Radioactive decay The

The products of nuclear fission reactions are radioactive and disintegrate according to their own time scales. Often disintegration leads to other radioactive products. A few of these secondary products emit neutrons that add to the pool of neutrons produced by nuclear fission. Very importantly, neutrons from nuclear fission occur before those from radioactive decay. The neutrons from nuclear fission are termed prompt. Those from radioacth e decay arc termed delayed. A nuclear bomb must function on only prompt neutrons and in so doing requires nearly 100 percent pure (or Pu) fuel. Although reactor... 

Uranium-235 and U-238 behave differently in the presence of a controlled nuclear reaction. Uranium-235 is naturally fissile. A fissile element is one that splits when bombarded by a neutron during a controlled process of nuclear fission (like that which occurs in a nuclear reactor). Uranium-235 is the only naturally fissile isotope of uranium. Uranium-238 is fertile. A fertile element is one that is not itself fissile, but one that can produce a fissile element. When a U-238 atom is struck by a neutron, it likely will absorb the neutron to form U-239. Through spontaneous radioactive decay, the U-239 will turn into plutonium (Pu-239). This new isotope of plutonium is fissile, and if struck by a neutron, will likely split. 

Figure 23. Measured ( °Th/ Th) ratios in basalts from Piton de la Fournaise (Reunion Island) as a function of their eraption ages deduced from mineral isochrons. These ratios decrease with increasing emption ages as a result of post-eraptive radioactive decay. The curve shows the theoretical evolution by radioactive decay for a rock with a Th/U ratio of 3.95 and a ( °Th/ Th) ratio of 0.93, similar to the values measured in presently erapted lavas. An approximate age can thus be obtained from the measured ( °Th/ Th) ratio of an old sample. Part of the dispersion around the theoretical curve are due to small source heterogeneities (slightly variable ( °Th/ rh) and Th/U ratios), also evidenced by Sr/ Sr ratios (Condomines et al. 1988, and unpublished results).

Progeny—The decay product or products resulting after a radioactive decay or a series of radioactive decays. The progeny can also be radioactive, and the chain continues until a stable nuclide is formed. 

For these reasons, since the pioneering work of Libby the measurement technique used has been different from mass spectrometry and has exploited the characteristics of the process of the radioactive decay. From the law of radioactive decay, the activity of a sample, namely the number of decays per unit time, is proportional to the number of radioactive isotopes (i.e. their concentration in the sample). Indeed, by differentiation, Equation (16.1) becomes ... 

The half-life of the process in Equation (8.32) is 5570 years. Following death, flora and fauna alike cease to breathe and eat, so the only 14C in a dead body will be the 14C it died with. And because the amounts of 14C decrease owing to radioactive decay, the amount of the 14C in a dead plant or person decreases whereas the amounts of the 12C and 13C isotopes do not. We see why the proportion of 14C decreases steadily as a function of time following the instant of death. 

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-...

So, now (1913) one has a set of rules which characterize the daughter atom in terms of a knowledge of the parent element and the type of radioactive decay. The rules work they give rise to the concept of isotopes elements which correspond to different atomic weights but which are chemically identical. However, the rules are purely empirical no explanation exists for the rules as the matter now stands. Something is still missing in this story. 

The concentration of the radioactive nuclide (reactant, such as Sm) decreases exponentially, which is referred to as radioactive decay. The concentration of the daughter nuclides (products, including Nd and He) grows, which is referred to as radiogenic growth. Note the difference between Equations l-47b and l-47c. In the former equation, the concentration of Nd at time t is expressed as a function of the initial Sm concentration. Hence, from the initial state, one can calculate how the Nd concentration would evolve. In the latter equation, the concentration of Nd at time t is expressed as a function of the Sm concentration also at time t. Let s now define time t as the present time. Then [ Nd] is related to the present amount of Sm, the age (time since Sm and Nd were fractionated), and the initial amount of Nd. Therefore, Equation l-47b represents forward calculation, and Equation l-47c represents an inverse problem to obtain either the age, or the initial concentration, or both. Equation l-47d assumes that there are no other ot-decay nuclides. However, U and Th are usually present in a rock or mineral, and their contribution to " He usually dominates and must be added to Equation l-47d. 

One of the most important observations of atoms is the set of relationships between elements that belong to one of the series of radioactive decays. The parent elements of uranium, thorium and actinium decay through many intermediates to the stable element lead. The Nobel Prize in Chemistry for 1921 was awarded in 1922 to Frederick Soddy for his complete characterization of these processes. The story is beautifully told in his Nobel Lecture entitled The origins of the conception of isotopes (25). 

Dividing through by 86Sr, which is stable and is not involved in radioactive decay, the following equation is obtained ... 

Because plants take in carbon dioxide as long as they live, any carbon-14 lost to decay is immediately replenished with fresh carbon-14 from the atmosphere. In this way, a radioactive equilibrium is reached where there is a constant ratio of about 1 carbon-14 atom to every 100 billion carbon-12 atoms. When a plant dies, replenishment of carbon-1.4 stops. Then the percentage of carbon-14 decreases at a constant rate given by its half-life, but the amount of carbon-12 does not change because this isotope does not undergo radioactive decay. The longer a plant or other organism is dead, therefore, the less carbon-14 it contains relative to the constant amount of carbon-12. 

This is similar to a first-order reaction in chemical kinetics and follows the same law as radioactive decay. The rate constant kv defined in this manner is the natural radiative rate constant which also defines the natural radiative lifetime... 

In addition, one must remember that as the result of radioactive decay, the daughter atom is usually a different chemical element than the mother atom. One must be sure that the presence of these foreign species and any related equilibria does not affect the observations. (For example, if both the mother and daughter atoms are (3 emitters, then one might see a increase in the count rate due to the inability to distinguish the (3 particles from the tracer and its daughter.)... 

Radioactive decay The natural process in which the unstable nuclei of some isotopes of certain elements give off energy in... 

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. 

Iodine is lost from herbage by the same processes which cause field loss of Sr, 137Cs and other nuclides (Section 2.13). There is also the possibility of revolatilisation of iodine. If XG is the rate constant of field loss (fraction of iodine per unit area of ground lost from vegetation per second) and X1 the rate constant of radioactive decay, the combined apparent or effective loss rate is XE = XG + Xt. The effective half-life is Te = 0.693/A . The use of the term half-life implies that field loss is exponential and TE invariant with time, which is not always true. 

Begemann Libby (1957) estimated that 1.1 kg of T was released to atmosphere for each megatonne (MT) thermonuclear explosion. The tests between 1954 and 1963 had a fusion yield of 320 MT. Allowing for radioactive decay, the global inventory in 1963, including tritium in the atmosphere, groundwater and oceans, was about 330 kg. French and Chinese thermonuclear tests between 1968 and 1977 may have added another 20-30 kg. In 1972, by which time most of the pre-1963 tritium had returned to the earth s surface, a world-wide survey of oceanic waters gave a total of 164 kg (Ostlund Fine, 1979). Corrected for radioactive decay, this is equivalent to an inventory of 270 kg in 1963. 

The combination of radiolabeled sulfide and the bimane-HPLC method is particularly powerful because one of the main obstacles to the use of labeled sulfide is, that aside from radioactive decay, the compound is subject to rapid oxidation in the presence of air. The breakdown products of chemical sulfide oxidation are the same as those of biological oxidation. Previously it has been impossible to check routinely the purity of the purchased isotope and its subsequent purity during a series of experiments. It is our experience that newly purchased sodium sulfide sometimes contains up to 10% thiosulfate as well as traces of sulfite and sulfate (Figure 2), and that the sulfide once hydrated readily oxidizes if stored in a normal refrigerator. 

The rate constant for the decay can be found from (20-2). Ninety percent decay corresponds to 10% or 0.10, survival. In dealing with radioactive decay, the total population of radioactive element is used in place of its concentration. (Remember that in first-order reactions, the rate constant and the half-life, as well, are independent of the concentration units.) So, in place of the concentration ratio [A]/[A]o, put the ratio of the numbers of atoms N/Nq, or moles, or masses, of radioactive element. The mass of radioactive element encountered in the laboratory is exceedingly small a typical sample can be measured only by its activity. Since its activity is proportional to its population, the observed ratio of activities, A/Aq, can be used in place of the number ratio, N/Nq. 

In radioactive decay, the decaying nucleus is called the parent, while the nucleus produced by the decay is called the daughter ... 

Since the decay of a single radionuclide in a large collection of atoms is not readily predictable, we must come up with some type of measurement tool for radioactive decay. The concept of half-life allows us to do this. The half-life of a given radionuclide is the time required for an initially large number of atoms to decay such that only half of the initial number of atoms is left. For instance, if we start with N0 atoms, after one half-life 1/2N0 remain. After two half-lives, 1/4N0 are left, 1/8N0 after three half-lives remain, and so forth. Note that after seven half-lives, only (1/2)7N0 remain, which corresponds to 0.78% of the original amount. 

To complete the picture new matter gushes out into free space where electronic structure adapts to the low-curvature environment as in a phase transition, which renders some nuclides unstable against radioactive decay. The end product is 264 stable nuclides in the solar system. 

Notice that with radioactive decay, the radioactive substance never totally disappears. The amount gets smaller and smaller but never becomes zero. This is called exponential decay, and a typical graph of it is shown in Figure 14.3. 

In the saturated zone, water is isolated from the atmosphere and the tritium concentration drops due to radioactive decay the original tritium concentration of 5TU drops to 2.5 TU after 12.3 years, only 1.2TU are left after another 12.3 years, and so on. 

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