# 3.63: Radioactive Half-life

Difficulty Level: At Grade Created by: CK-12

Assume that you cut a sheet of paper down the center to get two halves. Then you cut each half down the center to get four pieces. If you keep cutting the pieces of paper in half, you would soon a reach a point where the pieces are too small to cut again. A radioactive isotope is a little like that sheet of paper.

### What Is a Radioactive Isotope?

A radioactive isotope, or radioisotope, has atoms with unstable nuclei. The unstable nuclei naturally decay, or break down, by losing energy and particles of matter to become more stable. If they gain or lose protons as they decay, they become different elements. Over time, as the nuclei continue to decay, less and less of the original radioisotope remains.

### Rate of Radioactive Decay

A radioisotope decays and changes to a different element at a constant rate. The rate is measured in a unit called the half-life. This is the length of time it takes for half of a given amount of the radioisotope to decay. This rate is always the same for a given radioisotope, regardless of temperature, pressure, or other conditions outside the nuclei of its atoms.

Q: How is repeatedly cutting paper in half like the decay of a radioisotope?

A: As a radioisotope decays, the amount of the radioisotope decreases by half during each half-life, just as a piece of paper decreases in size by half each time you cut it down the center. You can see a video of this half-life analogy at the following URL. http://blip.tv/chemteam/an-analogy-for-half-life-4507204

### Half-Life Example

The concept of half-life is illustrated in the Figure below for the decay of phosphorus-32 to sulfur-32. The half-life of phosphorus-32 is 14 days. After 14 days, half of the original amount of phosphorus-32 has decayed, so only half remains. After another 14 days, half of the remaining amount (or a quarter of the original amount) is still left, and so on.

Q: What fraction of the original amount of phosphorus-32 remains after three half-lives?

A: After three half-lives, or 42 days, 1/8 (1/2 x 1/2 x 1/2) of the original amount of phosphorus-32 remains.

### Variation in Half-Lives

Different radioisotopes may vary greatly in their rate of decay. That’s because they vary in how unstable their nuclei are. The more unstable the nuclei, the faster they break down. As you can see from the examples in the Table below, the half-life of a radioisotope can be as short as a split second or as long as several billion years. You can simulate radioactive decay of radioisotopes with different half-lives at the URL below. http://www.colorado.edu/physics/2000/isotopes/radioactive_decay3.html

Isotope Half-life
Uranium-238 4.47 billion years
Potassium-40 1.28 billion years
Carbon-14 5,700 years
Hydrogen-3 12.3 years
Polonium-214 0.00016 seconds

Q: If you had 1 gram of carbon-14, how many years would it take for radioactive decay to reduce it to 1/4 gram?

A: 1 gram would decay to ¼ gram in 2 half-lives. One half-life is 5,700 years, so two half-lives are 11,400 years.

### Summary

• A radioisotope decays and changes to a different element at a certain constant rate called the half-life. This is the length of time it takes for half of a given amount of the radioisotope to decay.
• Different radioisotopes may vary greatly in their rate of decay. The more unstable their nuclei are, the faster they decay.

### Vocabulary

• half-life: Length of time it takes for half of a given amount of a radioisotope to decay.

### Practice

Complete the radioactivity worksheet at this URL: http://zimearth.pbworks.com/f/Radioactivity+Worksheet.pdf

### Review

1. Define half-life.
2. Why do radioisotopes differ in the length of their half-lives?
3. What fraction of a given amount of hydrogen-3 would be left after 36.9 years of decay? (Hint: Find the half-life of hydrogen-3 in the table above.)

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### Vocabulary Language: English

TermDefinition
half-life Length of time it takes for half of a given amount of a radioisotope to decay.

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7 , 8
Date Created:
Nov 14, 2012