Chemical kinetics radioactive decay

Moreover, the half-life of a single radioactive atom cannot be measured, and even if the half-life is knwon, the instant at which the atom will undergo disintegration cannot be predicted. Radioactive decay, chemical kinetics and chemical equilibria are governed by the laws of probability and many measurements with single atoms are necessai7 to establish the statistics and to obtain relevant results. With regard to chemical properties, it is important that all the atoms are present in the same chemical form (same species). 

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. 

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 following argument was used first by E. Y. Schweidler in 1905 to describe radioactive decay but it applies to all similar kinetic processes. The fundamental assumption is that the probability p of an event occurring over a time interval dt is independent of past history of a molecule it depends only on the length of time represented by dt and for sufficiently short intervals is just proportional to dL Thus, p — kdt where k is a constant of proportionality characteristic of the process being awaited. In fluorescence decay it is characteristic of the kind of molecule in chemical terms. 

When species i disappears by either radioactive decay or chemical reaction with first-order kinetics, the mass balance equation must be changed according to... 

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... 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

In Chapter 12, the concept of half-life was used in connection with the time it took for reactants to change into products during a chemical reaction. Radioactive decay follows first order kinetics (Chapter 12). First order kinetics means that the decay rate... 

Radioactive decay follows the same rate equation as first-order chemical kinetics (Section 2.5) the half-life t j2, the time required for one-half of the sample to decay, is given by (In 2)/(rate constant). Decay of a sample is considered arbitrarily to be practically complete after 10ti/2, which is 240,000 years for 239Pu. 

This is similar to a first-order reaction in chemical kinetics and follows the same law as radioactive decay. The rate constant kv defined in this manner is the natural radiative rate constant which also defines the natural radiative lifetime... 

The law governing radioactive decay (eq. (4.1)) is analoguous to that of first-order chemical kinetics. The excited state on top of the energy barrier corresponds to the activated complex, and s is equivalent to the activation energy. 

Note that the logs of the numbers in a geometric series will form an arithmetic series (e.g. 0, 1, 2, 3, 4,... in the above case). Thus, if a quantity y varies with a quantity x such that the rate of change in y is proportional to the value of y (i.e. it varies in an exponential maimer), a semi-log plot of such data will form a straight line. This form of relationship is relevant for chemical kinetics and radioactive decay (p. 236). 

Such a chemical reaction, in which molecules are not colliding with other atoms or molecules, is called a first-order reaction because the rate at which chemical concentration changes at any instant in time is proportional to the concentration raised to the first power. Certain chemical processes, such as radioactive decay, are described by first-order kinetics. In the absence of any other sources of the chemical, first-order kinetics may lead to exponential decay or first-order decay of the chemical concentration (i.e., the concentration of the parent compound decreases exponentially with time) ... 

Equation (9.15) describes a reversible reaction, whereby the reaction can proceed to the right as well as to the left. Not all kinetic reactions are reversible. For example, radioactive decay, many oxidation reactions, and organic matter degradation proceed, for all practical purposes, in only one direction until the reaction is inhibited or the reactant is effectively exhausted. Reversible reactions, such as CO2 hydration, other acid-base relationships and some precipitation-dissolution reactions will attain, at some point, a steady state in which both the forward and reverse reactions occur at the same rate and the concentrations of both reactants and products no longer change. This is the state of chemical equilibrium at which the product of the reaction products raised to the exponent of their stoichiometric coefficients divided by a similar arrangement for the reactants is equal to the apparent equilibrium constant, K (see Chapter 3) ... 

The conceptual approach is particularly effective when solving problems that have half-lives that are whole number values. For more complex problems, we need to use some ideas borrowed from chemical kinetics. Radioactive decay can be described as a first order processes, which means it can be described with the following equation ... 

Irreversible reactions can go one way only. Equilibrium is not possible in general, or for existing conditions of temperature and pressure. The status of such reactions can often be described using the concepts of chemical kinetics. Radioactive decay is generally such an irreversible reaction. For example... 

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. 

Schultz, E. (1997). Dice-shaking as an analogy for radioactive decay and first-order kinetics. Journal of Chemical Education, 74, 505-507. 

The kinetics of processes involving radioactive decay are similar in may respects to the treatment of rates of chemical reactions, but some diflerences arise in special cases. However, some of these cases are frequently encountered, so a brief description of the rate processes will be presented. 

From the large number of mathematical models for the transport of transformation products with kinetic reactions that can be considered in the Rockflow system we have chosen a first-order chemical nonequilibrium model to simulate the sorption reaction. It can be described by the governing solute transport equation with rate-limited sorption and first-order decay in aqueous and sorbed phases. This model includes the processes of advection, dispersion, sorption, biological degradation or radioactive decay of the contaminant in the aqueous and/or sorbed phases. Figure 6.1 illustrates the conceptual model for sequential decay of a reactive species. 

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 kinetic aspect needs special attention when a synthetic strategy is selected. The significance of time as a reaction parameter is of equal importance, as chemical yield has to be considered in the planning of a labeling synthesis. Since the radiochemical yield is a function of chemical yield and radioactive decay, the maximum radiochemical yield is attained before the reaction has proceeded to completion. This relation between time and concentration of reactants with respect to kinetics is described in some of the initial works on C-chemistry (Langstrom and... 

Besides chemical reactions, a number of nonchemical processes in nature also obey first-order kinetics. A particularly important example is radioactive decay, which is discussed in Chapter 17. 

The time taken for the concentration of reactant to he halved during a chemical reaction is called the half-life. Identical kinetic behaviour is exhibited by substances undergoing radioactive decay (see Chapter 2), with the exception that this physical process is unaffected by changes in temperature. For a reaction that has an overall order of 1, the half-life is constant and is independent of the initial concentration of the reactants (see Figure 16.7). 

How long do radioactive isotopes last This is measured by a quantity familiar to anyone who has studied chemical kinetics. You should recall studying first-and second-order reactions and discussing the concept of half-life in each case. (Incidentally, radioactive decay follows flrst-order kinetics.) Half-life is defined as the time required for the concentration of a reactant to decrease to half its initial concentration. Figure 10.3 shows the concentration of a radioactive isotope as a function of time. Note that after one half-life, one-half of the isotope remains after two half-lives, there is one-quarter of the original remaining and so forth. 

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