Defined half-life

Radioactive isotopes are characterized by a number of parameters in addition to those attributable to chemistry. These are radioactive half-life, mode of decay, and type and quantity of radioactive emissions. The half-life, defined as the time required for one-half of a given quantity of radioactivity to decay, can range from milliseconds to biUions of years. Except for the most extreme conditions under very unusual circumstances, half-life is independent of temperature, pressure, and chemical environment. 

The half-life, defined in the previous section and listed for each isotope in Table 6.1, is an important property when designing experiments using radioisotopes. Using an isotope with a short half-life (for example, 24Na with ty2 = 15 hr) is difficult because the radioactivity lost during the course of the experiment is significant. Quantitative measurements made before and after the experiment must be corrected for this loss of activity. Radioactive phosphorus, 32P, an isotope of significant value in biochemical research, has a relatively short half-life (14 days), so if quantitative measurements are made they must be corrected as described in Equations 6.7 and 6.8. More information about the choice of a radioisotope in an experiment, the detec-... 

In addition to the three parameters, clearance (CL), bioavailability (F), and volume of distribution (V) discussed previously, a fourth parameter, half-life ( 1/2), is also crucial in therapeutics. The decreasing order of importance of these four parameters is clearance, bioavailability, half-life, and volume. Clearance defines the dosing rate, bioavailability defines dose adjustment, and half-life defines the dosing interval. Volume of distribution defines the loading dose. 

The activity of a given sample (which is proportional to N) therefore decays exponentially. The rate of decay is conventionally specified in terms of the half-life, defined as the time required for the activity to decrease by a factor of 2. It may readily be shown from equation (1.4) that the relation between the half-life T112) decay constant is... 

The far better understanding of rescue consequences caused by the deterioration of functional features of materials is directly related to the practice of industrial applications and the durability studies accomplished on multipurpose products. The synergetic actions of various factors leads to the conclusion that the simple addition of individual effects is possible, if a predominant factor directs degradation of a specific way. One illustrative kinetic parameter that characterizes the diminution of certain property is half life, defined by Eq. (7) [32] ... 

Half-life defined as the time required for half the atoms in a radioisotope to decay. Half-lives range from tiny fractions of a second to tens of thousands of years. The release of radioisotopes with long half-lives is associated with significant environmental contamination and risk to health. 

Radioactive waste is characterized by volume and activity, defined as the number of disintegrations per second, known as becquerels. Each radionucHde has a unique half-life,, and corresponding decay constant, A = 0.693/tj 2 For a component radionucHde consisting of JS1 atoms, the activity, M, is defined as... 

As previously diseussed, the half-life of a reaetion is defined as the time it takes for the eoneentration of the reaetant to fall to half of its initial value. Determining the half-life of a reaetion as a funetion of the initial eoneentration makes it possible to ealeulate the reaetion order and its speeifie reaetion rate. 

The half-life is defined as the time required for the eoneentration to drop to half of its initial value, that is, at t = = l/2C o-... 

The half-life tvi is defined to be the time required for the reactant concentration to decay to one-half its initial value. To find tvi for a first-order reaction we use Eq. (2-6) with the substitutions Ca = c°/2 and t = finding... 

Six isotopes of element 106 are now known (see Table 31.8) of which the most recent has a half-life in the range 10-30 s, encouraging the hope that some chemistry of this fugitive species might someday be revealed. This heaviest isotope was synthsised by the reaction Cm( Ne,4n) 106 and the present uncertainty in the half-life is due to the very few atoms which have so far been observed. Indeed, one of the fascinating aspects of work in this area is the development of philosophical and mathematical techniques to define and deal with the statistics of a small number of random events or even of a single event. 

Three ranges of values of n were considered, >1, 0.7—1.0 and <0.7. When n> 1, and particularly when 3 < n < 4, the Weibull distribution readily reduces to a normal distribution if the Erofe ev function is symmetrical about a = 0.5. [The Weibull distribution is symmetrical for n = 3.26, i.e. (1 — In 2)-1, and the inflection point varies only slowly with n.] Thus, under these conditions (3 < n < 4 and symmetry about a = 0.5), we may derive the parameters of the corresponding normal distribution (where p defines the half-life of the reaction and the dispersion parameter, a, is a measure of the lack of homogeneity of the surface centres), viz. 

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. 

The half-life of a radioactive species is defined as the time it takes for the activity of the sample to drop by 50%. In this activity, you will investigate the decay of 137Bam, a metastable isotope of barium that undergoes gamma decay with a half-life of several minutes. 

The decay constant, X, defines the probability that a particular atom will decay within a given time (X = In 2/t1/2). The half-life (t1/2) describes a time interval after which N = NJ2. The observed counting rate or activity (A) is equal to XN. Another way to describe radioactive decay is in terms of the mean life (t) of a... 

The radioligand should also have a high specific activity so that very small quantities of bound ligand can be accurately measured. The specific activity, simply defined as the amount of radioactivity, expressed in becquerels (Bq) or curies (Ci) per mole of ligand, is dependent on the half-life of the isotope used and on the number of radioactive atoms incorporated into the ligand molecule. A radioisotope with a short half-life decays rapidly so that many disintegrations occur in unit time,... 

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