Fractional life-time

Other fractional lives could similarly be defined. For example, the life-time t is the time required for the concentration to decay to lie its initial value then we find T = l/k. The lifetime is the average time elapsed before a molecule reacts. In pharmaceutics, a shelf-life tgo is defined to be the time required for Ca to reach the value 0.90 Ca, giving tgo = O.lOSlkf)... 

Figure 1. (a) Schematic representation of the evolution by radioactive decay of the daughter-parent (N2/N1) activity ratio as a function of time t after an initial fractionation at time 0. The initial (N2/Ni)o activity ratio is arbitrarily set at 2. Time t is reported as t/T2, where T2 is the half-life of the daughter nuclide. Radioactive equilibrium is nearly reached after about 5 T2. (b) Evolution of (N2/N1) activity ratios for various parent-daughter pairs as a function of time since fractionation (after Williams 1987). Note that the different shape of the curves in (a) and (b) is a consequence of the logarithmic scale on the x axis in (b). 

Fractional lifetime method. The half-life, tm, of a reactant is the time required for its concentration to decrease to one-half its initial value. Measurement of tll2 can be used to determine kinetics parameters, although, in general, any fractional life, r, can be... 

Fractional Life Method The half-life method can be extended to any fractional life method in which the concentration of reactant drops to any fractional value F = C /Cao in time The derivation is a direct extension of the half-life method giving... 

Let us first consider the irradiation of bulk monomer the ionization of monomer molecules by radiation results in the formation of cations and electrons. The former are formed through the removal of one electron from neutral molecules, so that they have an unpaired electron as well as positive excess charge and therefore are termed cation radicals. Most of the cation radicals and the electrons recombine immediately with each other, and only a fraction of them have a life-time long enough to enable themselves to act as primary active intermediates to bring about ionic reactions. However, both primary intermediates may react with monomer molecules, so that both cationic and anionic reactions of monomer may proceed and the whole reaction scheme is too complex to be studied distinctly. 

Fractional life Half-life Quarter-life t /4 Relaxation time r... 

It is clear that the wetted surface is destroyed within a fraction of a second. Link [60] investigated the residence time of a liquid droplet onto a solid particle, and found that the liquid evaporates within the range of few seconds. The life-time of the film is thus greater than the time taken for the liquid film to be destroyed. The reason for this limitation of absorption by the liquid-phase mass transfer is the permanent destruction of the liquid film. 

Polymer name o-Ps Life- time x3(ns) Free- Volume Radius (A) o-Ps Inten- sity %) Free- Volume Fraction (%) Longer o-Ps Lifetime X4 (ns) Longer o-Ps Intensity I4 (%) Ref Comments... 

Fractional-life methods. If a reaction is known to be first order and at constant fluid density, its apparent rate coefficient can be found very quickly. For batch and differential recycle reactors, the relationship between the rate coefficient and the time ty required for all but a fraction y of the reactant to be consumed is... 

As the steady state is approached, the curves in the first-order plots become parallel straight lines. Accordingly, the fractional-life equation 5.8 can be used to obtain an estimate of from the time required to approach this condition closely. The individual coefficients kn and can then be obtained from their sum and the equilibrium constant Kn = k12 /k21 ... 

Cumuiative exposure ievei (vaiues in [ ]) Typioai ooncentration [2x10 f/mL] x Life span [70 years] x Fraction of time outdoors [0.1]... 

Table 15 Various properties related to hydrogen bonds in urea-water mixtures, gives the mole fraction of urea, and itx gives the number of hydrogen bonds around molecules of the type X. T y gives the life time (in fs) for hydrogen bonds between molecules x and y, with x being the donor and y the acceptor. The two entries for each concentration shows the results for the two different models for urea. All results are from ref. 52...

The composition and rate of formation of all the products have been studied as a function of flash times. The mass balances are excellent. The results clearly show that the reaction begins with depolymerization processes giving rise to a short life time intermediate confound (ILC) that is liquid at reaction terrq)erature but solid at room temperature. This product partially decomposes into condensible vapours. A fraction of them undergoes a thermal cracking producing gases inside or in the vicinity of the sample. For heat flux densities higher than approximately 9 x 10 W m, no char is observed. 

The rate (frequency) of disintegration is an inherent property of a given radioisotope and varies widely among isotopes. The half-life (time of survival of half the initial set of radioactive atoms) may be millions of years (e.g., Np) to a fraction of a second (e.g., P). Since disintegrations in a small interval of time are rare and independent of other time intervals, disintegration in equal finite intervals follows the Poisson distribution. The probability of atoms still being radioactive, P(0) (in which 0 indicates no nuclear transformations), after t intervals with a decay constant 6 (= fraction of radioactive atoms decayed per interval, if seconds, 5 if days) thus equals... 

La - fraction of the active ingredient in the dry film released during the life time t, assumed to be 0.7... 

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