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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
