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.)

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

• Exponential decay
• Mean lifetime
• Radioactive decay
• Tables of nuclides with color-coding of half-lives:
  • Isotope table (divided) with
  • Isotope table (complete)