Half-Life
Definition and meaning of Half-Life in chemistry.
Half-life (t½) is the time required for the amount of a radioactive isotope, or the concentration of a reactant in a first-order reaction, to decrease to exactly one-half of its initial value.
In more detail
For radioactive decay and first-order kinetics, half-life is constant and independent of how much material is present, related to the rate (or decay) constant k by t½ = ln2/k ≈ 0.693/k. This means each successive half-life removes half of whatever remains, producing an exponential decay curve rather than a straight-line decrease. Because t½ does not depend on concentration, it is widely used to date archaeological and geological samples and to plan storage or dosing schedules for radioactive materials and drugs. Reactions with orders other than first order have half-lives that do depend on initial concentration.
Key facts
| Formula | t½ = ln2/k (first-order/radioactive decay) |
|---|---|
| Field | Physical Chemistry |
| Example isotope | Carbon-14, t½ ≈ 5,730 years |
| Key property | Constant, independent of initial amount (first-order only) |
Carbon-14 has a half-life of about 5,730 years. A sample starting with 80 mg of carbon-14 will contain 40 mg after 5,730 years, 20 mg after 11,460 years, and 10 mg after 17,190 years.
Frequently asked questions
Does half-life depend on how much substance you start with?
For radioactive decay and first-order reactions, no, the half-life is a fixed constant regardless of the starting amount. For second-order reactions, however, half-life does depend on the initial concentration.
Is half-life the same as mean lifetime?
No. Mean lifetime (average lifetime, τ = 1/λ) is longer than the half-life; they are related by t½ = τ·ln2.