RATES OF RADIOACTIVE DECAY

Sources of alpha radiation outside the body are relatively harmless, because the radiation is absorbed by the skin. 

Beta and gamma radiations have an RBE of about 1, whereas neutron radiation has an RBE of about 5 and alpha radiation an RBE of about 10.  

The effects of radiation on a person depend not only on the dosage but also on the length of time in which the dose was received. A series of small doses has less overall effect than these dosages given all at once. A single dose of about 500 rems is fatal to most people, and survival from a much smaller dose can be uncertain or leave the person chronically ill. Detectable effects are seen with doses as low as 30 rems. Continuous exposure to such low levels of radiation may result in cancer or leukemia. At even lower levels, the answer to whether the radiation dose is safe depends on the possible genetic effects of the radiation. Because radiation can cause chromosome damage, heritable defects are possible. 

The background radiation to which we are all subjected has increased slightly since the advent of nuclear technology. Fallout from atmospheric testing of nuclear weapons increased this background by several percent, but it has decreased since atmospheric testing was banned. The radiation contributed by nuclear power plants is only a fraction of a percent of the natural background. 

The rate of radioactive decay—that is, the number of nuclei disintegrating per unit time—is found to be proportional to the number of radioactive nuclei in the sample. You can express this rate mathematically as 

As pointed out in Chapter 11, radioactive decay is a first-order process. This means that the following equations, discussed on pages 340-342, apply  

Activity can be expressed in terms of the number of atoms decaying per second, or becquerels (Bq). 

Alternatively, activity may be cited in disintegrations per minute or, perhaps most commonly, in caries (Ci). 

Substitute into the formula relating half-Kfe and rate constant in a first-order reaction. 0.693 

Find the number of nuclei N in 1.00 g of Ra-226 using Avogadro s number and 226 g/raol as the molar mass of Ra-226. 

A liquid scintillation counter. This instrument is used to detect radiation and measure disintegrations per minute quickly and accurately. 

Click Coached Problems for a self-study module on half-life and radiochemical dating. 

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Activity, nuclear Rate of radioactive decay number of atoms decaying per unit time, 518... 

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 usual procedure for radiocarbon dating is to bum a tiny sample of the object to be dated, collect the CO2 that is produced, and compare its rate of radioactive decay with that of a fresh CO2 sample. The ratio of counts gives Nq jN, which can then be substituted into Equation to calculate t. Mass spectroscopic isotope analysis can also be used to obtain the Nq jN value, as Example illustrates. 

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-...

While radioactive decay is itself a random process, the Gaussian distribution function fails to account for probability relationships describing rates of radioactive decay Instead, appropriate statistical analysis of scintillation counting data relies on the use of the Poisson probability distribution function ... 

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). 

Decay Constant. A constant A that relates the instant rate of radioactive decay of a radioactive species to the number of atoms N present at a given time r. 

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 ... 

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. 

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)... 

Heye objects to this theory that measurements of the growth rates of radioactive decay products have been carried out with two different pairs of elements, and that it is improbable that both pairs of metals would have the same adsorption behavior to pretend the identical growth rates. 

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. 

Rates of radioactive decay are described in terms of half-life, the time it takes for of a sample to disappear. 

The last discovery of an alkali metal occurred almost 80 years later. In 1939, Parisian physicist Marguerite Perey (1909-75) observed an unusual rate of radioactive decay in a sample of a salt of actinium (element 89). She managed to isolate the new element, showed that it was an alkali metal, and named it francium in honor of her native country, France. Because francium s longest-lived isotope has a half-life of only 21 minutes, francium is the rarest element below element 98 in the periodic table, which explains why francium was discovered much later than the other radioactive elements in that part of the table. 

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. 

Ri rate of radioactive decay of nuclei/ the nominally constant ... 

The probability that a radioactive nucleus will decay in a given time is a constant, independent of temperature, pressure, or the decay of other neighboring nuclei. The disintegrations of individual nuclei are statistically independent events and are subject to random fluctuations. In a large number of nuclei, however, the fluctuations average out, and the fraction that decays in unit time is a constant and is numerically equal to the probability that a single nuclei will decay in that time. This rate of radioactive decay is known as the decay constant X, with dimensions of reciprocal time. 

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