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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.
A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. (If N(t) is discrete, then this is the median life-time rather than the mean life-time.) This time is called the half-life, and often denoted by the symbol t 1/2. The half-life can be ...
Absorption half-life 1 h, elimination half-life 12 h. 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.
Currently, the most precise results come from the Super-Kamiokande water Cherenkov radiation detector in Japan: [13] a lower bound on the proton's half-life of 2.4 × 10 34 years via positron decay, and similarly, 1.6 × 10 34 years via antimuon decay, close to a supersymmetry (SUSY) prediction of 10 34 –10 36 years. [14]
When radionuclides are used pharmacologically, for example in radiation therapy, they are eliminated through a combination of radioactive decay and biological excretion.An effective half-life of the drug will involve a decay constant that represents the sum of the biological and physical decay constants, as in the formula:
As an extreme example, the half-life of the isotope bismuth-209 is 2.01 × 10 19 years. The isotopes in beta-decay stable isobars that are also stable with regards to double beta decay with mass number A = 5, A = 8, 143 ≤ A ≤ 155, 160 ≤ A ≤ 162, and A ≥ 165 are theorized to undergo alpha decay.
For example, for decays of 132 Cs, 98.13% are ε (electron capture) or β + decays, and 1.87% are β − decays. The half-life of this isotope is 6.480 days, [2] which corresponds to a total decay constant of 0.1070 d −1. Then the partial decay constants, as computed from the branching fractions, are 0.1050 d −1 for ε/β + decays, and 2.14 ...
Considering all decay modes, various models indicate a shift of the center of the island (i.e., the longest-living nuclide) from 298 Fl to a lower atomic number, and competition between alpha decay and spontaneous fission in these nuclides; [83] these include 100-year half-lives for 291 Cn and 293 Cn, [55] [78] a 1000-year half-life for 296 Cn ...