Half-life is the time required for half of the radioactive nuclei in a sample to decay. It is a measure of the stability and decay rate of radioactive isotopes.
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The half-life of a substance is constant and does not depend on the initial amount of the substance.
Half-life can be used to determine the age of archaeological samples through radiocarbon dating.
The formula to calculate remaining quantity after a certain number of half-lives is $N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$, where $N(t)$ is the remaining quantity, $N_0$ is the initial quantity, $t$ is time elapsed, and $T_{1/2}$ is the half-life.
Different isotopes have different half-lives, ranging from fractions of a second to billions of years.
Knowledge of half-life helps in medical applications such as cancer treatments using radioisotopes.
Review Questions
What does it mean when we say an isotope has a half-life of 5 years?
How would you calculate the remaining amount of a radioactive substance after three half-lives?
Why is understanding half-life important in fields like archaeology and medicine?