THE RATE OF RADIOACTIVE DECAY

Radioactive nuclei decay at a characteristic rate, regardless of the chemical substance in which they occur. The decay rate, or activity (si), of a radioactive sample is the change in number of nuclei (TT) divided by the change in time (t). As we saw with chemical reaction rates, because the number of nuclei is decreasing, a minus sign precedes the expression for the decay rate  

The SI unit of radioactivity is the becquerel (Bq) it is defined as one disintegration per second (d/s) 1 Bq = 1 d/s. A much larger and more common unit of radioactivity is the curie (Ci) 1 curie equals the number of nuclei disintegrating each second in 1 g of radium-226  

Because the curie is so large, the millicurie (mCi) and microcurie ( xCi) are commonly used. We often express the radioactivity of a sample in terms of specific activity, the decay rate per gram. 

Combining the two rate expressions just given, we obtain 

Note that the activity depends only on Jf raised to the first power (and on the constant value of k). Therefore, radioactive decay is a first-order process (see Section 16.3). The only difference in the case of nuclear decay is that we consider the number of nuclei rather than their concentration. 

The changing of radioactive elements into other elements through radioactive emissions is called either radioactive decay or radioactive disintegration. By using radioactive rays, it is possible to detect whether a substance is radioactive or not. There are several methods to detect the types of radiations and their intensities. The most commonly used device to check the intensity of radioactivity is the Geiger-Mtiller counter. 

The radioactivity of each element is not the same. Each radioactive element undergoes a characteristic rate of decay. It is the intensity of this decay which is determined by a Geiger-Miiller counter. 

The rate of radioactive decay of an element is the number of atoms emitting a radioactive ray per a unit time. The rate of decay is directly proportional to the initial amount of substance and the structure of the nuclei. On the other hand, the rate of decay is independent of the physical and chemical properties of a radioactive atom. Temperature does not affect the rate of decay. The rate of 

The half-life of a radioactive decay is the period of time required for half of the initial amount of the substance to disintegrate. The shorter the half-life of a radioactive decay, the higher the rate of radioactive decay and the more radioactivity. The half-life is the characteristic property of each element. 

The changing number of atoms of a radioactive isotope with time. 

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The basic concepts of nuclear structure and isotopes are explained Appendix 2. This section derives the mathematical equation for the rate of radioactive decay of any unstable nucleus, in terms of its half life. 

Equation (9.6) is the basic equation describing the decay of all radioactive particles, and, when plotted out, gives the familiar exponential decay curve. The parameter X is characteristic of the parent nucleus, but is not the most readily visualized measure of the rate of radioactive decay. This is normally expressed as the half life (7/ 2). which is defined as the time taken for half the original amount of the radioactive parent to decay. Substituting N = Na/2 into the Equation (9.6) gives ... 

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 . 

Figure 5.1 Radioactive decay. The rate of radioactive decay is proportional to the number of unstable atoms present and although theoretically there should always be some activity left (a), in practice the activity does eventually fall to zero. A plot of the logarithm of the activity against time (b) results in a straight line from which the half-...

The spontaneous disintegration of a nucleus is a first-order kinetic process. That is, the rate of radioactive decay of TV atoms (—dN/dt, the change of TV with time, t) is proportional to the number of radioactive atoms present (Equation 6.4). 

Radioactive decay is what chemists refer to as a first-order reaction that is, the rate of radioactive decay is proportional to the number of each type of radioactive nuclei present in a given sample. So, if we double the number of a given type of radioactive nuclei in a sample, we double the number of particles emitted by the sample per unit time.2 This relation may be expressed as follows ... 

What are the factors affecting the rate of radioactive decay Does temperature affect the rate of radioactive decay Explain. 

