The half-life of a radioactive substance is the time required for half of a sample to undergo radioactive decay. Radioactive decay is the set of various processes by which unstable atomic nuclei (nuclides) emit subatomic particles. ...

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.) A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ...

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. Given an assembly of elements, the number of which decreases ultimately to zero, the lifetime (also called the mean lifetime) is a certain number that characterizes the rate of reduction (decay) of the assembly. ...

Decay by two or more processes

A radioactive element may decay via two or more different processes. These processes may have different probabilities of occuring, and thus there is also a different half-life associated with each process.

As an example, for two decay modes, the ammount of substance left after time t is given by

In a fashion similar to the previous section, we can calculate the new total half-life and we'll find it to be

or, in terms of the two half-lives

Where is the half-life of the first process, and is the half life of the second process.

Related topics

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