Isotopes, radioactive decay

The Development of Modern Chemistry. Harper and Row, New York, 1964, xii + 851 pp. including illustrations, Appendixes, (Discovery of the Elements, Discovery of Natural Radioactive Isotopes, Radioactive Decay Series, Nobel Prize Winners in Chemistry, Physics, and Medicine), and Bibliographic Notes. 

All elements of atomic number greater than 83 exhibit radioactive decay K, Rb, Ir and a few other light elements emit p particles. The heavy elements decay through various isotopes until a stable nucleus is reached. Known half-lives range from seconds to 10 years. 

Isotope Dilution Another important quantitative radiochemical method is isotope dilution. In this method of analysis a sample of analyte, called a tracer, is prepared in a radioactive form with a known activity. Ax, for its radioactive decay. A measured mass of the tracer, Wf, is added to a sample containing an unknown mass, w, of a nonradioactive analyte, and the material is homogenized. The sample is then processed to isolate wa grams of purified analyte, containing both radioactive and nonradioactive materials. The activity of the isolated sample, A, is measured. If all the analyte, both radioactive and nonradioactive, is recovered, then A and Ax will be equal. Normally, some of the analyte is lost during isolation and purification. In this case A is less than Ax, and... 

Other isotopes can be used to determine the age of samples. The age of rocks, for example, has been determined from the ratio of the number of radioactive atoms to the number of stable gfPb atoms produced by radioactive decay. For rocks that do not contain uranium, dating is accomplished by comparing the ratio of radioactive fgK to the stable fgAr. Another example is the dating of sediments collected from lakes by measuring the amount of g Pb present. 

Table 13.1 provides a list of several isotopes commonly used as tracers. The half-lives for these isotopes also are listed. What is the rate constant for the radioactive decay of each isotope ... 

Lead occurs naturally as a mixture of four non-radioactive isotopes, and Pb, as well as the radioactive isotopes ° Pb and Pb. All but Pb arise by radioactive decay of uranium and thorium. Such decay products are known as radiogenic isotopes. 

Ratios of lead isotopes depend on the source of the lead. They vary because lead is an end product of radioactive decay from elements of greater atomic number. 

Argon-40 [7440-37-1] is created by the decay of potassium-40. The various isotopes of radon, all having short half-Hves, are formed by the radioactive decay of radium, actinium, and thorium. Krypton and xenon are products of uranium and plutonium fission, and appreciable quantities of both are evolved during the reprocessing of spent fuel elements from nuclear reactors (qv) (see Radioactive tracers). 

Neutron-rich lanthanide isotopes occur in the fission of uranium or plutonium and ate separated during the reprocessing of nuclear fuel wastes (see Nuclearreactors). Lanthanide isotopes can be produced by neutron bombardment, by radioactive decay of neighboring atoms, and by nuclear reactions in accelerators where the rate earths ate bombarded with charged particles. The rare-earth content of solid samples can be determined by neutron... 

The isotope plutonium-238 [13981 -16-3] Pu, is of technical importance because of the high heat that accompanies its radioactive decay. This isotope has been and is being used as fuel in small terrestrial and space nuclear-powered sources (3,4). Tu-based radioisotope thermal generator systems dehvered 7 W/kg and cost 120,000/W in 1991 (3). For some time, %Pu was considered to be the most promising power source for the radioisotope-powered artificial heart and for cardiovascular pacemakers. Usage of plutonium was discontinued, however, after it was determined that adequate elimination of penetrating radiation was uncertain (5) (see PROSTHETIC AND BIOMEDICAL devices). 

Rhenium, atomic wt 186.2, occurs in nature as two nucHdes Re [14391-28-7] mass 184.9530, in 37.500% abundance and Re [14391-29-8], mass 186.9560, in 62.500% abundance. The latter isotope is radioactive, emitting very low energy radiation and having a half-life estimated at 4.3 ( 0.5) X 10 ° yr. The radioactive decay of this isotope has been used to date accurately the time of Earth s formation. 

The abundance of a trace element is often too small to be accurately quantihed using conventional analytical methods such as ion chromatography or mass spectrometry. It is possible, however, to precisely determine very low concentrations of a constituent by measuring its radioactive decay properties. In order to understand how U-Th series radionuclides can provide such low-level tracer information, a brief review of the basic principles of radioactive decay and the application of these radionuclides as geochronological tools is useful. " The U-Th decay series together consist of 36 radionuclides that are isotopes (same atomic number, Z, different atomic mass, M) of 10 distinct elements (Figure 1). Some of these are very short-lived (tj j 1 -nd are thus not directly useful as marine tracers. It is the other radioisotopes with half-lives greater than 1 day that are most useful and are the focus of this chapter. 

The nature of the radioactive decay is characteristic of the element it can be used to fingerprint die substance. Decay continues until bodi die original element and its daughter isotopes are non-radioactive. The half-life, i.e. die time taken for half of an element s atoms to become non-radioactive, varies from millions of years for some elements to fractions of a second for odiers. 

Radon daughters The series of unstable isotopes that are formed as radon atoms undergo radioactive decay. 

Uranium (symbol U atomic number 92) is the heaviest element to occur naturally on Earth. The most commonly occurring natural isotope of uranium, U-238, accounts for approximately 99.3 percent of the world s uranium. The isotope U-235, the second most abundant naturally occurring isotope, accounts for another 0.7 percent. A third isotope, U-234, also occurs uatiirally, but accounts for less than 0.01 percent of the total naturally occurring uranium. The isotope U-234 is actually a product of radioactive decay of U-238. 

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. 

Unstable isotopes decompose (decay) by a process referred to as radioactivity. Ordinarily the result is the transmutation of elements the atomic number of the product nucleus differs from that of the reactant. For example, radioactive decay of produces a stable isotope of nitrogen, N. The radiation given off (Figure 2.6) may be in the form of—... 

Perhaps the most important first-order reaction is that of radioactive decay, in which an unstable nucleus decomposes (Chapter 2). Letting X be the amount of a radioactive isotope present at time t,... 

The sequences of radioactive decays that lead to lead are well-known and the rates of decay have been carefully measured. We shall consider the sequence based upon the relatively slow decomposition of the most abundant uranium isotope, mass 238 (natural abundance, 99%) ... 

All radioactive decay processes follow first-order kinetics. The half-life of the radioactive isotope tritium (3H, or T) is 12.3 years. How much of a 25.0-mg sample of tritium would remain after 10.9 years ... 

STRATEGY The total mass of isotope in a sample is proportional to the number of nuclei of that isotope that the sample contains therefore, the time dependence of the mass follows the radioactive decay law, Eq. 3. We let m denote the total mass of the radioactive isotope at time t and m0 its initial mass. 

The law of radioactive decay implies that the number of radioactive nuclei decreases exponentially with time with a characteristic half-life. Radioactive isotopes are used to determine the ages of objects. 

The most abundant isotope is which constitutes almost 99% of the carbon in nature. About 1% of the carbon atoms are There are, however, small but significant differences in the relative abundance of the carbon isotopes in different carbon reservoirs. The differences in isotopic composition have proven to be an important tool when estimating exchange rates between the reservoirs. Isotopic variations are caused by fractionation processes (discussed below) and, for C, radioactive decay. Formation of takes place only in the upper atmosphere where neutrons generated by cosmic radiation react with nitrogen ... 

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. 

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