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Exponential decay. A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant (λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Instead, the half-life is defined in terms of probability: "Half-life is the time required for exactly half of the entities to decay on average". In other words, the probability of a radioactive atom decaying within its half-life is 50%. [2] For example, the accompanying image is a simulation of many identical atoms undergoing radioactive decay.
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 ...
Effective half-life. In pharmacokinetics, the effective half-life is the rate of accumulation or elimination of a biochemical or pharmacological substance in an organism; it is the analogue of biological half-life when the kinetics are governed by multiple independent mechanisms. This is seen when there are multiple mechanisms of elimination ...
Biological half-life (elimination half-life, pharmacological half-life) is the time taken for concentration of a biological substance (such as a medication) to decrease from its maximum concentration (C max) to half of C max in the blood plasma. [1][2][3][4][5] It is denoted by the abbreviation . [2][4] This is used to measure the removal of ...
A recurrence relation is an equation that expresses each element of a sequence as a function of the preceding ones. More precisely, in the case where only the immediately preceding element is involved, a recurrence relation has the form. where. is a function, where X is a set to which the elements of a sequence must belong.
The doubling time is a characteristic unit (a natural unit of scale) for the exponential growth equation, and its converse for exponential decay is the half-life. As an example, Canada's net population growth was 2.7 percent in the year 2022, dividing 72 by 2.7 gives an approximate doubling time of about 27 years.
The Bateman equation is a classical master equation where the transition rates are only allowed from one species (i) to the next (i+1) but never in the reverse sense (i+1 to i is forbidden). Bateman found a general explicit formula for the amounts by taking the Laplace transform of the variables. (it can also be expanded with source terms, if ...
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