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# Half-life and Radioactive Dating

## Radioactive decay can be used to measure the age of rocks and fossils.

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Half-life and Radioactive Dating

The Grand Canyon, pictured above, was carved by the rushing waters of the Colorado River over millions of years. The exposed rocks at the bottom of the canyon are almost 2 billion years old. The youngest rocks near the top are about 230 million years old. Therefore, from top to bottom, the rocks provide a continuous record of more than 1.5 billion years of geological history in this region.

Q: How have scientists been able to determine the ages of rocks in the Grand Canyon?

A: The ages are based on the gradual decay, or break down, of radioactive isotopes.

### What Is Radioactive Dating?

Radioactive isotopes, or radioisotopes, can be used to estimate the ages of not only of rocks, but also of fossils and artifacts made long ago by human beings. Even the age of Earth has been estimated on the basis of radioisotopes. The general method is called radioactive dating . To understand how radioactive dating works, you need to understand radioisotopes and radioactive decay.

A radioisotope has atoms with unstable nuclei. Unstable nuclei naturally decay, or break down. They lose energy and particles and become more stable. As nuclei decay, they gain or lose protons, so the atoms become different elements. This is illustrated in the Figure below . The original, unstable nucleus is called the parent nucleus. After it loses a particle (in this case a type of particle called an alpha particle), it forms a daughter nucleus, with a different number of protons.

The nucleus of a given radioisotope decays at a constant rate that is unaffected by temperature, pressure, or other conditions outside the nucleus. This rate of decay is called the half-life. The half-life is the length of time it takes for half of the original amount of the radioisotope to decay to another element.

Q: How can the half-life of a radioisotope be used to date a rock?

A: After a rock forms, nuclei of a radioisotope inside the rock start to decay. As they decay, the amount of the original, or parent, isotope decreases, while the amount of its stable decay product, or daughter isotope, increases. By measuring the relative amounts of parent and daughter isotopes and knowing the rate of decay, scientists can determine how long the parent isotope has been decaying. This provides an estimate of the rock’s age.

### Different Isotopes, Different Half-Lives

Different radioisotopes decay at different rates. You can see some examples in the Table below . Radioisotopes with longer half-lives are used to date older rocks or other specimens, and those with shorter half-lives are used to date younger ones. For example, the oldest rocks at the bottom of the Grand Canyon were dated by measuring the amounts of potassium-40 in the rocks. Carbon-14 dating, in contrast, is used to date specimens that are much younger than the rocks in the Grand Canyon. You can read more carbon-14 dating below.

Parent Isotope Daughter Isotope Half-Life
potassium-40 argon-40 1.3 billion years
uranium-235 lead-207 700 million years
uranium-234 thorium-230 80,000 years
carbon-14 nitrogen-14 5,700 years

### Focus on Carbon-14 Dating

One of the most familiar types of radioactive dating is carbon-14 dating. Carbon-14 forms naturally in Earth’s atmosphere when cosmic rays strike atoms of nitrogen-14. Living things take in and use carbon-14, just as they do carbon-12. The carbon-14 in living things gradually decays to nitrogen-14. However, as it decays, it is constantly replaced because living things keep taking in carbon-14. As a result, there is a constant ratio of carbon-14 to carbon-12 in organisms as long as they are alive. This is illustrated in the top part of the Figure below .

After organisms die, the carbon-14 they already contain continues to decay, but it is no longer replaced (see the bottom part of the Figure below ). Therefore, the carbon-14 in a dead organism constantly declines at a fixed rate equal to the half-life of carbon-14. Half of the remaining carbon-14 decays every 5,700 years. If you measure how much carbon-14 is left in a fossil, you can determine how many half-lives (and how many years) have passed since the organism died. Carbon-14 dating is illustrated in the video at this URL: http://www.youtube.com/watch?v=udkQwW6aLik .

Q: Why can’t carbon-14 dating be used to date specimens older than about 60,000 years?

A: Carbon-14 has a half-life of 5700 years. After about 60,000 years, too little carbon-14 is left in a specimen to be measured.

### Summary

• The age of a rock or other specimen can be estimated from the remaining amount of a radioisotope it contains and the radioisotope’s known rate of decay, or half-life. This method of dating specimens is called radioactive dating.
• Radioisotopes with longer half-lives are used to date older specimens, and those with shorter half-lives are used to date younger ones.
• Carbon-14 dating is used to date specimens younger than about 60,000 years old. It is commonly used to date fossils of living things and human artifacts.

### Vocabulary

• radioactive dating : Method of determining the age of fossils or rocks that is based on the rate of decay of radioisotopes.

### Practice

Play the radioactive dating game at the following URL, and then answer the questions below. http://phet.colorado.edu/en/simulation/radioactive-dating-game

1. What is the half-life of carbon-14? What is the half-life of uranium-238?
2. Compare the decay rates of carbon-14 and uranium-238. How long does it take for 75 percent of a sample of carbon-14 atoms to decay? How long does it take for 75 percent of a sample of uranium-238 to decay? Do these rates depend on the number of atoms in the samples?
3. What percentage of carbon-14 remains in a sample after 10,000 years? How many years does it take for uranium-238 to decay to this same percentage?
4. Why would you not use carbon-14 to measure the age of the rock?

### Review

1. What is radioactive dating?
2. Which radioisotope in the table in the article (see above) could you use to date a fossil thought to be about 500 million years old? Explain your choice.
3. Why does the amount of carbon-14 in an organism remain the same throughout the organism’s life? Why does the amount change after the organism dies?

### Vocabulary Language: English

Method of determining the age of fossils or rocks that is based on the rate of decay of radioisotopes.