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## Half-lifeThe The term
The table at right shows the reduction of the quantity in terms of the number of half-lives elapsed. It can be shown that, for exponential decay, the half-life where - ln(2) is the natural logarithm of 2 (approximately 0.693), and
- λ is the
**decay constant**, a positive constant used to describe the rate of exponential decay.
The half-life is related to the mean lifetime τ by the following relation:
## ExamplesThe constant λ can represent many different specific physical quantities, depending on what process is being described. - In an RC circuit or RL circuit, λ is the reciprocal of the circuit's time constant. For simple RC and RL circuits, λ equals 1 /
*R**C*or*R*/*L*, respectively. - In first-order chemical reactions, λ is the reaction rate constant.
- In radioactive decay, it describes the probability of decay per unit time:
*d**N*= λ*N**d**t*, where dN is the number of nuclei decayed during the time dt, and N is the quantity of radioactive nuclei. - In biology (specifically pharmacokinetics), from MeSH:
*Half-Life: The time it takes for a substance (drug, radioactive nuclide, or other) to lose half of its pharmacologic, physiologic, or radiologic activity. Year introduced: 1974 (1971)*.
## Decay by two or more processesSome quantities decay by two processes simultaneously (see Decay by two or more processes). In a fashion similar to the previous section, we can calculate the new total half-life or, in terms of the two half-lives i.e., half their harmonic mean. ## Simple Formulam(t) mass left depending on time.
m(0) = initial mass
## DerivationQuantities that are subject to exponential decay are commonly denoted by the symbol where When Substituting into the formula above, we have ## Experimental determinationThe half-life of a process can be determined easily by experiment. In fact, some methods do not require advance knowledge of the law governing the decay rate, be it exponential decay or another pattern. Most appropriate to validate the concept of half-life for radioactive decay, in particular when dealing with a small number of atoms, is to perform experiments and correct computer simulations. See in [1] how to test the behavior of the last atoms. Validation of physics-math models consists in comparing the model's behavior with experimental observations of real physical systems or valid simulations (physical and/or computer). The references given here describe how to test the validity of the exponential formula for small number of atoms with simple simulations, experiments, and computer code. In radioactive decay, the exponential model ## See also- Exponential decay
- Mean lifetime
- Elimination half-life
- For non-exponential decays, see half-life in the article Rate equation
## References**^**John Ayto "20th Century Words" (1999) Cambridge University Press.
Categories: Radioactivity | Chemical kinetics |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Half-life". A list of authors is available in Wikipedia. |