## half-life
Half-life, denoted t_{½}, is a useful concept by which
to express the rate of radioactive decay.
After one half-life, half of the original number of atoms of a radioactive
element will remain. After two half-lives, one-quarter (= ½ ×
½) will remain. After three half-lives, 1/8 (= ½ × ½
× ½) will remain, and so on. The mathematical relationship is exponential and at any time t the number remaining n is given byn = n_{0} exp(- λt),
where n_{0} is the original number and λ
is the decay constant, which is equal to 0.693t_{½}.
The following relationships also exist between the half-life ( t_{½}),
decay constant (λ), and average lifetime (τ):
There are extreme variations in the half-lives of the various radionuclides, e.g. from 7.2 × 10 ^{24} years for tellurium-128
down to 2 × 10^{-16} seconds for beryllium-8.
## Related categories• ATOMIC AND NUCLEAR PHYSICS• PARTICLE PHYSICS | |||||||||

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