The half-life of polonium-214 is 164 microseconds. Every 164 microseconds, half of the atoms that are left decay, so after 2 half-lives (328 µs) a quarter is left, and after 10 (1,640 µs) about 0.10%.
Written as a rate, the decay constant is λ = ln 2 ÷ T½ = 4.227 × 10³ per second, and the average atom survives for the mean life τ = 237 microseconds. One gram of the pure isotope contains 2.81 × 10²¹ atoms and has an activity of 11.9 YBq.
Polonium-214 decay table
Each row is a number of half-lives, the time that takes for Po-214, 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 | 164 µs | 50% | 1 in 2 |
| 2 | 328 µs | 25% | 1 in 4 |
| 3 | 492 µs | 13% | 1 in 8 |
| 4 | 656 µs | 6.3% | 1 in 16 |
| 5 | 820 µs | 3.1% | 1 in 32 |
| 6 | 984 µs | 1.6% | 1 in 64 |
| 8 | 1,312 µs | 0.39% | 1 in 256 |
| 10 | 1,640 µs | 0.10% | 1 in 1,024 |
N = N₀ × 2^(−t ÷ 164 microseconds). With only 400 atoms in the simulation the count scatters about the curve, because each atom decays at a random time.
How long until Po-214 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% | 24.9 µs | 0.152 half-lives |
| 50% | 164 µs | 1.00 half-lives |
| 25% | 328 µs | 2.00 half-lives |
| 10% | 545 µs | 3.32 half-lives |
| 1.0% | 1,090 µs | 6.64 half-lives |
| 0.10% | 1,634 µs | 9.97 half-lives |
About polonium-214
Polonium-214 is a member of the uranium-238 decay chain, formed from bismuth-214, and it decays by emitting an alpha particle to lead-210. Its half-life of 164 microseconds is so short that it was identified only through the timing of its decay and its energetic alpha particle, about 7.7 MeV.
At this rate even a visible sample would be gone in a blink: a millisecond is 6.10 half-lives, so only 1.5% would be left. Isotopes this short-lived can only be studied as they are made by a longer-lived parent.
A worked example
How much of a polonium-214 sample is left after 1 millisecond?
1 ms ÷ 164 microseconds = 6.10 half-lives, so the fraction left is 2^(−6.10) = 1.5%.
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
- Iodine-131 half-life 8.02 days
- Technetium-99m half-life 6.0 hours
Frequently asked questions
What is the half-life of polonium-214?
164 microseconds. After that time half of any sample has decayed, and half remains.
How much Po-214 is left after 3 half-lives?
One eighth, 13%, after 492 µs.
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 Po-214 gone?
It never reaches exactly zero, but after 10 half-lives (1,640 µs) only 0.10% remains, which is the usual rule of thumb for “gone”.
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