The half-life of uranium-238 is 4.47 billion years. Every 4.47 billion years, half of the atoms that are left decay, so after 2 half-lives (8.94 bn y) a quarter is left, and after 10 (44.7 bn y) about 0.10%.
Written as a rate, the decay constant is λ = ln 2 ÷ T½ = 4.914 × 10⁻¹⁸ per second, and the average atom survives for the mean life τ = 6,448,846,833 years. One gram of the pure isotope contains 2.53 × 10²¹ atoms and has an activity of 12.4 kBq.
Uranium-238 decay table
Each row is a number of half-lives, the time that takes for U-238, 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 | 4.47 bn y | 50% | 1 in 2 |
| 2 | 8.94 bn y | 25% | 1 in 4 |
| 3 | 13.4 bn y | 13% | 1 in 8 |
| 4 | 17.9 bn y | 6.3% | 1 in 16 |
| 5 | 22.3 bn y | 3.1% | 1 in 32 |
| 6 | 26.8 bn y | 1.6% | 1 in 64 |
| 8 | 35.8 bn y | 0.39% | 1 in 256 |
| 10 | 44.7 bn y | 0.10% | 1 in 1,024 |
N = N₀ × 2^(−t ÷ 4.47 billion years). With only 400 atoms in the simulation the count scatters about the curve, because each atom decays at a random time.
How long until U-238 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% | 0.679 bn y | 0.152 half-lives |
| 50% | 4.47 bn y | 1.00 half-lives |
| 25% | 8.94 bn y | 2.00 half-lives |
| 10% | 14.8 bn y | 3.32 half-lives |
| 1.0% | 29.7 bn y | 6.64 half-lives |
| 0.10% | 44.5 bn y | 9.97 half-lives |
About uranium-238
Uranium-238 has a half-life of 4.47 billion years, within a few percent of the age of the Earth, about 4.54 billion years. Roughly half the uranium-238 that formed with the planet is still here, which is why it is a useful clock for the oldest rocks and zircon crystals, the oldest of which are about 4.4 billion years old.
It does not decay in one step. It passes through a chain of 14 steps, including radon-222 and polonium-214, before it ends as stable lead-206. Natural uranium is 99.3% uranium-238 and 0.7% uranium-235, the isotope used in reactors and weapons; see how Oppenheimer made the first nuke.
A worked example
A zircon crystal has kept 90% of its original uranium-238. How old is it?
t = −4.47 bn y × log₂(0.90) = 4.47 × 0.152 = 0.679 bn y. In practice geologists use the ratio of uranium to lead, which also tells how much has decayed.
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
- Iodine-131 half-life 8.02 days
- Polonium-214 half-life 164 microseconds
- Technetium-99m half-life 6.0 hours
Frequently asked questions
What is the half-life of uranium-238?
4.47 billion years. After that time half of any sample has decayed, and half remains.
How much U-238 is left after 3 half-lives?
One eighth, 13%, after 13.4 bn y.
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 U-238 gone?
It never reaches exactly zero, but after 10 half-lives (44.7 bn y) only 0.10% remains, which is the usual rule of thumb for “gone”.
Part of the learning path Stars and scale, from the Sun to a neutron star.
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