A half-life is the time it takes for half of the radioactive atoms in a sample to decay, so activity falls to 50 percent after one half-life, 25 percent after two and below 0.1 percent after ten. A half-life is not a safety timer: the starting activity decides whether what remains is harmless, and a mixture of isotopes does not follow a single half-life.
Part of Radiation Safety
Radioactive decay is statistical: no single atom can be predicted, but a large sample loses half its atoms in a fixed time that is characteristic of each isotope.
Each Half-Life Halves What Is Left
The parent article, Nuclear Safety, gives the sequence: after one half-life 50 percent remains, after two 25 percent, after seven less than 1 percent and after ten less than 0.1 percent. The arithmetic is (1/2)^n:
- n = 7: 2^-7 = 1/128 = 0.78 percent.
- n = 10: 2^-10 = 1/1,024 = 0.098 percent.
Half-Lives Of The Isotopes That Matter
These figures are from the parent article’s table:
| Isotope | Half-life | Source | Concern |
|---|---|---|---|
| Iodine-131 | 8 days | Reactor accidents, bombs | Thyroid cancer, dangerous for weeks |
| Cobalt-60 | 5.3 years | Medical and industrial sources | Intense gamma, lethal in minutes at close range |
| Strontium-90 | 29 years | Reactor fuel, fallout | Mimics calcium, deposits in bones |
| Caesium-137 | 30 years | Reactor fuel, fallout | Soil contamination for centuries |
| Carbon-14 | 5,730 years | Natural, reactors | Low activity, minimal concern |
| Plutonium-239 | 24,100 years | Reactor fuel, weapons | Lung cancer if inhaled, area denial |
Worked Example: Waiting Out Iodine-131 And Caesium-137
Ten half-lives of iodine-131 is 10 x 8 days = 80 days, which is why the parent article advises avoiding milk from contaminated pasture for at least 90 days (about 11 half-lives). Ten half-lives of caesium-137 is 10 x 30 years = 300 years, so waiting is not a strategy for soil carrying it; the practical response is to avoid the ground, keep food from it out of the diet, and survey; see Contamination Pathways.
Short Half-Life Means Intense Then Gone, Long Means Faint And Lasting
For the same number of atoms, a short-lived isotope emits far more radiation per second than a long-lived one, because its atoms decay faster. That is why fresh fallout is dangerous in hours and days while carbon-14 is of little concern. The same logic gives the fallout rule of thumb: the parent article’s 7-10 rule says dose rate falls by a factor of 10 for every sevenfold increase in time, so 1/10 at 7 hours and 1/100 at 49 hours. See Fallout Patterns.
Common Mistakes
- “Ten half-lives is always safe.” The parent article calls under 0.1 percent generally considered safe, but 0.1 percent of a very large activity is still large.
- Applying one half-life to fallout. Fallout contains many isotopes with different half-lives; the dose rate follows the 7-10 rule rather than a single halving time, and the rule is a guide for a single detonation, not for a reactor release.
- Confusing half-life with biological removal. The body also clears some isotopes by itself; that is a separate, slower or faster process and is not covered here.
Safety
Decay does not make an unknown area safe on a schedule
You cannot compute how much activity is left without knowing what was released and how much. Time since an event is a reason for caution to relax gradually, never a basis for entering a site without survey. Use Survey Procedures and treat unknown ground as hazardous.
What’s Next
- Learn next: Units of Measurement — activity versus dose
- Combine with: Fallout Patterns — how decay governs shelter time