Context: Radioactive decay is the breakdown of unstable elements into stable elements. To understand this process, recall that the atoms of all elements contain the particles protons, neutrons, and electrons. An element is defined by the number of protons it contains. All atoms of a given element contain the same number of protons. The number of neutrons in an element may vary. Atoms of an element with different numbers of neutrons are called isotopes. Consider carbon as an example. Two isotopes of carbon are shown in Figure 11.15. Compare their protons and neutrons. Both contain 6 protons. But carbon-12 has 6 neutrons and carbon-14 has 8 neutrons. Almost all carbon atoms are carbon-12. This is a stable isotope of carbon. Only a tiny percentage of carbon atoms are carbon-14. Carbon-14 is unstable. Figure 11.16 shows carbon dioxide, which forms in the atmosphere from carbon-14 and oxygen. Neutrons in cosmic rays strike nitrogen atoms in the atmosphere. The nitrogen forms carbon- 14. Carbon in the atmosphere combines with oxygen to form carbon dioxide. Plants take in carbon dioxide during photosynthesis. In this way, carbon-14 enters food chains. Like other unstable isotopes, carbon-14 breaks down, or decays. For carbon-14 decay, each carbon-14 atom loses an alpha particle. It changes to a stable atom of nitrogen-14. This is illustrated in Figure 11.17. The decay of an unstable isotope to a stable element occurs at a constant rate. This rate is different for each isotope pair. The decay rate is measured in a unit called the half-life. The half-life is the time it takes for half of a given amount of an isotope to decay. For example, the half-life of carbon-14 is 5730 years. Imagine that you start out with 100 grams of carbon-14. In 5730 years, half of it decays. This leaves 50 grams of carbon-14. Over the next 5730 years, half of the remaining amount will decay. Now there are 25 grams of carbon-14. How many grams will there be in another 5730 years? Figure 11.18 graphs the rate of decay of carbon-14. The rate of decay of unstable isotopes can be used to estimate the absolute ages of fossils and rocks. This type of dating is called radiometric dating. The best-known method of radiometric dating is carbon-14 dating. A living thing takes in carbon-14 (along with stable carbon-12). As the carbon-14 decays, it is replaced with more carbon-14. After the organism dies, it stops taking in carbon. That includes carbon-14. The carbon-14 that is in its body continues to decay. So the organism contains less and less carbon-14 as time goes on. We can estimate the amount of carbon-14 that has decayed by measuring the amount of carbon-14 to carbon-12. We know how fast carbon-14 decays. With this information, we can tell how long ago the organism died. Carbon-14 has a relatively short half-life. It decays quickly compared to some other unstable isotopes. So carbon- 14 dating is useful for specimens younger than 50,000 years old. Thats a blink of an eye in geologic time. But radiocarbon dating is very useful for more recent events. One important use of radiocarbon is early human sites. Carbon-14 dating is also limited to the remains of once-living things. To date rocks, scientists use other radioactive isotopes. The isotopes in Table 11.1 are used to date igneous rocks. These isotopes have much longer half-lives than carbon- 14. Because they decay more slowly, they can be used to date much older specimens. Which of these isotopes could be used to date a rock that formed half a million years ago? Unstable Isotope Decays to At a Half-Life of (years) Potassium-40 Uranium-235 Uranium-238 Argon-40 Lead-207 Lead-206 1.3 billion 700 million 4.5 billion Dates Rocks Aged (years old) 100 thousand - 1 billion 1 million - 4.5 billion 1 million - 4.5 billion 
 Question: Absolute ages are based on evidence from
Output: radiometric dating.