The half-life of iodine-131 is 8.02 days. Every 8.02 days, half of the atoms that are left decay, so after 2 half-lives (16.0 d) a quarter is left, and after 10 (80.2 d) about 0.10%.
Written as a rate, the decay constant is λ = ln 2 ÷ T½ = 1.000 × 10⁻⁶ per second, and the average atom survives for the mean life τ = 11.6 days. One gram of the pure isotope contains 4.60 × 10²¹ atoms and has an activity of 4.6 PBq.
Iodine-131 decay table
Each row is a number of half-lives, the time that takes for I-131, and what is left. The fraction is 2 raised to minus the number of half-lives, for any sample size.
| Half-lives | Time | Fraction left | Odds an atom survives |
|---|---|---|---|
| 1 | 8.02 d | 50% | 1 in 2 |
| 2 | 16.0 d | 25% | 1 in 4 |
| 3 | 24.1 d | 13% | 1 in 8 |
| 4 | 32.1 d | 6.3% | 1 in 16 |
| 5 | 40.1 d | 3.1% | 1 in 32 |
| 6 | 48.1 d | 1.6% | 1 in 64 |
| 8 | 64.2 d | 0.39% | 1 in 256 |
| 10 | 80.2 d | 0.10% | 1 in 1,024 |
N = N₀ × 2^(−t ÷ 8.02 days). With only 400 atoms in the simulation the count scatters about the curve, because each atom decays at a random time.
How long until I-131 drops to a given level
Running the law backwards gives the time for the sample to fall to a chosen fraction, t = −T½ log₂(fraction). This is also how a measured fraction becomes an age.
| Fraction left | Time needed | Half-lives |
|---|---|---|
| 90% | 1.22 d | 0.152 half-lives |
| 50% | 8.02 d | 1.00 half-lives |
| 25% | 16.0 d | 2.00 half-lives |
| 10% | 26.6 d | 3.32 half-lives |
| 1.0% | 53.3 d | 6.64 half-lives |
| 0.10% | 79.9 d | 9.97 half-lives |
About iodine-131
Iodine-131 collects in the thyroid gland, which is why it is both a treatment for thyroid disease and the isotope that worries doctors after a reactor accident. A half-life of 8.02 days is short enough that it fades within a few months and long enough to travel with the wind and be taken up by milk and food before it does.
A common rule of thumb is that a radioactive source is essentially gone after ten half-lives, which is 80.2 d here, at which point 0.10% remains.
A worked example
A dose is measured at 100 MBq. How much is left 24 days later?
24 days = 2.99 half-lives, so the activity is 100 × 2^(−2.99) = 12.6 MBq.
Compare with other isotopes
The half-lives in the simulation span twenty orders of magnitude, from microseconds to billions of years. Each has its own page.
| Isotope | Half-life | Activity per gram |
|---|---|---|
| Carbon-14 | 5,730 years | 165 GBq |
| Uranium-238 | 4.47 billion years | 12.4 kBq |
| Iodine-131 | 8.02 days | 4.6 PBq |
| Polonium-214 | 164 microseconds | 11.9 YBq |
| Technetium-99m | 6.0 hours | 195 PBq |
This page is one case from the full guide, Half-life and radioactive decay simulator, which covers every case, the assumptions behind the model and what it leaves out.
Other cases
- Carbon-14 half-life 5,730 years
- Uranium-238 half-life 4.47 billion years
- Polonium-214 half-life 164 microseconds
- Technetium-99m half-life 6.0 hours
Frequently asked questions
What is the half-life of iodine-131?
8.02 days. After that time half of any sample has decayed, and half remains.
How much I-131 is left after 3 half-lives?
One eighth, 13%, after 24.1 d.
Does the half-life depend on how much there is?
No. Each atom has the same chance of decaying in any moment, so the time for half of a sample to decay is the same for a gram or a ton. Heat, pressure and chemistry do not change it for ordinary decay.
When is I-131 gone?
It never reaches exactly zero, but after 10 half-lives (80.2 d) only 0.10% remains, which is the usual rule of thumb for “gone”.
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