Nuclear chemistry decay kinetics

One application of these equations in nuclear chemistry involves the decay of rapidly moving particles. The muon, a heavy electron, has a lifetime, t, at rest, of 2.2 p,s. When the particle has a kinetic energy of 100 GeV (as found in cosmic rays), we observe a lifetime of yT or about 103t. (This phenomenon is called time dilation and explains why such muons can reach the surface of Earth.)... 

Nuclear chemistry represents a particularly simple limiting form of kinetics in which unstable nuclei decay with a constant probability during anytime interval. Its richness arises from the multiplicity of decay paths that are possible, which arise from the mass-energy relationships that determine nuclear stability. 

Special cases such as that arising from a nuclide decaying by more than one process simultaneously are treated exactly as the case for parallel reactions (see Chapter 2). In nuclear chemistry, this situation is referred to as branching because the overall process is taking different courses. After any given time, the ratio of the product nuclides is the same as the ratio of the decay constant producing them (see Section 2.3). However, there are some situations that arise when describing the kinetics of radioactivity that deserve special mention. 

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. 

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. 

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... 

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. 

Both unimolecular and bimolecular reactions are common throughout chemistry and biochemistry. Binding of a hormone to a reactor is a bimolecular process as is a substrate binding to an enzyme. Radioactive decay is often used as an example of a unimolecular reaction. However, this is a nuclear reaction rather than a chemical reaction. Examples of chemical unimolecular reactions would include isomerizations, decompositions, and dis-associations. See also Chemical Kinetics Elementary Reaction Unimolecular Bimolecular Transition-State Theory Elementary Reaction... 

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. 

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