- For other uses, see Half-life (disambiguation).
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% |
| ... |
... |
| N |
 |
| ... |
... |
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.
Decay by two or more processes
A radioactive element may decay via two or more different processes. These processes may have different probabilities of occurring, and thus there is also a different half-life associated with each process.
As an example, for two decay modes, the amount of substance left after time t is given by
In a fashion similar to the previous section, we can calculate the new total half-life  and we'll find it to be
or, in terms of the two half-lives
Where  is the half-life of the first process, and  is the half life of the second process.
Related topics
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