Half-Life
Definition and meaning of Half-Life in chemistry.
Half-life is the time it takes for half of a radioactive isotope, or half of a reactant in a first-order reaction, to disappear. After one half-life, exactly 50% of the original amount remains. This value stays constant no matter how much material you start with, as long as the decay or reaction is first order.
In more detail
The half-life, written t½, relates to the rate constant k through the equation t½ = ln2 / k, which is approximately 0.693 / k. Because the half-life is fixed, each successive half-life removes half of whatever amount remains, not half of the original amount. This produces a curve that drops steeply at first and then levels off, called exponential decay, rather than a straight line.
Since t½ does not depend on how much material is present, scientists use it to date archaeological and geological samples with a reliable, predictable clock. Doctors and pharmacists also use half-life to plan dosing schedules for radioactive tracers and many drugs, since it tells them how quickly a substance clears from the body.
Reactions that are not first order behave differently. Their half-lives change depending on how much reactant is present at the start, which makes calculations more complex. Nuclear medicine uses isotopes with short half-lives, such as technetium-99m, so that a diagnostic dose delivers its imaging signal and then decays away quickly, limiting a patient's radiation exposure.
Key facts
| Formula | t½ = ln2 / k (first-order and radioactive decay) |
|---|---|
| Field | Physical Chemistry |
| Example isotope | Carbon-14, t½ approximately 5,730 years |
| Key property | Constant, independent of starting amount (first-order only) |
| Common application | Radiocarbon dating and drug dosing schedules |
Carbon-14 has a half-life of about 5,730 years. A sample that starts with 80 milligrams of carbon-14 will have 40 milligrams left after 5,730 years, 20 milligrams after 11,460 years, and 10 milligrams after 17,190 years. Archaeologists use this steady decay in a method called radiocarbon dating to estimate the age of organic remains up to roughly 50,000 years old.
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, half-life does depend on the initial concentration.
Is half-life the same as mean lifetime?
No. Mean lifetime, the average lifetime, is longer than the half-life. The two are related by t½ = τ · ln2.
Why does carbon-14 dating stop working after about 50,000 years?
After many half-lives, too little carbon-14 remains to measure accurately. That limit is what caps how far back the method can reliably date a sample.