Life, half-, of nuclides

Secular equilibrium materials. For materials that have remained a closed system for sufficient time that secular equilibrium has been achieved, the half-lives of nuclides within the decay chain can be calculated from the relationship A,pP = A,dD. If the atom ratio P/D is measured, and one of the decay constants is well known, then the other can be readily calculated. Limitations on this approach are the ability to measure the atom ratios to sufficient precision, and finding samples that have remained closed systems for a sufficient length of time. This approach has been used to derive the present recommended half lives for °Th and (Cheng et al. 2000 Ludwig et al. 1992). 

TABLE 21.3 The Half-Lives of Nuclides in the Decay Series Nuclide Particle Produced Half-Life... 

After t 1/2(2) (in practice, after about 10 half-lives of nuclide 2), radioactive equilibrium is established and the following relations hold ... 

Since the radioactive half-lives of the known transuranium elements and their resistance to spontaneous fission decrease with increase in atomic number, the outlook for the synthesis of further elements might appear increasingly bleak. However, theoretical calculations of nuclear stabilities, based on the concept of closed nucleon shells (p. 13) suggest the existence of an island of stability around Z= 114 and N= 184. Attention has therefore been directed towards the synthesis of element 114 (a congenor of Pb in Group 14 and adjacent superheavy elements, by bombardment of heavy nuclides with a wide range of heavy ions, but so far without success. 

FIGURE 17.16 The uranium-238 decay series. The times are the half-lives of the nuclides (see Sei tion 17.7). The unit a, for annum, is the SI abbreviation for year. 

The Earth s age can be estimated by using the half-lives of unstable nuclides that are still present and the half-lives of those that are missing. Among those listed in Table 22-4. the shortest-lived naturally occurring nuclide is... 

The uranium and thorium decay-series contain radioactive isotopes of many elements (in particular, U, Th, Pa, Ra and Rn). The varied geochemical properties of these elements cause nuclides within the chain to be fractionated in different geological environments, while the varied half-lives of the nuclides allows investigation of processes occurring on time scales from days to 10 years. U-series measurements have therefore revolutionized the Earth Sciences by offering some of the only quantitative constraints on time scales applicable to the physical processes that take place on the Earth. 

The need to understand the processes operating on Earth, coupled to recent analytical advances, have ensured that the U-series nuclides have seen widespread application since the last Ivanovich and Harmon book (1992). This volume does not set out to repeat material in that book, but is an attempt to bring together the advances in the subject over the last ten years, highlighting the excitement and rapid expansion of U-series research. The scope of the various chapters in this book is laid out at the end of this introduction. The remainder of this chapter introduces some of the basic concepts of U-series geochemistry, the chemical behavior of the elements involved, and the half-lives of the U- and Th-series nuclides. This chapter is not intended to be an exhaustive summary of the nuclear or radio-chemistry of the U-series nuclides and for additional information, the reader is referred to Ivanovich (1992). 

The previous section showed that if the decay chain remains undisturbed for a period of approximately 6 times the longest half-lived intermediate nuclide then the chain will be in a state of secular equilibrium (i.e., equal activities for all the nuclides). The key to the utility of the U-series is that several natural processes are capable of disrupting this state of equilibrium. 

Application of the U-series theory outlined above relies on accurate knowledge of the half-lives of the various nuclides, especially when U-series based chronologies are... 

Decay of the nuclide itself. The conceptually simplest approach is to take a known quantity of the nuclide of interest, P, and repeatedly measure it over a sufficiently long period. The observed decrease in activity with time provides the half-life to an acceptable precision and it was this technique that was originally used to establish the concept of half-lives (Rutherford 1900). Most early attempts to assess half lives, such as that for " Th depicted on the front cover of this volume, followed this method (Rutherford and Soddy 1903). This approach may use measurement of either the activity of P, or the number of atoms of P, although the former is more commonly used. Care must be taken that the nuclide is sufficiently pure so that, for instance, no parent of P is admixed allowing continued production of P during the experiment. The technique is obviously limited to those nuclides with sufficiently short half-lives that decay can readily be measured in a realistic timeframe. In practice, the longest-lived isotopes which can be assessed in this way have half-lives of a few decades (e.g., °Pb Merritt et al. 1957). 

Calorimetry. Radioactive decay produces heat and the rate of heat production can be used to calculate half-life. If the heat production from a known quantity of a pure parent, P, is measured by calorimetry, and the energy released by each decay is also known, the half-life can be calculated in a manner similar to that of the specific activity approach. Calorimetry has been widely used to assess half-lives and works particularly well for pure a-emitters (Attree et al. 1962). As with the specific activity approach, calibration of the measurement technique and purity of the nuclide are the two biggest problems to overcome. Calorimetry provides the best estimates of the half lives of several U-series nuclides including Pa, Ra, Ac, and °Po (Holden 1990). 

However, the short half-lives of these nuclides make them more useful for constraining the timescales of processes occurring closer to the eruption, such as degassing or crystal fractionation at crustal depths (Condomines et al. 2003). 

Half-lives have typically been determined by measuring the activity (rate of decay) of a sample containing a known number of atoms of the nuclide in question and calculating the decay constant via the equation NX= a, where a is the measured activity. The half-lives of all of the nuclides pertinent to °Th and Pa dating have been determined in this fashion. Among those that are known most precisely are those of... 

Another coupled system is the Sm-Nd system, with two Sm isotopes ( Sm and Sm) undergoing ot-decay to become two Nd isotopes ( Nd and Nd). The half-life of Sm is 106 billion years and that of is 103 million years. In principle, the concepts for the U-Pb system (such as concordia and discordia, Nd-Nd isochron) can also be applied to the Sm-Nd system. However, the Sm-Nd coupled system has not found many applications. One reason is that the half-life of " Sm is so short that it is an extinct nuclide. Secondly, the half-lives of Sm and " Sm are very different, by a factor of 1000 (in contrast, the half-lives of and 235 differ only by a factor of 6.3). Hence, the coupled system has found only limited applications to very old rocks, such as meteorites and very old terrestrial rocks. 

The half-lives of many nuclides are much shorter than the age of the Earth. For... 

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