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Half-life
The half-life of a radioactive substance is the time required for half of a sample to undergo radioactive decay.
More generally, for a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value. (This article is a narrow discussion of half-life. For phenomena where half-life is applied, see "Related topics" below.)
| After # of Half-lives | Percent of quantity remaining |
|---|---|
| 0 | 100% |
| 1 | 50 |
| 2 | 25 |
| 3 | 12.5 |
| 4 | 6.25 |
| 5 | 3.125 |
| 6 | 1.5625 |
| 7 | 0.78125% |
The table at right shows the reduction of the quantity in terms of the number of half-lives elapsed.
Quantities subject to exponential decay are commonly denoted by the symbol N. (This convention suggests a decaying number of discrete items. This interpretation is valid in many, but not all, cases of exponential decay.) If the quantity is denoted by the symbol N, the value of N at a time t is given by the formula:
where
- N0 is the initial value of N (at t=0)
- λ is a positive constant (the decay constant).
When t=0, the exponential is equal to 1, and N(t) is equal to N0. As t approaches infinity, the exponential approaches zero.
In particular, there is a time 
such that:
Substituting into the formula above, we have:
Thus the half-life is 69.3% of the mean lifetime.
Related topics
- Exponential decay
- Mean lifetime
- Radioactive decay
- Tables of nuclides with color-coding of half-lives:
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