Half-life

Intermediate

Time for half the nuclei to decay.

Key relationT½ = ln2/λ

T½ = ln 2/λ = 0.693/λ: time for half the nuclei to decay, regardless of how many there are. Ranges from 10⁻²¹ s to 10²⁴ years.

Worked example

Iodine-131: 8 days; carbon-14: 5730 years.

Common mistake

After two half-lives, ¼ remains, not zero.

In more detail

The half-life is the time for half of a sample of radioactive nuclei to decay, T½ = ln2/λ. It is a fixed property of each isotope.

Carbon-14 has a half-life of about 5,730 years, used for dating.
Medical isotopes are chosen for half-lives suited to their use.
Medical staff use the half-life of a tracer to plan how long it stays active in a patient before it decays away.

Does half-life change with conditions?

No, it is independent of temperature, pressure and chemical state for most nuclei.

After two half-lives, how much is left?

One quarter of the original number.

How many half-lives until almost nothing is left?

After ten half-lives, less than one part in a thousand of the original nuclei remain.