Radioactive decay chemical reactions

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). 

Gray, Harry B., John D. Simon, and William C. Trogler. Braving the Elements. Sausalito, Calif. University Science Books, 1995. This book is an introduction to the basic principles of chemistry, with elementary explanations of radioactive decay, chemical bonding, oxidation-reduction reactions, and acid-base chemistry. Practical applications of specific chemical compounds and classes of compounds are presented. 

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. 

This is an important scheme. It is characteristic not only of radioactive decay but also of many chemical systems. In the model shown, the reversion of I to A is taken to be unimportant we shall consider the effect of a back reaction in Section 4.3. The differential equations are... 

As in a unimolecular chemical reaction, the rate law for nuclear decay is first order. That is, the relation between the rate of decay and the number N of radioactive nuclei present is given by the law of radioactive decay ... 

The only reactions that are strictly hrst order are radioactive decay reactions. Among chemical reactions, thermal decompositions may seem hrst order, but an external energy source is generally required to excite the reaction. As noted earlier, this energy is usually acquired by intermolecular collisions. Thus, the reaction rate could be written as... 

As an example of the use oftbe expooneiniaL d logarithmic functions in physical chtStustiy, CQij er a finst-oider chemical reaction, such as a radioactive decay. It follows the rate law... 

The half-life of radioactive decay or of a chemical reaction is the length of time required for exactly half the material under study to be consumed, e.g. by chemical reaction or radioactive decay. We often give the half-life the symbol t /2, and call it tee half. 

The only difference between a chemical and a radioactive half-life is that the former reflects the rate of a chemical reaction and the latter reflects the rate of radioactive (i.e. nuclear) decay. Some values of radioactive half-lives are given in the Table 8.2 to demonstrate the huge range of values t j2 can take. The difference between chemical and radioactive toxicity is mentioned in the Aside box on p. 382. A chemical half-life is the time required for half the material to have been consumed chemically, and a radioactive half-life is the time required for half of a radioactive substance to disappear by nuclear disintegration. 

Exothermic chemical reactions, 25 299-301 catalytic converter, 10 45 formaldehyde manufacture by, 12 115 temperature-dependent enthalpy changes for, 25 303-305 Exothermic polymerization, 10 709 Exotic radioactive decays, 21 305-306 Expandable polystyrene (EPS),... 

The excited state of a molecule can last for some time or there can be an immediate return to the ground state. One useful way to think of this phenomenon is as a time-dependent statistical one. Most people are familiar with the Gaussian distribution used in describing errors in measurement. There is no time dependence implied in that distribution. A time-dependent statistical argument is more related to If I wait long enough it will happen view of a process. Fluorescence decay is not the only chemically important, time-dependent process, of course. Other examples are chemical reactions and radioactive decay. 

This results in the transmutation of parent element X into daughter Y, which has an atomic number two less than X. The particular isotope of element Y which is formed is that with an atomic mass of four less than the original isotope of X. Note that, as in chemical reactions, these nuclear reactions must be numerically balanced on either side of the arrow. Many of the heavy elements in the three naturally occurring radioactive decay chains (see below) decay by a-emission. 

Because radioactive decay is a nuclear process, the rate of radioactive decay is totally unaffected by any external factors. Unlike chemical reactions, therefore, there is no dependency on temperature, or pressure, or any of the other environmental factors which affect the rate at which normal chemical reactions occur. This is the reason why radioactive decay chronometers, such as 14C, Ar-Ar, and U-series methods, are so important in geology and archaeology - they provide an absolute clock . 

Chapter 1) that its concentration in the reservoir can be modified only by processes taking place at the boundaries. Species i can be added to or subtracted from the system by solid, liquid or gaseous input and output, not by chemical reaction or radioactive decay inside the reservoir. For the sake of illustration, we will consider a water reservoir, whose properties will be labeled liq . Mass balance requires... 

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 mean reaction time during a reaction varies as the concentration varies if the reaction is not a first-order reaction. Expressions of mean reaction time of various types of reactions are listed in Table 1-2. In practice, half-lives are often used in treating radioactive decay reactions, and mean reaction times are often used in treating reversible chemical reactions. 

For a closed system, the total mass of the system is conserved. For a component that is made of nonradioactive and nonradiogenic nuclides, the concentration of the component in the whole system can increase or decrease only through chemical reactions. The mass of a radioactive component decreases with time due to decay, whereas that of a radiogenic component increases with time (nuclear reaction). On the basis of mass conservation, some relations can be derived... 

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... 

Equation (20.3) is in the form of first-order decay equation which describes a first-order chemical reaction or radioactive decay. It es-... 

In this section we shall present a few of the elementary type reactions that have been solved exactly. By elementary we mean unimolecular and bimolecular reactions, and simple extensions of them. In a more classical stochastic context, these reactions may be thought of as birth and death processes, unimolecular reactions being linear birth and death processes and bimolecular being quadratic. These reactions may be described by a finite or infinite set of states, (x), each member of which corresponds to a specified number of some given type of molecule in the system. One then describes a set of transition probabilities of going from state x to x — i, which in unimolecular reactions depend linearly upon x and in bimolecular reactions depend quadratically upon x. The simplest example is that of the unimolecular irreversible decay of A into B, which occurs particularly in radioactive decay processes. This process seems to have been first studied in a chemical context by Bartholomay.6... 

The reason why the boundaries in physical problems are often natural becomes obvious by looking at the simple example of radioactive decay in IV.6. The probability for an emission to take place is proportional to the number n of radioactive nuclei, and therefore automatically vanishes at n = 0. The same consideration applies when n is the number of molecules of a certain species in a chemical reaction, or the number of individuals in a population. Whenever by its nature n cannot be negative any reasonable master equation should have r(0) = 0. However, this does not exclude the possibility that something special happens at low n by which the analytic character of r(n) is broken, as in the example of diffusion-controlled reactions. A boundary that is not natural will be called artificial in section 7. 

Internal fluctuations are caused by the discrete nature of matter. The density of a gas fluctuates because the gas consists of molecules fluctuations in a chemical reaction arise because the reaction consists of individual reactive collisions current fluctuations exist because the current is made up of electrons radioactive decay fluctuates owing to the individuality of the nuclei. Incidentally, this explains why the formulas for fluctuations in physical systems always contain atomic constants, such as Avogadro s number, the mass of a molecule, or the charge of an electron. 

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