Half-lives definition

Appendix Lifetime and Half-Life Definitions and Their Relationship References... 

Litde is known about metaboHc inactivation of ( -endorphin and the dynorphins. NEP, and to a lesser extent APN, are only weaMy active against P-endorphin (183). Enzymes are known which degrade P-endorphin in vitro under nonphysiological conditions (202) or which inactivate P-endorphin by N-acetjlation (203). Alack of specific degradative enzymes for these peptides may account for their relatively long half-life in vivo though this has not been definitively estabUshed. 

Coagulation factors are glycoproteins named by roman numbers (the numbers being ascribed at the time of the components definition, not sequence of activation) (Table 1). Besides von Willebrand factor (vWF), the coagulation factors are synthesized in the liver. They have very different half-lifes and different concentrations in the plasma. Several coagulation factors are stored in platelets and endothelial cells and can be released during activation of these cells, which can result in a much higher local concentration of the respective factor (e.g., vWF). 

A free radical (often simply called a radical) may be defined as a species that contains one or more unpaired electrons. Note that this definition includes certain stable inorganic molecules such as NO and NO2, as well as many individual atoms, such as Na and Cl. As with carbocations and carbanions, simple alkyl radicals are very reactive. Their lifetimes are extremely short in solution, but they can be kept for relatively long periods frozen within the crystal lattices of other molecules. Many spectral measurements have been made on radicals trapped in this manner. Even under these conditions, the methyl radical decomposes with a half-life of 10-15 min in a methanol lattice at 77 K. Since the lifetime of a radical depends not only on its inherent stabihty, but also on the conditions under which it is generated, the terms persistent and stable are usually used for the different senses. A stable radical is inherently stable a persistent radical has a relatively long lifetime under the conditions at which it is generated, though it may not be very stable. 

Disintegration, Nuclear—A spontaneous nuclear transformation (radioactivity) characterized by the emission of energy and/or mass from the nucleus. When large numbers of nuclei are involved, the process is characterized by a definite half-life (see Transformation, Nuclear). 

After a length of time equal to one half-life fi/2, the concentration of A will be [A], which, from the definition of half-life, has a value of [A]0. 

Since all of the above-mentioned interconversion reactions are reversible, any kinetic analysis is difficult. In particular, this holds for the reaction Sg - Sy since the backward reaction Sy -+ Sg is much faster and, therefore, cannot be neglected even in the early stages of the forward reaction. The observation that the equilibrium is reached by first order kinetics (the half-life is independent of the initial Sg concentration) does not necessarily indicate that the single steps Sg Sy and Sg Sg are first order reactions. In fact, no definite conclusions about the reaction order of these elementary steps are possible at the present time. The reaction order of 1.5 of the Sy decomposition supports this view. Furthermore, the measured overall activation energy of 95 kJ/mol, obtained with the assumption of first order kinetics, must be a function of the true activation energies of the forward and backward reactions. The value found should therefore be interpreted with caution. 

In computational science and engineering, researchers frequently speak of multiple time-scale problems. These are problems ivhere the characteristic times for events span many orders of magnitude. More often than not, the full range of desired time-scales is not experimentally accessible. The combined experimental and numerical approach must settle for analysis of a narrow ivindoiv of time-scales. For most of our purposes, the half-life of an event w ill prove to be a useful definition of characteristic time-scale... 

A simple way to characterize the rate of a reaction is the time it takes for the concentration to change from the initial value to halfway between the initial and final (equilibrium). This time is called the half-life of the reaction. The half-life is often denoted as ti/z. The longer the half-life, the slower the reaction. The half-life is best applied to a first-order reaction (especially radioactive decay), for which the half-life is independent of the initial concentration. For example, using the decay of " Sm as an example, [ Sm] = [ Sm]o exp( kt) (derived above). Now, by definition,... 

To avoid confusion and maintain consistency, we need a unique definition of diffusion distance, similar to the concept of half-life. In this book, a midconcentration distance for diffusion is defined. The midconcentration distance... 

The half-life of a reactant and the mean reaction time of a reaction are two measures of the time to reach equilibrium. The half-life ty2 is the time for the reactant to decrease to half of its initial concentration, or more generally, the time for it to decrease to halfway between the initial and the final equilibrium concentration. The mean reaction time t is roughly the time it takes for the reactant concentration to change from the initial value to 1/e toward the final (equilibrium) value. The rigorous definition of the mean reaction time t is through the following equation (Equation 1-60) ... 

Because a diffusion profile does not end abruptly (except for some special cases), it is necessary to quantify the meaning of diffusion distance. To do so, examine Equation 3-40a. Define the distance at which the concentration is halfway between Co and to be the mid-distance of diffusion, Xmid- The concept of Xmid is similar to that of half-life ti/2 for radioactive decay. From the definition, Xmid can be solved from the following ... 

Fractional Change Method From the equations of half life tor reactions of various orders except first order reaction, time required to complete a definite fraction of the reaction is inversely proportional to af- where n is the order of reaction and a is initial concentration. 

Appendix B reviews some important animal studies of cholinesterase reactivator chemicals. The extensive literature reviewed offers little definitive information with which to project possible long-term effects or delayed sequelae in human subjects tested at Edgewood. These compounds have a short biologic half-life of 1 to 3 h. However, no chronic studies were found. Consequently, the carcinogenic potential of cholinesterase reactivators remains... 

UDP-apiose (5) is very unstable under a variety of conditions of pH and temperature this instability had previously prevented 7 the isolation of sufficient quantities of UDP-apiose for definitive identification. UDP-[U-l4C]apiose is degraded at pH 8.0 to uridine 5 -phosphate and 3-C-(hydroxymethyl)-a-D-[U-14C] erythrofuranosyl 1,2-phosphate at 80, 25, and 4°. The half-lives of UDP-[U-14C]apiose under these conditions are 31.6 seconds, 97.2 minutes, and 16.5 hours, respectively.7 The half-life of UDP-[U-,4C]apiose at pH 3.0 and 40° is 4.67 minutes. It is degraded7 to uridine 5 -pyrophosphate and D-[U-I4C]apiose. At pH 6.2-6.6 and 4°, degradation (of both the... 

According to this definition the lifetime is the time required for the luminescence intensity to drop from 1(0) to /t = I (0)/e it should not be confused with the half-life often used for radioactive decays, this being the time t j2 required to decrease the intensity of emission from 1(0) to I (0)/2. 

The half-life for a given nuclide can be derived from Equation (3.6) when the value of the decay constant is known. In accordance with the definition of the term half-life, when A /A0 = 1 /2, then t = tx /2. Substituting these values into Equation (3.6) gives... 

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