Half-life

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The time in which one half of the atoms of a particular radioactive substance disintegrates into another nuclear form. Measured halflives vary from millionths of a second to billions of years. Also called physical or radiological halflife.

Radioactive decay is a random process. As such, one cannot state with certainty when an unstable nuclide will decay. The probability that an atom will decay during the time dt is given by kdt where k is the constant of proportionality known as the decay constant. In a system where there are N(0) atoms present initially, the number of atoms decaying in time dt is given by � dN = -k Ndt . In the limit of very small time intervals, this can be expressed as


dN/dt = -k N


Integration with respect to time gives the number of atoms present at any time t , i.e.


N(t) = N(0)e^{-kt}


The half-life, \tau, is used to denote the time at which the number of atoms has decreased to half the initial value, i.e. 1/2 = e^{-k\tau} . Hence the half-life is related to the decay constant through the relation


\tau = ln2/k0.693/k


See also Mean lifetime


References:

Wikipedia on halflife

J. Magill and J. Galy, Radioactivity Radionuclides Radiation, Springer Verlag, 2005.

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