Kinetics of radioactive decay

All radioactive decays obey first-order kinetics. Therefore, the rate of radioactive decay at any time t is given by 

Most nuclear scientists (and some general chemistry books) use the symbol A instead of k for the rate constant of nuclear reactions. 

Although Equation 14.3 uses concentrations o a reactant at times t and 0, it is the ratio of Ihe two that is important so we can also use the number of radioactive nudei in this equation 

These two rate constants, after conversion to the same time unit, differ by many orders of magnitude. Furthermore, the rate constants are unaffected by changes in environmental conditions such as temperature and pressure. These highly unusual features are not seen in ordinary chemical reactions (see Table 20.1). 

The half-lives of radioactive isotopes have been used as atomic clocks to determine the ages of certain objects. Some examples of dating by radioactive decay measurements will be described here. The carbon-14 isotope is produced when atmospheric nitrogen is bombarded by cosmic 

The radioactive carbon-14 isotope decays according to the eqiration 

This reaction is the basis of radiocarbon or carbon-14 dating. To determine the age of an object, we measure the activity (disintegrations per secortd) of arrd corrrpare it to the activity of 0 in living matter. 

There is one important practical difference between chemical kinetics and nuclear kinetics. In chemical kinetics the concentration of a reactant or product is monitored over time, and the rate of a reaction is then found from the rate of change of that concentration. In nuclear kinetics the rate of occurrence of decay events, —dN/dt, is measured directly with a Geiger counter or other radiation detector. This decay rate—the average disintegration rate in numbers of nuclei per unit time—is called the activity A. 

FIGURE 19.5 A graph of the logarithm of the activity of a radioactive nuclide against time is a straight line with slope -k = -(In 2)/t /2. The decay rate can also be measured as the ratio of the activity to the number of atoms of the radioisotope, if the latter is known. 

Because the activity is proportional to the number of nuclei N, it also decays exponentially with time  

unit of activity is the becquerel (Bq), defined as 1 radioactive disintegration per second. An older and much larger unit of activity is the curie (abbreviated Ci), which is defined as 3.7 X 10 ° disintegrations per second. The activity of 1 g of radium is 1 Ci. 

TABLE 19.2 Decay Characteristics of Some Radioactive Nuclei 

We saw in section 1.1.1, how atoms with identical atom number but with different amount of neutrons are called isotopes. Likewise did we see that the combined number of protons and neutrons are called nucleons and that radioactive species decay under emission of different types of radiation. The rate of such decay is in principle similar to the rate of reaction for the transition of reactants to products in a chemical reaction. We imagine that for a specific time r = 0 we have an amount of specie with No radioactive nuclei. It has been found that all nuclei have a specific probability of decaying within the next second. If this probability is e.g. 1/100 pr. second this means that on an average 1% of all nuclei decay each second. The number of radioactive nuclei is thereby a decreasing function with time and may formally be written as N(t). The rate for the average number of decays pr. time is thereby defined analogously to equation (3-1) as  

By integration it may be shown that N(t) depends of the eonstant of deeay k, time t and the number of radioaetive nuelei initially No as  

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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. 

Kinetics of radioactive decay first order decay with half-life tyx = ln2/ = 0.693/k. 

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. 

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