**decay constant**Radioactive decay involves only the nucleus of the parent atom, and thus the rate of decay is independent of all physical and chemical conditions (e.g. pressure, temperature, etc.). The decay was shown byRutherford to follow an exponential law. The fundamental equation describing the rate of disintegration may be written as: −(

*dN/dt*) = λ

*N*, where λ is the decay constant, representing the probability that an atom will decay in unit time

*t*, and

*N*is the number of radioactive atoms present. It is a fundamental assumption in geochronology that λ is a constant and that the only alteration in the amount of daughter or parent in the system is due to radioactive decay. The constant λ is usually expressed in units of 10

^{-10}per year (e.g.

^{235}U is 9.72,

^{40}K is 5.31,

^{87}Rb is 0.139, and

^{238}U is 1.54). The total lifetime of a radioactive parent in a given system cannot be specified; in theory it is infinite. It is a simple matter, however, to specify the time for half of the radioactive parent atoms in a system to decay. This is called the ‘half-life’ (

*T*), which is related to the decay constant by the expression

*T*= 0.693/λ. See also DECAY CURVE.

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