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Unit 12: Kinetics and Nuclear Chemistry—Rates of Reaction

Section 8: Half-Life and Radiometric Dating

While there is no way to predict exactly when any particular unstable nucleus will decay, a large collection of nuclei will decay in a predictable fashion—every radioactive isotope has a unique half-life: The time it takes for half of the sample to decay. If an isotope is unstable and decays very quickly, its half-life is short; if it is stable and decays slowly, its half-life is long. The range of half-lives is quite large:

IsotopeHalf-life
Uranium-2384.5 X 109 years
Carbon-145,715 years
Strontium-9028.8 years
Scandium-46 83.8 days
Copper-629.67 minutes
Meitnerium-2263.4 milliseconds
Decay of a Radioactive Substance

Figure 12-14. Decay of a Radioactive Substance

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Decay of a Radioactive Substance

Figure 12-14. Decay of a Radioactive Substance

Most people consider that after 10 half-lives have passed, a radioactive substance is gone, as less than one-tenth of a percent of what was there originally remains.

Figure 12-14 shows the decay of 1000 g of a radioactive isotope. Note that the amount of isotope decreases by half with every half-life.

Because radioactive substances decay in such a predictable way, they can be used to determine the age of fossils and archeological artifacts. Radiocarbon dating is used for organic substances up to about 60,000 years old, and it is based on the ratio of carbon-14 (radioactive) to carbon-12 (stable) in the substance. Carbon-14 is formed in the atmosphere when nitrogen is bombarded with cosmic rays; the carbon-14 enters the food chain when plants absorb CO2 in photosynthesis. So long as a plant or animal is alive and exchanging carbon with the atmosphere, it will have the same ratio of carbon-14 to carbon-12 as its surroundings. When the organism dies, this exchange stops; as the carbon-14 undergoes radioactive decay, the ratio drops. By measuring the ratio, the age can be determined. (Figure 12-15)

Radiocarbon Dating

Figure 12-15. Radiocarbon Dating

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Radiocarbon Dating

Figure 12-15. Radiocarbon Dating

Plants take up radioactive carbon-14 formed in the atmosphere. The radioactive carbon then enters the food chain. So long as a plant or animal is alive, the amount of carbon-14 remains constant. Once the life form is dead, the carbon-14 can only decay, though it takes several hundred years for the decay to be measurable.

Radiocarbon dating works best for substances that are less than 60,000 years old. If too much time has passed, the amount of carbon-14 falls to levels that are impossible to detect. To determine the age of older substances or non-living minerals, scientists use other radioactive elements such as uranium. As shown in the sidebar, Decay Chains and Radon, uranium-238 undergoes a series of decays until it reaches lead-206. While each step in this process has its own half-life, the overall half-life for the entire decay chain is about 4.5 billion years. By comparing the amounts of uranium-238 and lead-206 in ancient rocks, geologists have concluded that approximately one half-life has elapsed since the Earth formed; the age of the Earth is 4.54 billion years.

Glossary

Half-life (radioactive)

The time needed for half of a radioactive substance to decay.

Radiocarbon dating

A method of determining the age of ancient artifacts by measuring the amounts of different carbon isotopes in the artifact.

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