Nuclide daughter

Calculations are for Z = 60 daughter nuclide. Values are from computer code that calculates values from relations in Ref 4. 

STRATEGY Write the nuclear equation for each reaction, representing the daughter nuclide as E, with atomic number Z and mass number A. Then find Z and A from the requirement that both mass number and atomic number are conserved in a nuclear reaction, (a) In a decay, two protons and two neutrons are lost. As a result, the mass number decreases by 4 and the atomic number decreases by 2 (see Fig. 17.7). (b) The loss of one negative charge when an electron is ejected from the nucleus (Fig. 17.8) can be interpreted as the conversion of a neutron into a proton within the nucleus ... 

Identify the daughter nuclides in each step of the radioactive decay of uranium-235, if the string of particle emissions is a, p, a, P, ct, a, a, P, a, p, a. Write a balanced nuclear equation for each step. 

One of the behaviors of the system not easy to grasp is why the return to equilibrium is mostly controlled by the half-life of the daughter nuclide This can be investigated by considering the Ra/ °Th system ( °Th decays to form Ra with a half-life of 1599 years). If fractionation by some process results in an activity ratio greater than 1 at time t = 0, the equation describing the return to equilibrium, as shown above, is ... 

Figure 3. Parent daughter disequilibrium will return to equilibrium over a known time scale related to the half-life of the daughter nuclide. To return to within 5% of an activity ratio of 1 requires a time period equal to five times the half-life of the daughter nuclide. Because of the wide variety of half-lives within the U-decay-series, these systems can be used to constrain the time scales of processes from single years up to 1 Ma.

Figure 5. Ejection of daughter nuclide out of a grain due to recoil. Only a fraction of the nuclides located in a cone will be ejected for a given range 8. As shown on the diagram, at a distance x from the surface of the grain, the only nuclide to escape by recoil will be located in a cone with an angle a.

The solution to the general decay equations is often given in textbooks (e.g., Faure 1986). However, this solution is given for initial abundances of the daughter nuclides that are equal to zero. In the most general cases, the initial abundances of the daughter nuclides are not equal to zero. For example, in many geological examples, we make the assumptions that the decay chain is in secular equilibrium. The solutions of these equations can also be used to solve simple box models of U-series nuclides where first order kinetics are assumed. 

U-series elements are unusual in that, although they are trapped as one species at the time of crystal growth, they will decay to a different species with time. Consequently, the possibility exists for a highly compatible parent to decay to a highly incompatible daughter nuclide. With time the daughter will be expelled from the lattice, typically by diffusion. This creates a balance between uptake and decay that is not a consideration for stable trace elements, and so deserves brief mention here. 

N2)q and (N2/Ni)q represent the initial activity and activity ratio, respectively, just after the fractionation between parenf and daughter nuclides. 

In magmatic processes, both parent and daughter nuclides are usually present in the solid sources, magmas and crystallizing minerals, so that (N2), which is a priori unknown, cannot be neglected. In order to solve Equation (I) for t, the age of fractionation, both terms of this equation are divided by the concentration of a stable isotope (or the activity of a long-lived isotope) of the daughter element. Such a normalization, similar to those used in other classical radiometric methods (Rb-Sr, Sm-... 

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 9. A schematic and ideal model showing how the residence time of the magma in a steady-state reservoir of constant mass M, replenished with an influx O of magma and thoroughly mixed, can be calculated from disequilibrium data, in the simplifying case where crystal fractionation is neglected (Pyle 1992). The mass balance equation describing the evolution through time of the concentration [N2] (number of atoms of the daughter nuclide per unit mass of magma) in the reservoir is ...

Differences in residence time can lead to increased support of a daughter nuclide if the parent residence time in the melting column exceeds that of the daughter (see Bourdon et al. 2003). We can quantify this effect using the system as an... 

In contrast to the full equilibrium transport model, melt could be incrementally removed from the melting solid and isolated into channels for melt ascent. This model is the disequilibrium transport model of Spiegelman and Elliott (1993). Instead of substituting Equation (A7) in for Cs, the problem becomes one of separately keeping track of the concentrations of parent and daughter nuclides in the solid and the fluid. In this case, assuming steady state, two equations are used to account for the daughter nuclide ... 

Figure 2. (A.) The radionuclides in an aquifer are divided into three reservoirs groundwater, the host aquifer minerals, and adsorbed onto active surfaces. Also shown are the processes adding to a daughter nuclide (closed circles) in the groundwater of weathering, advection, recoil from decay of parent atoms ( P ) in the aquifer minerals, and production by parent decay, the processes of losses of a radionuclide of advection and decay, and exchange between dissolved and adsorbed atoms.

From the diversity of potential sites for U and Th, it is clear that the weathering release of and Th, as well as of the recoil and leaching release of daughter nuclides, must be determined for each site. Nonetheless, most studies assume that and Th have similar distributions, so that the values for si (the fraction released by recoil) and wi (the weathering release constant) is assumed to be approximately equal for all nuclides I. 

The chemical behavior of U and its daughter nuclides in the ocean environment was extensively studied in the 1960s and 1970s and has been well summarized (Cochran 1992). The most important mechanism by which nuclides are separated from one another to create disequilibrium is their differing solubility. For U, this solubility is in turn influenced by the redox state. The process of alpha-recoil can also play an important role in producing disequilibrium. 

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