Similar half-lives

As the difference between the half-lives of mother nuclide and daughter nuclide becomes smaller and smaller, the attainment of radioactive equilibrium is more and more delayed, as can be seen from eq. (4.20) and from Fig. 4.2, provided that ti/2(l) 1/2 (2). In this situation, the following questions are of practical interest  

In answering question (a), it is assumed that an error s can be accepted in measuring the decay curve  

Introducing the half-lives, the following equations are calculated for the time after which the decay curve of the longer-lived radionuclide is observed with an error e  

Application of this formula to the case of the sequence of radionuclides 

In order to answer question (b), eq. (4.17) is differentiated with respect to time and d V2/df is set equal to zero. The resulting equation is 

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In Table 15.7 the reaction quantum yields are given for some selected organic pollutants. As can be seen, reaction quantum yields vary over many orders of magnitude, with some compounds exhibiting very small Oir values. However, since the reaction rate is dependent on both ka and Oir (Eq. 15-34), a low reaction quantum yield does not necessarily mean that direct photolysis is not important for that compound. For example, the near-surface direct photolytic half-life of 4-nitrophenolate (Oir = 8.1 x 10 6) at 40°N latitude is estimated to be in the order of only a few hours, similar to the half-life of the neutral 4-nitrophenol, which exhibits a Oir more than 10 times larger (Lemaire et al., 1985). The reason for the similar half-lives is the much higher rate of light absorption of 4-nitrophenolate as compared to the neutral species, 4-nitrophenol (compare uv/vis spectra in Fig. 15.5 and Illustrative Example 15.3). As a second example, comparison of the near-surface photolytic half-lives (summer, 40°N... 

Intermediate-duration studies have also been conducted with radioactively labeled OCDD. OCDD had similar patterns of distribution and similar half-lives as 2,3,7,8-TCDD in Sprague-Dawley (Norback et al. 1975) and Fischer 344 rats (Bimbaum and Couture 1988 Bimbaum et al. 1989a). Most of the absorbed amount (50-97%) was found in the liver and was associated with the microsomal fractions. Skin- and adipose-tissue levels were much lower. Radioactivity was also detected in the kidneys, heart, testes, skeletal muscle, and serum. 

The AUC increases in a dose dependent manner for 200 to 1600 mg single doses [21], Individual enantiomers show similar half-lives [40]. Following radiolabeled etodolac administration, 69% to 76% of the dose was recovered in urine over 7 days. Urine and feces together accounted for 80% to 92% of dose [15]. Biliary excretion is a minor route for the elimination of etodolac [40]. 

More commonly, Kr has been combined with other dating tracers, in particular with tritium. This tracer combination is particulary useful because the two isotopes have similar half-lives but experienced completely different input histories (Fig. 6). The basic idea in the interpretation of H- Kr data, which can be generalised to all multi-tracer approaches, is to calculate the expected concentrations of and Kr for different mean ground-water residence times and/or different models of mixing in the aquifer, and to compare the measured concentrations with the model predictions (Loosli 1992 Loosli et al. 2000). This approach has been used successfully to derive mean residence times and to quantify admixing of old, tracer-free ground water, which is identified by concentrations of and Kr below those predicted by the models (Purtschert 1997 Mattie 1999). 

There is an interference with bromine in irradiated samples (e.g. urine) containing some bromine in that radioisotopes of bromine ( Br) and arsenic( As) both have their prominent gamma-intensities at 0.56 MeV and very similar half lives (36 h and 26,7 h respectively). Thus it is necessary, if no chemical separation is performed prior to gamma counting, to subtract the contribution from Br in the 0.55 MeV gamma peak (Norin, 1983). 

A phase 1 clinical trial showed that oral doses of 125, 250, 375, and 500 mg OPZ had similar half-lives, with no significant differences between clearances at the 125 and 250 mg levels. Peak plasma levels ranged from 0.35 to 4.92 pg/ mL, with marked intersubject variability being noted. Administration of a daily dose of 125 mg OPZ for 6 months was well tolerated [8]. The rapid clearance of OPZ from the body can explain the low steady-state concentrations however, these concentrations are sufficient to induce phase 2 enzymes in cultured liver cells [8, 9, 83]. 

On silica gel and alumina, the PAHs show a wide range of photolytic activity suggesting a relationship between structure and activity. On the fly ash, similar half-lives were observed that would indicate, in this instance, that the process is independent of the PAH structure and dependent on the physical and chemical properties of the substrate. The PAHs are more stable on the carbon black and there is little variation among the different compounds. For comparison, the vapor-phase half-lives have been calculated and in most instances are shorter than those observed on the particles. Pyrene is a noted exception showing more rapid degradation on silca gel and alumina than by the hydroxyl radical process in the vapor phase. 

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