Each half-life halves what remains
The number of half-lives elapsed is the time divided by the half-life. Raise one half to that power to get the surviving fraction. Two half-lives leaves a quarter, three leaves an eighth. Time and half-life only need to be in the same unit.
Fraction left after each half-life
| Half-lives passed | Fraction left | Percent |
|---|---|---|
| 1 | 1/2 | 50% |
| 2 | 1/4 | 25% |
| 3 | 1/8 | 12.5% |
| 4 | 1/16 | 6.25% |
| 5 | 1/32 | 3.13% |
| 10 | 1/1024 | ~0.10% |
After about 10 half-lives a sample is treated as gone (under 0.1% left).
The exponential form and the decay constant
- Two ways, one answer. The half-life form and the e-to-the-minus-lambda-t form give identical results; λ = 0.693 / t½ ties them together.
- Fixed by the nucleus. Half-life does not change with temperature, pressure, or chemistry — it is intrinsic to the isotope.
- Mean lifetime differs. The average atom lasts τ = t½ / ln 2 ≈ 1.44 × t½, longer than the half-life.
Half-lives of common isotopes
| Isotope | Half-life | Used for |
|---|---|---|
| Technetium-99m | 6.0 hours | Medical imaging |
| Iodine-131 | 8.0 days | Nuclear medicine |
| Cobalt-60 | 5.27 years | Cancer therapy |
| Carbon-14 | 5,730 years | Archaeological dating |
| Uranium-238 | 4.47 billion years | Geological dating |
Common questions
How do I calculate how much is left after a given time?
Raise one half to the power of time divided by the half-life, then multiply by the starting amount. After 3 half-lives you have (1/2) cubed, which is 1/8, or 12.5 percent left. The units of time and half-life just have to match.
How long until a radioactive sample is essentially gone?
There is no true zero, but after about 10 half-lives less than 0.1 percent remains, which is usually treated as gone. For iodine-131 (8-day half-life) that is roughly 80 days.
Does temperature or pressure change the half-life?
No. Half-life is a fixed property of the nucleus and does not depend on temperature, pressure, or the chemical form of the atom.
