Half-life
The half-life of a radioactive isotope is the time it takes for half of the atoms in a sample to decay. It is the same no matter how large the sample is.
After each half-life, half of what was left remains.
| Half-lives | Fraction remaining |
|---|---|
| 0 | 1 |
| 1 | 1/2 |
| 2 | 1/4 |
| 3 | 1/8 |
| 4 | 1/16 |
amount remaining = starting amount × (1/2)n, where n is the number of half-lives
Decay is random for any single atom, but a large sample follows this pattern closely. Half-lives range from fractions of a second to billions of years. Carbon-14, with a half-life of 5730 years, is used to date material that was once alive.
Worked example: iodine-131
Iodine-131 has a half-life of 8 days. How much of an 80.0 g sample remains after 24 days?
Number of half-lives: 24 days ÷ 8 days = 3
80.0 g → 40.0 g → 20.0 g → 10.0 g
Common mistake
Thinking the sample is gone after two half-lives. Each half-life removes half of what remains, not half of the original. After two half-lives, one quarter is left.