Kinetics of nuclear decay

Apply the kinetics of nuclear decay to the dating of rocks or artifacts (Section 19.3, Problems 25-30). 

Equation 11.8 relates the half-life of any first-order reaction to its rate constant. Because k does not depend on the amount of substance present, neither does t. The half-life is most often used to describe the kinetics of nuclear decay. All... 

There are many potential advantages to kinetic methods of analysis, perhaps the most important of which is the ability to use chemical reactions that are slow to reach equilibrium. In this chapter we examine three techniques that rely on measurements made while the analytical system is under kinetic rather than thermodynamic control chemical kinetic techniques, in which the rate of a chemical reaction is measured radiochemical techniques, in which a radioactive element s rate of nuclear decay is measured and flow injection analysis, in which the analyte is injected into a continuously flowing carrier stream, where its mixing and reaction with reagents in the stream are controlled by the kinetic processes of convection and diffusion. 

Although similar to chemical kinetic methods of analysis, radiochemical methods are best classified as nuclear kinetic methods. In this section we review the kinetics of radioactive decay and examine several quantitative and characterization applications. 

J. Godfrey, R. McLachlan and C.H. Atwood (1991) Journal of Chemical Education, vol. 68, p. 819 - An article entitled Nuclear reactions versus inorganic reactions provides a useful comparative survey and includes a resume of the kinetics of radioactive decay. 

Abstract At present there are over 3,000 known nuclides (see the Appendix in Vol. 2 on the Table of the Nuclides ), 265 of which are stable, while the rest, i.e., more than 90% of them, are radioactive. The chemical applications of the specific isotopes of chemical elements are mostly connected with the latter group, including quite a number of metastable nuclear isomers, making the kinetics of radioactive decay an important chapter of nuclear chemistry. After giving a phenomenological and then a statistical interpretation of the exponential law, the various combinations of individual decay processes as well as the cases of equilibrium and nonequilibrium will be discussed. Half-life systematics of the different decay modes detailed in Chaps. 2 and 4 of this volume are also summarized. 

What Do We Need to Know Already Nuclear processes can be understood in terms of atomic structure (Section B and Chapter 1) and energy changes (Chapter 6). The section on rates of radioactive decay builds on chemical kinetics (particularly Sections 13.4 and 13.5). 

The important phenomenon of exponential decay is the prototype first-order reaction and provides an informative introduction to first-order kinetic principles. Consider an important example from nuclear physics the decay of the radioactive isotope of carbon, carbon-14 (or C). This form of carbon is unstable and decays over time to form nitrogen-14 ( N) plus an electron (e ) the reaction can be written as... 

The classic example of reactions of this type is a sequence of radioactive decay processes that result in nuclear transformations. The differential equations that govern kinetic systems of this type are most readily solved by working in terms of concentration derivatives. For the first reaction,... 

As discussed above, this discrepancy may be caused by classically forbidden electronic transitions—that is, cases in which a proposed hopping process is rejected due to a lack of nuclear kinetic energy. Figure 11c supports this idea by showing the absolute numbers of successful (thick fine) and rejected (thin line) surface hops. In accordance with the initial decay of the adiabatic population, the number of successful surface hops is largest during the first 20 fs. For larger times, the number of rejected hops exceeds the number of successful surface hops. This behavior clearly coincides with the onset of the deviations between the two classically evaluated curves Nk t) and P t). We therefore conclude that the observed breakdown of the consistency relation (42) is indeed caused by classically forbidden electronic transitions. 

The value of the critical nuclearity allowing the transfer from the monitor depends on the redox potential of this selected donor S . The induction time and the donor decay rate both depend on the initial concentrations of metal atoms and of the donor [31,62]. The critical nuclearity corresponding to the potential threshold imposed by the donor and the transfer rate constant value, which is supposed to be independent of n, are derived from the fitting between the kinetics of the experimental donor decay rates under various conditions and numerical simulations through adjusted parameters (Fig. 5) [54]. By changing the reference potential in a series of redox monitors, the dependence of the silver cluster potential on the nuclearity was obtained (Fig. 6 and Table 5) [26,63]. 

The second paper of 1940 [3 ], entitled Kinetics of Uranium Chain Decay, is no less significant than the first. This pioneering work yielded a whole series of brilliant results for the first time, the need to take into account the role of delayed neutrons in the kinetics of chain nuclear reactions was shown (it is precisely the delayed neutrons which ensure easy control of nuclear reactors), the influence of heating on the kinetics of a chain process was considered in detail, and a number of conclusions were reached which are of much importance for the theory of reactor control. This same paper predicted the formation in the process of chain fission of new, previously unknown, nuclei which strongly absorb neutrons, a prediction which was later fully confirmed. 

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