Half-life
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, non-exponential) decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time.
| Number of half-lives elapsed | Fraction remaining | Percentage remaining | |
|---|---|---|---|
| 0 | 1⁄1 | 100 | |
| 1 | 1⁄2 | 50 | |
| 2 | 1⁄4 | 25 | |
| 3 | 1⁄8 | 12 | .5 |
| 4 | 1⁄16 | 6 | .25 |
| 5 | 1⁄32 | 3 | .125 |
| 6 | 1⁄64 | 1 | .5625 |
| 7 | 1⁄128 | 0 | .78125 |
| n | 1⁄2n | 100⁄2n | |
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The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s. Rutherford applied the principle of a radioactive element's half-life in studies of age determination of rocks by measuring the decay period of radium to lead-206.
Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.