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The term "half-life" is almost exclusively used for decay processes that are exponential (such as radioactive decay or the other examples above), or approximately exponential (such as biological half-life discussed below). In a decay process that is not even close to exponential, the half-life will change dramatically while the decay is happening.
The exponential time-constant for the process is =, so the half-life is (). The same equations can be applied to the dual of current in an inductor. Furthermore, the particular case of a capacitor or inductor changing through several parallel resistors makes an interesting example of multiple decay processes, with each resistor representing ...
Derivation of equations that describe the time course of change for a system with zero-order input and first-order elimination are presented in the articles Exponential decay and Biological half-life, and in scientific literature. [1] [7] = C t is concentration after time t
In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. [1]
The absorption rate constant K a is a value used in pharmacokinetics to describe the rate at which a drug enters into the system. It is expressed in units of time −1. [1] The K a is related to the absorption half-life (t 1/2a) per the following equation: K a = ln(2) / t 1/2a.
The voltage (v) on the capacitor (C) changes with time as the capacitor is charged or discharged via the resistor (R) In electronics, when a capacitor is charged or discharged via a resistor, the voltage on the capacitor follows the above formula, with the half time approximately equal to 0.69 times the time constant, which is equal to the product of the resistance and the capacitance.
Using the Eyring equation, there is a straightforward relationship between ΔG ‡, first-order rate constants, and reaction half-life at a given temperature. At 298 K, a reaction with Δ G ‡ = 23 kcal/mol has a rate constant of k ≈ 8.4 × 10 −5 s −1 and a half life of t 1/2 ≈ 2.3 hours, figures that are often rounded to k ~ 10 −4 s ...
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.