The Kinetics of Radioactive Decay

The decay series from to Each nuclide in the series except fPb is unstable, and the successive transformations (shown by the arrows) continue until Pb is finally formed. Note that horizontal arrows indicate processes where h is unchanged, whereas diagonal arrows signify that both k and Z change. 

The negative sign is included because the number of nuclides is decreasing. We now insert a proportionality constant It to give 

Recall from Chapter 15 that this is the rate law for a first-order process. The integrated first-order rate law is 

How did all the matter around us originate The scientific answer to this question is a theory called stellar nucleosynthesis or, literally, the formation of nuclei in the stars. 

Many scientists believe that our universe originated as a cloud of neutrons that became unstable and produced an immense explosion, giving this model its name—the big bang theory. The model postulates that following the initial explosion, neutrons decomposed into protons and electrons. 

Radioactive decay of any nuclide follows w order kinetics. However, the observed kinetics of the decay may be complicated by the decay of the daughter nuclide. In the discussion below, we consider only a single decay step. 

The integrated form of this rate equation may be written as in equation 2.6, or in the form of equation 2.7 which emphasizes that the decay is exponential. 

From equation 2.6, it follows that a plot of In A against t is linear, and the rate constant k is found from the gradient of the line (see problem 2.5 at the end of the chapter). 

The half-life of a radioactive nuclide is the time taken for the number of nuclides present at time t, Nt, to fall to half of its 

First determine the time taken for the number of moles of Rn to decrease from 0.045 to half this value (0.0225) this is the first half-life. From the graph, (fpi 3.8 days. 

A = number of nuclides at time t Nq = number of nuclides present at / = 0 

In a sample containing radioactive nuclides of a given type, each nuclide has a certain probability of undergoing decay. Suppose that a sample of 1000 atoms of a certain nuclide produces 10 decay events per hour. This means that over the span of an hour, 1 out of every 100 nuclides will decay. Given that this probability of decay is characteristic for this type of nuclide, we could predict that a 2000-atom sample would give 20 decay events per hour. Thus, for radioactive nuclides, the rate of decay, which is the negative of the change in the number of nuclides per unit time 

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The image of a bone scan of a normal chest (posterior view). Radioactive technetium-99m is injected into the patient and is then concentrated in bones, allowing a physician to look for abnormalities such as might be caused by cancer. 

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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. 

Radioactive decay of an unstable nucleus is another example of a first-order process. For example, the half-life for the decay of uranium-235 is 7.1X10 yr. After 710 million years, a 1-kg sample of uranium-235 will contain 0.5 kg of uranium-235, and a 1-mg sample of uranium-235 will contain 0.5 mg. (We discuss the kinetics of radioactive decay thoroughly in Chapter 23.) Whether we consider a molecule or a radioactive nucleus, the decomposition of each particle in a first-order process is independent of the number of other particles present. 

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 Kinetics of Radioactive Decay Medical Applications of Radioactivity Breeder Reactors... 

The Kinetics of Radioactive Decay Rate of Radioactive Decay Radioisotopic Dating... 

The kinetics of radioactive decay is used to date objects and artifacts. The age of materials that were once part of living organisms is measured by carbon-14 dating. The age of ancient rocks and even Earth itself is determined by uranium/lead dating. 

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