomic weight of the isotope — the sum of the number of protons and neutrons in the nucleus.

• rubidium-87 decays to strontium-87 with a half-life of 49 billion years.

• uranium-238 decays (in a series of steps) to lead-206 with a half-life of 4.5 billion years.

• potassium-40 decays to argon-40 with a half-life of 1.25 billion years.

• carbon-14 decays to nitrogen-14 with a half-life of only 5570 years.

Radioactivity is a random process. This means that the exact time when an individual atom decays is impossible to determine. Yet the average time for half of a very large number of atoms to decay is well determined. In other words the concept of half-life is only meaningful in a statistical sense. Let's take an everyday example. If you had a pan of popcorn cooking, it would be possible to measure when the time at which half of the kernels had popped. If you repeated the experiment many times this "popcorn half-life" would be a well-measured number. Yet it would be impossible for you to stare at a particular kernel and predict when it would pop. This situation is like the random radioactive decay at the subatomic level.

Early in the twentieth century, physicists realized that the process of radioactive decay could help determine the date when a given rock formed. Here's how the method works. Suppose we could determine the original number of parent and daughter isotope atoms in a rock meaning at the time when the rock first formed. This can be done by counting the relative numbers of different isotopes in the minerals of the rock. Then, if we simply count the present numbers of parent and daughter isotope atoms in the rock, we can tell how many parent atoms have decayed into daughter atoms and hence tell how old the rock is. For instance, if half the parent atoms have decayed, the age of the rock equals one half-life of the radioactive parent element being studied. This technique of dating rocks is called radioactive dating.

Radioactive dating is a powerful technique that is used throughout science. Since radioactive elements have half-lives that range from a fraction of a second to billions of years, we choose a parent isotope that is matched in half-life to the approximate age of the phenomenon we want to measure.

One important example is the use of carbon isotopes to measure the ages of organic materials. Every living thing takes in carbon — animals by the carbon in their food and plants by the carbon dioxide they absorb from the air. Most carbon is in the stable form of carbon-12. However carbon in the natural environment has one in a million atoms of the isotope carbon-14, which has a half-life of 5570 years. When living things die, no more carbon-14 is introduced and the existing amount diminishes steadily by the radioactive decay. The remaining fraction of carbon-14 gives a good estimate of how long since the living material died. This is how we know the age of wooden artifacts taken from an Egyptian tomb, for example. In another celebrated case, the Shroud of Turin — reputed to be the burial cloth of Jesus — was shown to be a fraud dating from the 12th century. By using this idea and a different isotope with a longer half-life, we can measure the age of dinosaur fossils.


Portrait of Antoine Henri Becquerel. Click here for original source URL.