Parent/daughter pairs

Based on Equation (3), in the case of a system where there is an initial disequilibrium in the chain (namely A,jNj A,2N2), it is generally stated that the system returns to secular equilibrium after -six half-lives of the daughter. The wide variety of parent-daughter pairs allows disequilibria to provide temporal constraints over a wide range in time scales (Fig. 3). 

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). 

Figure 4. Evolution of the (N2/N1) ratio in a reservoir in the two cases of closed system evolution (as a function of t/T2, where t is the time since fractionation), or in an open-system, steady-state reservoir (the steady-state (N2/N1) ratio is plotted as a function of x/ T2, where x is the residence time of the magma in the reservoir). Initial fractionation results in an arbitrarily chosen ratio of 2, which is kept constant for the iirfluent magma in the continuously replenished reservoir. The diagram shows that radioactive equilibrium is reached sooner in a closed system evolution. It also illustrates the fact that the radioactive parent-daughter pair should be chosen such as T2 is commensmate with the residence time of the magma in the reservoir (e.g., x/ T2 between 0.1 and 10). If T2 is much longer than the residence time x, then the (N2/N1) ratio will remain close to the initial value (here 2). If T2 is much shorter than x, equilibrium will be nearly established in the reservoir.

One other highly useful chronometer is measurement of °Po- b disequilibria. °Po has a half-life of 138.4 days making the chronometer active for 2 yrs. °Po- °Pb fractionation is based on Po but not Pb partitioning into volatiles during degassing (Gill et al. 1985). Ey repeat analysis of °Po, Rubin et al. (1994) constrained the time of eruption of several samples from 9°N EPR to windows of-100 days. These dates are consistent with eruption windows based on submersible observation. Thus, this technique can provide critical age constraints for other U-series parent-daughter pairs but requires that samples be collected and analyzed as soon as possible after eruption. 

The near vertical lines (solid) are isochrons. Ages reported in Ma. The secular equilibrium case, where the activity ratios of all parent-daughter pairs in the U-series decay chains are unity is shown by a dashed line. Ages (in Ma) are represented by squares. 

The development of PET radiopharmaceuticals labeled with generator-produced radionuclides has facilitated greater use of PET in clinical nuclear medicine. The 68Ge/68Ga parent/daughter pair is ideal as a source of PET radiopharmaceuticals as a result of the favorable half-lives of both the parent and daughter radionuclides (43-45). The 271 days half-life of the 68Ge parent... 

Eluent. When evaluating the various concentrations of THIO solutions as an eluent, we found that the yield of Au-195m depends on the THIO concentration similarly as shown in Figure 1. However, for the real parent/daughter pair, 91% "elution yield" is not reached, but, depending on the generator loading, only 25-45 ... 

Ion exchange and solvent extraction techniques have been used extensively as the basis for radiochemical generators exploiting the differences in absorption behavior between the parent nuclide and its useful daughter nuclide. Many parent/daughter pairs of nuclides have sufficiently different polarographic half wave potentials so that their electrochemical behavior may be exploited for rapid separation of the daughter from the parent with minimal contamination of the product with the parent isotope. ... 

A radionuclide generator can be described as a parent-daughter pair from which the daughter nuclide is separated from the parent in as pure a nuclear form as possible throughout the operating life of the system. A variety of publications (1-3) have emphasized the general principles of the medical use and qualitative aspects of radionuclide generators. The most frequent example discussed is the Mo-99/Tc-99m system. 

Figure 3 Crust-mantle differentiation patterns for the decay systems Rb-Sr, Sm-Nd, Lu-Hf, and Re-Os. The diagram illustrates the depletion-enrichment relationships of the parent-daughter pairs, which lead to the isotopic differences between continental crust and the residual mantle. For example, the Sm/Nd ratio is increased, whereas the Rb/Sr ratio is decreased in the residual mantle. This leads to the isotopic correlation in mantle-derived rocks plotted in Figure 4(a). The construction is similar to that used in Figure 2, but D values have been adjusted slightly for greater clarity.

The temporal resolution of the multiple parent-daughter pairs within the uranium decay chain, 238U- Th (approaching secular equilibrium with a 75 ka half-life), °Th- Ra (1,500 a) and (—32 ka) is a powerful tool. It has been used to estimate the elapsed time between subduction modification of the mantle and lava emption to the surface, and to identify multiple... 

Any disturbance from secular equilibrium decays back toward secular equilibrium through the decay of the shorter-lived supported chains. If the chains have significantly different decay rates, they are reasonably well decoupled and can be used to date processes comparable to the lifetimes of each chain (e.g., Condomines et al., 1988 Rubin et al., 1994 Thompson et al., 2003). As a useful rule of thumb, the time taken for a parent-daughter pair to return to approximate secular equilibrium, is about five half-lives of the shorter lived nuclide. In five half-lives, —97% of initial disequilibrium has decayed. Whether any detectable disequilibrium actually remains depends on the precision of measurements and degree of initial disequilibrium. 

The decay products of the long-lived radioactive systems are important tools for tracing geological time and Earth processes. The main parent-daughter pairs used for studies in the Earth and Planetary sciences are Rb-Sr, Th-U-Pb, Sm-Nd, Lu-Hf, and Re-Os. Traditionally most practitioners have not focused their careers... 

Many environmentally important fission products have short half-lives hence their behavior in the reactors is determined by proxy, by examining the distribution of stable daughters. Such parent/ daughter pairs include Sr/ °Zr, Cs/ Ba, I Cs/i Ba, I29i/i29xe Tc/ Ru. The... 

For a parent-daughter pair of a radioactive series in a closed system the relationship between parent and daughter is... 

The temporal resolution of the multiple parent-daughter pairs within the uranium decay chain, 23 u 230rj (approaching secular equilibrium with a 75 ka half-life), (1,500 a) and... 

These values indicate the extent to which an element is fractionated into the crust relative to the depleted mande. For example, Rb is the element most concentrated in the crust reladve to the depleted mande whereas Sr, Sm and Lu are the least concentrated. Alternatively, a parent-daughter element-pair may behave coherendy and not be fractionated and yet behave in a very different manner from the parent-daughter pair of another isotopic system. A good example is the contrast between the Sm-Nd system, in which both elements share very similar chemical and physical characteristics, and the Rb-Sr system, in which the elements are... 

Potential parent/daughter pairs for the in vivo generator concept... 

The highly different ocean chemistries of a large spectrum of parent-daughter pairs have been reviewed by Cochran (1992). The tracer pairs can be subdivided into three categories Rutgers van der Loeff and Boudreau, 1997). 

Other Parent-Daughter Pairs A summary of elements that contain one or more radiogenic nuclides and for which the isotopic composition is studied by (multicollector) ICP-MS is provided in Table 1.2. Elements with radiogenic nuclides not included in Table 1.2 either are not amenable to ICP-MS analysis (e.g., Ar) or have such long half-lives that the variation in their isotopic compositions is too limited to be quantified using present-day ICP-MS instrumentation. 

Isotope ratio measurements are also essential in nuclear forensics applications centered on age determination. As an example, it is critical to determine the age of Pu, that is, the period of time that has passed since the material was purified from U and fission products. Age determination of Pu can be based upon several parent-daughter pairs, including... 

In a study entitled Nuclear archeology in a bottle, Schwantes et al. [41] utilized quadrupole-based ICP-MS to investigate the isotopic composition and age of a sample of several hundred milligrams of Pu excavated from a waste burial trench at Hanford (WA, USA) in 2004. Isotopic analysis of three independent parent-daughter pairs, " Pu- " Am, Pu- U, and °Pu- U, conducted on the... 

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