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    half-life

    decay curve
    Decay curve of tritium (H-3) – half-life 12.3 years
    Credit: European Nuclear Society
    The time taken for a substance or collection of particles to decay by half of its original amount.

    Half-life, denoted T½, 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 by

    N = N0 exp(- λt),

    where N0 is the original number and λ is the decay constant, which is equal to 0.693T½. The following relationships also exist between the half-life (T½), decay constant (λ), and average lifetime (τ):
    T½ = λ-1 · ln 2 = 0.693/λ
    λ = T½ · ln 2 = 0.693/T½
    τ = 1.44 T½
    There are extreme variations in the half-lives of the various radionuclides, e.g. from 7.2 × 1024 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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