Radioactive Half-life
Jean Brainard, Ph.D.
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Printed: January 19, 2015
AUTHOR
Jean Brainard, Ph.D.
www.ck12.org
C HAPTER
Chapter 1. Radioactive Half-life
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Radioactive Half-life
• Define the half-life of a radioisotope.
• Explain variation in half-lives.
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
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Half-Life Example
The concept of half-life is illustrated in the Figure 1.1 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.
FIGURE 1.1
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 × 1/2 × 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 1.1,
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
TABLE 1.1: Half Life
Isotope
Uranium-238
Potassium-40
Carbon-14
Hydrogen-3
Radon-222
Polonium-214
Half-life
4.47 billion years
1.28 billion years
5,700 years
12.3 years
3.82 days
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
1
4
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.
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Chapter 1. Radioactive Half-life
Explore More
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 1.1.)
References
1. Christopher Auyeung. Diagram illustrating half-life of radioactive samples . CC BY-NC 3.0
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