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Any one of decay constant, mean lifetime, or half-life is sufficient to characterise the decay. The notation λ for the decay constant is a remnant of the usual notation for an eigenvalue . In this case, λ is the eigenvalue of the negative of the differential operator with N ( t ) as the corresponding eigenfunction .
There is a half-life describing any exponential-decay process. For example: As noted above, in radioactive decay the half-life is the length of time after which there is a 50% chance that an atom will have undergone nuclear decay. It varies depending on the atom type and isotope, and is usually determined experimentally. See List of nuclides.
Alternatively, since the radioactive decay contributes to the "physical (i.e. radioactive)" half-life, while the metabolic elimination processes determines the "biological" half-life of the radionuclide, the two act as parallel paths for elimination of the radioactivity, the effective half-life could also be represented by the formula: [1] [2]
This value is in the denominator of the decay correcting fraction, so it is the same as multiplying the numerator by its inverse (), which is 2.82. (A simple way to check if you are using the decay correct formula right is to put in the value of the half-life in place of "t".
In principle a half-life, a third-life, or even a (1/√2)-life, could be used in exactly the same way as half-life; but the mean life and half-life t 1/2 have been adopted as standard times associated with exponential decay. Those parameters can be related to the following time-dependent parameters:
In practice, this means that alpha particles from all alpha-emitting isotopes across many orders of magnitude of difference in half-life, all nevertheless have about the same decay energy. Formulated in 1911 by Hans Geiger and John Mitchell Nuttall as a relation between the decay constant and the range of alpha particles in air, [ 1 ] in its ...
Sometimes a partial half-life is given, but this term is misleading; due to competing modes, it is not true that half of the particles will decay through a particular decay mode after its partial half-life. The partial half-life is merely an alternate way to specify the partial decay constant λ, the two being related through:
Half time is the time taken by a quantity to reach one half of its extremal value, where the rate of change is proportional to the difference between the present value and the extremal value (i.e. in exponential decay processes). It is synonymous with half-life, but used in slightly different contexts.