The rate of radioactive decay is by convention expressed as the half-life, T1/2, defined as the time span during which a given concentration of the radioactive element atoms decays to half their initial value. T1/2 of tritium is 12.3 years. Thus, after 12.3 years one-half the initial concentration of tritium atoms is left, after 24.6 years only one-quarter is left, and so on. A radioactive decay curve of tritium is given in Fig. 10.1. Using the decay curve it is possible to determine, for example, how many years it takes for a given amount of tritium to decay to 20% of the initial amount. The answer, obtained from Fig. 10.1, is 29 years. Similarly, one can determine what percentage of an initial amount of tritium will be left after 20 years. The answer is 32% (read from Fig. 10.1). 

The energy of these emissions covers a wide range of values but is typically 190 million electron volts (MeV) for fission, 17 MeV for fusion, 5 MeV for alphas, 1 MeV for gammas, and 0.5 MeV for betas. The rate of radioactive decay is expressed through the half-life, the time required for the decay rate of the unstable nuclide to decrease by a factor of two. The half-lives range from less... 

Note that the rate of radioactive decay depends only upon the number of nuclei present in an element... 

Geiger-Miiller counter (Geiger counter) an instrument that measures the rate of radioactive decay based on the ions and electrons produced as a radioactive particle passes through a gas-filled chamber. (21.4)... 

Radioactive decay (radioactivity) the spontaneous decomposition of a nucleus to form a different nucleus. (21.1) Radiocarbon dating (carbon-14 dating) a method for dating ancient wood or cloth based on the rate of radioactive decay of the nuclide gC. (21.4)... 

Amounts of radioactive material are usually expressed in units of activity, the rate of radioactive decay. The accepted unit is the curie (Ci) and its metric multiples and fractions, the mega, kilo, milli-, and microcurie. A curie is 3.73 X1010disintegrations per sec. A common unit is millicuries per millimole. Packaging and shipment of radioactive materials, which are highly toxic, must be in accord with official requirements. Consult IATA and DOT shipping regulations for labeling and other instructions. 

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

We shall begin the process of constructing a mathematical model of the nuclear reactor by considering the behaviour of the precursor groups in more detail. Let C, be the concentration of nuclei per m of the /th precursor group at time, t. The rate of radioactive decay, Ri, will be proportional to the existing concentration. 

Aii radioactive decay processes foiiow first-order kinetics. What does this mean What happens to the rate of radioactive decay as the number of nuciides is haived Write the first-order rate law and the integrated first-order rate law. Define the terms in each equation. What is the half-life equation for radioactive decay processes How does the half-life depend on how many nuclides are present Are the half-life and rate constant k directly related or inversely related ... 

A radioactive nucleus which emits a particle to become transformed to another nucleus is described as decaying to that nucleus. Such a radioactive event is called radioactive decay. Radionuclides decay at different rates. Some can decay in millionths of a second, others take millions of years. Decay is independent of all the variables which affect chemical reactions such as temperature, pressure, and concentration. This poses particular difficulty with regard to the disposal of nuclear wastes. The rate of radioactive decay is characterized by the loss of a constant percent per unit time, not a constant number of moles per unit time. We therefore characterize the decay rate by specifying the time required for 50 percent of the original material to decay. This period of time is called the half-life, given the symbol, tj/j- The constant percent change means that 50 percent will be lost during the first half-life, 50 percent of what is left after the first half-life will decay over the second half-life, etc. 

The rate of radioactive decay is typically expressed in terms of either the radioactive half-life or the radioactive decay constant. They are related as follows ... 

The rate of radioactive decay for an isotope is usually expressed as a half-life. Solving these problems is straightforward if the given amount of time is an exact multiple of the half-life. For example, the half-life of Pa is 27.0 days. This... 

A measure of the rate of radioactive decay is the half-life t ii, the time it takes for half of its atoms to disintegrate. The half-Ufe can be related to the decay constant k by noting that after time t = fi/2, N is reduced to Nq. Therefore,... 

A unit used to describe the rate of radioactive decay. One Becquerel equals one disintegration per second. 

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