Radioactivity, Radioactive Decay

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... 

Used (particularly He, Ar) to provide an inert atmosphere, e.g. for welding, and in electric light bulbs, valves and discharge tubes (particularly Ne). Liquid He is used in cryoscopy. The amounts of He and Ar formed in minerals by radioactive decay can be used to determine the age of the specimen. Xe and to a lesser extent Kr and Rn have a chemistry the other noble gases do not form chemical compounds. 

There are other less common types of radioactive decay. Positron emission results in a decrease by one unit in the atomic number K capture involves the incorporation of one of the extranuclear electrons into the nucleus, the atomic number is again decreased by one unit. 

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. 

Classic examples are the spontaneous emission of light or spontaneous radioactive decay. In chemistry, an important class of monomolecular reactions is the predissociation of metastable (excited) species. An example is the fonnation of oxygen atoms in the upper atmosphere by predissociation of electronically excited O2 molecules [12, 13 and 14] ... 

Although similar to chemical kinetic methods of analysis, radiochemical methods are best classified as nuclear kinetic methods. In this section we review the kinetics of radioactive decay and examine several quantitative and characterization applications. 

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 ... 

What mass of carbon is needed to give a percent relative standard deviation of 1.0% for the activity of a sample if counting is limited to 1 h How long must the radioactive decay from a 0.50-g sample of carbon be monitored to give a percent relative standard deviation of 1 % for the activity ... 

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. 

From the radioactive decay constants and measurement of the amount of argon in a rock sample, the length of time since formation of the rock can be estimated. Essentially, the dating method requires fusion of a rock sample under high vacuum to release the argon gas that has collected through radioactive decay of potassium. The amount of argon is determined mass spectrometrically,... 

Radon-222 [14859-67-7] Rn, is a naturally occuriing, iaert, radioactive gas formed from the decay of radium-226 [13982-63-3] Ra. Because Ra is a ubiquitous, water-soluble component of the earth s cmst, its daughter product, Rn, is found everywhere. A major health concern is radon s radioactive decay products. Radon has a half-life of 4 days, decayiag to polonium-218 [15422-74-9] Po, with the emission of an a particle. It is Po, an a-emitter having a half-life of 3 min, and polonium-214 [15735-67-8] