Radioactive decay rate half-life

Many of the nuclides in the actinide family—U, Np, Pu, etc.—fission spontaneously as one of the modes of radioactive decay. Usually, for a nuclide with multiple modes of radioactive decay, the half-life of the nuclide is determined from the total decay rate, representing all the decay processes for that nuclide. However, in the case of spontaneous fission, a separate half-life for that process alone is used. Examples of nuclides that undergo spontaneous fission are given in Table 2.5. 

FIGURE 4.25 Indoor radon concentration as a function of the ventilation rate. Although radon-222 undergoes radioactive decay, its half-life, 3.8 days, is long compared with the ventilation rates in the graph. Therefore, radioactive decay is a relatively minor sink for indoor radon. The graph also can be applied for other indoor chemicals whose concentration is determined primarily by the balance between source strength and loss by ventilation (US EPA, 1986). 

Half-life is defined as the time required for a radioisotope to reduce its initial radioactivity (disintegration rate) to one-half (or 50%). The half-life is represented by the symbol, t a, and it is unique for a given radioisotope. The useful lifetimes of radiopharmaceuticals are usually determined by radioactive decay, which constantly decreases the amount of radioactivity present. The half-life is related to decay constant, X of a radioisotope (discussed in the subsequent section), as follows ... 

Radioactive decay rates are statistical averages of large numbers of decaying atoms. Because of the relatively short half-life of carbon-14, only trace amounts would be left after 50,000 years—too little to be statistically accurate. 

The constancy of the half-life for a first-order reaction is illustrated in Figure 12.7. Each successive half-life is an equal period of time in which the reactant concentration decreases by a factor of 2. We ll see in Chapter 22 that half-lives are widely used in describing radioactive decay rates. 

The experimentally measured rates of decay of radioactive atoms show that the decay is first order, where the number of atoms decomposing in a unit of time is proportional to the number present—this can be expressed in the following equation dN/dt = —X N. Another term used for characterizing rate of decay is half-life (t 1/2), the time required for half of the initial number of atoms to decay. Isotopes are considered to be in secular equilibrium, when the rate of decay of the parent is equal to that of its daughter. 

Radioactive decay rates are measured in half-lives. A half-life is the time required for one-half of a radioisotope s nuclei to decay into its products. For example, the half-life of the radioisotope strontium-90 is 29 years. If you had 10.0 g of strontium-90 today, 29 years from now you would have 5.0 g left. Table 25-4 shows how this decay continues through four half-lives of strontium-90. Figure 25-13 presents the data from the table in terms of the percent of strontium-90 remaining after each half-life. 

Cesium-137 is a fallout radioisotope from nuclear weapons tests and does not occur naturally. The first significant appearance of Cs-137 in the atmosphere was in the early 1950s, and it was present in peak quantities in 1963-1964. Like Pb-210, Cs-137 is carried down by rainwater and accumulates in the sediment, where it decays radioactively with a half-life of 30 years. Thus, a profile of Cs-137 concentration with depth (Figure 14.28) shows a maximum activity at a depth corresponding to 1963 and a tail , where cesium-137 is first detectable associated with deposition in the 1950s. The early 1980s peak is associated with the fallout from the 1986 accident at Chernobyl. This peak is also used to determine sediment accumulation rates in selected Northern European wetlands. In these wetlands, the Chernobyl peaks can be used to measure sedimentation ratios from 1963 to 1986 and 1986 to present. 

SECTIONS 21.4 AND 21.5 The SI unit for the activity of a radioactive source is the becquerel (Bq), defined as one nuclear disintegration per second. A related unit, the curie (Ci), corresponds to 3.7 X 10 disintegrations per second. Nuclear decay is a first-order process. The decay rate (activity) is therefore proportional to the number of radioactive nuclei. The half-life of a radionuclide, which is a constant, is the time needed for one-half of the nuclei to decay. Some radioisotopes can be used to date objects C, for example, is used to date organic objects. Geiger counters and scintillation counters count the emissions from radioactive samples. The ease of detection of radioisotopes also permits their use as radiolracers to follow elements through reactions. 

The rate of decay of any radioactive isotope can be represented by its characteristic half-life, the period required for one-half of the radioactive material originally present to undergo radioactive decay. Short half-lives are the results of high rates of decay, and long half-lives are the results of low rates of decay. 

The half-life is the time it takes for one-half of the parent nuclides in a radioactive sample to decay to the daughter nuclides. One can relate the half-life of objects to find their radioactive decay rates. 

Fixing the dates of relics and stone implements or pieces of charcoal from ancient campsites is an application based on radioactive decay rates. Because the rate of radioactive decay of a nuclide is constant, this rate can serve as a clock for dating very old rocks and human implements. Dating wood and similar carbon-containing objects that are several thousand to fifty thousand years old can be done with radioactive carbon, carbon-14, which has a half-life of 5730 y. 

Radioactivity. Radioactive decay is a process governed by statistics. At any given instant of time, each radioactive atom has a measurable probability of decaying. The rate of decay depends upon the number of original atoms present and upon the instantaneous fraction of atoms decaying per unit time, the decay constant. Another term used in discussing radioactivity is the half-life. This is defined as the amount of time it takes for... 

Radioactive decay rates Radioactive decay rates are measured in half-lives. A half-life is the time required for one-half of a radioisotope s nuclei to decay. Each radioisotope has a different half-life. The decay of a radioisotope is described as follows. 

Decay products of the principal radionuclides used in tracer technology (see Table 1) are not themselves radioactive. Therefore, the primary decomposition events of isotopes in molecules labeled with only one radionuclide / molecule result in unlabeled impurities at a rate proportional to the half-life of the isotope. Eor and H, impurities arising from the decay process are in relatively small amounts. Eor the shorter half-life isotopes the relative amounts of these impurities caused by primary decomposition are larger, but usually not problematic because they are not radioactive and do not interfere with the application of the tracer compounds. Eor multilabeled tritiated compounds the rate of accumulation of labeled impurities owing to tritium decay can be significant. This increases with the number of radioactive atoms per molecule. 

The same chemical separation research was done on thorium ores, leading to the discovery of a completely different set of radioactivities. Although the chemists made fundamental distinctions among the radioactivities based on chemical properties, it was often simpler to distinguish the radiation by the rate at which the radioactivity decayed. For uranium and thorium the level of radioactivity was independent of time. For most of the radioactivities separated from these elements, however, the activity showed an observable decrease with time and it was found that the rate of decrease was characteristic of each radioactive species. Each species had a unique half-life, ie, the time during which the activity was reduced to half of its initial value. 

Approximately 25—30% of a reactor s fuel is removed and replaced during plaimed refueling outages, which normally occur every 12 to 18 months. Spent fuel is highly radioactive because it contains by-products from nuclear fission created during reactor operation. A characteristic of these radioactive materials is that they gradually decay, losing their radioactive properties at a set rate. Each radioactive component has a different rate of decay known as its half-life, which is the time it takes for a material to lose half of its radioactivity. The radioactive components in spent nuclear fuel include cobalt-60 (5-yr half-Hfe), cesium-137 (30-yr half-Hfe), and plutonium-239 (24,400-yr half-Hfe). 

A radioactive sample contains 3.25 X 1018 atoms of a nuclide that decays at a rate of 3.4 X 1013 disintegrations per 15 min. (a) What percentage of the nuclide will have decayed after 150 d (b) How many atoms of the nuclide will remain in the sample (c) What is the half-life of the nuclide ... 

A radioactive isotope X with a half-life of 27.4 d decays into another radioactive isotope Y with a half-life of 18.7 d, which decays into the stable isotope Z. Set up and solve the rate laws for the amounts of the three nuclides as a function of time, and plot your results as a graph. 

Calorimetry. Radioactive decay produces heat and the rate of heat production can be used to calculate half-life. If the heat production from a known quantity of a pure parent, P, is measured by calorimetry, and the energy released by each decay is also known, the half-life can be calculated in a manner similar to that of the specific activity approach. Calorimetry has been widely used to assess half-lives and works particularly well for pure a-emitters (Attree et al. 1962). As with the specific activity approach, calibration of the measurement technique and purity of the nuclide are the two biggest problems to overcome. Calorimetry provides the best estimates of the half lives of several U-series nuclides including Pa, Ra, Ac, and °Po (Holden 1990). 

The SI unit of activity is the becquerel (Bq) 1 Bq = that quantity of radioactive material in which there is 1 transformation/second. Since activity is proportional to the number of atoms of the radioactive material, the quantity of any radioactive material is usually expressed in curies, regardless of its purity or concentration. The transformation of radioactive nuclei is a random process, and the number of transformations is directly proportional to the number of radioactive atoms present. For any pure radioactive substance, the rate of decay is usually described by its radiological half-life, TR, i.e., the time it... 

The decay constant, X, defines the probability that a particular atom will decay within a given time (X = In 2/t1/2). The half-life (t1/2) describes a time interval after which N = NJ2. The observed counting rate or activity (A) is equal to XN. Another way to describe radioactive decay is in terms of the mean life (t) of a... 

Some radioisotopes decay emitting only gamma rays, but many do so by the concurrent emission of beta and gamma radiation. The rate at which radiation is emitted from the nuclei of different radioisotopes varies considerably. Each radioisotope has a unique form of decay that is characterized by its half-life (tV2), the time it takes for the radioactivity of the radioisotope to decrease by one-half of its original value (see Textbox 14). 

Radioactive decay is a stochastic process that occurs at random in a large number of atoms of an isotope (see Textbox 13). The exact time when any particular atom decayed or will decay can be neither established nor predicted. The average rate of decay of any radioactive isotope is, however, constant and predictable. It is usually expressed in terms of a half-life, the amount of time it takes for half of the atoms in a sample of a radioactive isotope to decay to a stable form. 

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