http://www.ck12.org Chapter 3. Chemical Interactions
Half-Life Example
The concept of half-life is illustrated in theFigure3.113 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 3.113
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 theTable
3.14, 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
TABLE3.14:Half Life
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
Radon-222 3.82 days
Polonium-214 0.00016 secondsQ: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^14 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.