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In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to fall to half of its initial value. In a first-order reaction the half-life of the reactant is ln(2)/λ, where λ (also denoted as k) is the reaction rate constant.
Caesium in the body has a biological half-life of about one to four months. Mercury (as methylmercury) in the body has a half-life of about 65 days. Lead in the blood has a half life of 28–36 days. [29] [30] Lead in bone has a biological half-life of about ten years. Cadmium in bone has a biological half-life of about 30 years.
Here stands for concentration in molarity (mol · L −1), for time, and for the reaction rate constant. The half-life of a first-order reaction is often expressed as t 1/2 = 0.693/k (as ln(2)≈0.693).
where / is the combined or total half-life for the process, and are so-named partial half-lives of corresponding processes. Terms "partial half-life" and "partial mean life" denote quantities derived from a decay constant as if the given decay mode were the only decay mode for the quantity.
As useful rules of thumb, a first-order reaction with a rate constant of 10 −4 s −1 will have a half-life (t 1/2) of approximately 2 hours. For a one-step process taking place at room temperature, the corresponding Gibbs free energy of activation (ΔG ‡) is approximately 23 kcal/mol.
Therefore, the half-life for this process (which differs from the mean lifetime by a factor of ln(2) ≈ 0.693) is 611 ± 1 s (about 10 min, 11 s). [ 3 ] [ 4 ] The beta decay of the neutron described in this article can be notated at four slightly different levels of detail, as shown in four layers of Feynman diagrams in a section below .
Holiday travelers setting out for what is expected to be one of the busiest travel weekends of the year are already facing delays as a severe round of storms rolls into the Southern US.
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.