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# 10.9: Radioactive Decay as a Measure of Age

Difficulty Level: Basic Created by: CK-12
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Practice Radioactive Decay as a Measure of Age

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When do you stop counting?

Pretend that the large green cylinder is a parent isotope. Now you can visualize the decay of the parent to the daughter. It's easy to see that the second cylinder is half the size of the first. The third is half the size of the second. But when the cylinders get small the differences are much harder to see. At some point there is too little of the parent left. That isotope pair is no longer useful for dating.

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.

#### Isotopes

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 below. Compare their protons and neutrons. Both contain 6 protons. But carbon-12 has 6 neutrons and carbon-14 has 8 neutrons.

Isotopes are named for their number of protons plus neutrons. If a carbon atom had 7 neutrons, what would it be named?

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. It is a radioactive isotope of carbon. Figure below 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.

Carbon-14 forms in the atmosphere. It combines with oxygen and forms carbon dioxide. How does carbon-14 end up in fossils?

#### Decay of Unstable Isotopes

Like other unstable isotopes, carbon-14 breaks down, or decays. The original atoms are called the parent isotopes. For carbon-14 decay, each carbon-14 atom loses an alpha particle. It changes to a stable atom of nitrogen-14. The stable atom at the end is the daughter product. This is illustrated in Figure below.

Unstable isotopes, such as carbon-14, decay by losing atomic particles. They form different, stable elements when they decay. In this case, the daughter is nitrogen-14.

The decay of an unstable isotope to a stable element occurs at a constant rate. This rate is different for each parent-daughter 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 below graphs the rate of decay of a substance.

The rate of decay of a substance is stable over time.

### Vocabulary

• daughter product: The product of the radioactive decay of a parent isotope.
• half-life: The amount of time required for half of the atoms of a radioactive substance to decay to the daughter product.
• isotope: Atoms of an element that have a different number of neutrons.
• parent isotope: An unstable isotope that will undergo radioactive decay.
• radioactive decay: Emission of high-energy particles by unstable isotopes.
• radioactive isotope: Substance that is unstable and likely to decay into another isotope.

### Summary

• A half life is the time it takes for half of the parent isotopes of an element to change to the daughter product.
• With alpha decay, the nucleus loses two protons and two neutrons.
• Carbon-14 has a half life of 5730 years.

### Practice

Use this resource to answer the questions that follow.

1. What is an isotope?
2. Describe Carbon-14.
3. What is average atomic mass?
5. What is carbon dating?

### Review

2. What is a parent isotope and a daughter product?
3. Describe half-life. Use an example.

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

TermDefinition
daughter product Product of the radioactive decay of a parent isotope.
half-life Amount of time required for half of the atoms of a radioactive substance to decay to the daughter product.
isotope Atoms of an element that have a different number of neutrons.
parent isotope Unstable isotope that will undergo radioactive decay.
radioactive decay Emission of high-energy particles by unstable isotopes.
radioactive isotope Substance that is unstable and likely to decay into another isotope.

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