Nuclear decay, kinetics

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. 

Our goal in this chapter is to help you learn about nuclear reactions, including nuclear decay as well as fission and fusion. If needed, review the section in Chapter 2 on isotopes and the section in Chapter 13 on integrated rate laws which discusses first-order kinetics. And just like the previous nineteen chapters, be sure to Practice, Practice, Practice. 

Many important natural processes ranging from nuclear decay to uni-molecular chemical reactions are first order, or can be approximated as first order, which means that these processes depend only on the concentration to the first power of the transforming species itself. A cellular automaton model for such a system takes on an especially simple form, since rules for the movements of the ingredients are unnecessary and only transition rules for the interconverting species need to be specified. We have recently described such a general cellular automaton model for first-order kinetics and tested its ability to simulate a number of classic first-order phenomena.70... 

Some nuclei were formed that were stable, never undergoing further reactions. Others have lifetimes ranging from 10 years to 10 second. The usual method of describing nuclear decay is in terms of the half-life, or the time needed for half the nuclei to react. Because decay follows first-order kinetics, the half-life is a well-defined value, not dependent on the amount present. In addition to the overall curve of nuclear stability, which has its most stable region near atomic number Z = 26, combinations of protons and neutrons at each atomic number exhibit different stabilities. In some elements such as fluorine ( F), there is only one stable isotope (a specific combination of protons and neutrons). In others, such as chlorine, there are two... 

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

Radioactive decay is a first-order kinetic process. Recall that a first-order process has a characteristic half-life, which is the time required for half of any given quantity of a substance to react. (Section 14.4) Nuclear decay rates are commonly expressed in terms of half-lives. Each isotope has its own characteristic half-life. For example, the half-life of strontium-90 is 28.8 yr ( FIGURE 21.6). If we start with lO.O g of strontium-90, only 5.0 g of that isotope remains alter 28.8 yr, 2.5 g remains after another 28.8 yr, and so on. Strontium-90 decays to yttrium-90 ... 

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... 

Nuclear Chemistry Though not included in the text proper, we have written a chapter on nuclear chemistry, which is available through Thomson Brooks/Cole s custom publishing division. Coverage in this chapter includes fundamentals of nuclear reactions, nuclear stability and radioactivity, decay kinetics, and the energetic consequences of nuclear processes. 

The Z-resolutions of these variants are fairly similar. Differences are due to the properties of the detectors and the resolution also depends on the nuclear charge and kinetic energy of the fragments. A typical example of a spectrum of different members of a nuclear decay chain is given inO Fig. 4.25. 

Most nuclear decay processes obey first-order reaction kinetics. An example is the radioactive decay of carbon-14 (an unstable radioactive isotope of carbon) to nitrogen-14 (which is the stable isotope of nitrogen) via the emission of an electron and an antineutrino (Vg) ... 

Natural Radioactivity and Nuclear Transmutation Unstable nuclei undergo spontaneous decay with the emission of radiation and particles. All nuclear decays obey first-order kinetics. The half-lives of several radioactive nuclei have been used to date objects. Stable nuclei can also be made radioactive by bombardment with elementary particles or atomic nuclei. Many new elements have been created artificially in particle accelerators where such bombardments occur. 

Kinetics of consecutive reactions are easily applicable to nuclear decay processes, in which a parent isotope produces a radioactive daughter isotope that also decays. (In fact, in the early twentieth century, such sequential processes were a major complicating factor in trying to understand this new phenomenon.) One such example is... 

Thus, we see that the first-order kinetic equation is much simpler than the consideration of the decay mechanism. From a geological point of view, this shows that any primal amount of Pm would have rapidly decayed in the lifetime of the Earth of over 4 billion years. In fact the age of the Earth has been estimated by the presence or absence of radioactive isotopes in the cmst of the Earth related to their isotopes, although the original amounts have to be estimated. Nuclear decay is a prime example of first-order kinetics and as with the case of any kinetic problem, the decay is totally dependent on... 

The next example is a classic problem in both nuclear chemistry as well as chemical engineering. (By the way, a student who complained thathe would never see this problem in real life was sitting in a seminar the very next day when another student was presenting the results of his PhD research showing a time-dependent series of NMR peaks. In the data, a certain peak (A) decreased to form a second peak (B) and that peak reached a maximum but then decreased to form a final peak (C). The PhD candidate then proceeded to use this solution to analyze the kinetics of his data ) The idea is obvious for nuclear processes because nuclear decay follows successive step-by-step transformations from one isotope to... 

Considering the many apphcations of this type of problem such as nuclear decay and various forms of time-dependent spectroscopy (NMR, UV-VIS, etc.) there is sufficient detail to the solution presented above to allow it to be used in a number of situations and it is certainly one of the essential aspects of basic kinetics in physical chemistry. 

Chemistry is concerned with the study of molecular structures, equilibria between these structures and the rates with which some stractures are transformed into others. The study of molecular structures corresponds to study of the species that exist at the minima of multidimensional PESs, and which are, in principle, accessible through spectroscopic measurements and X-ray diffraction. The equihbria between these structures are related to the difference in energy between their respective minima, and can be studied by thermochemistry, by assuming an appropriate standard state. The rate of chemical reactions is a manifestation of the energy barriers existing between these minima, barriers that are not directly observable. The transformation between molecular structures implies varying times for the study of chemical reactions, and is the sphere of chemical kinetics. The journey from one minimum to another on the PES is one of the objectives of the study of molecular dynamics, which is included within the domain of chemical kinetics. It is also possible to classify nuclear decay as a special type of unimolecular transformation, and as such, nuclear chemistry can be included as an area of chemical kinetics. Thus, the scope of chemical kinetics spans the area from nuclear processes up to the behaviour of large molecules. 

Dorfman et al have used theoretical models to examine the probabilities of photoinduced charge separation in solid matrices which are relatively concentrated in acceptors ([donor) [acceptor]). " Hoffman et al have presented a readable discussion of the coupling between slow nuclear motions of environmental species, such as might be the case for some conformational changes, and electron transfer processes.Such coupling has been labeled gated electron transfer. Simon and Su have used the fluorescence Stokes shift, band shape, and decay kinetics of 6w-(dimethylaminophenyl)-sulfone, which has a twisted intramolecular charge transfer excited state, to examine... 

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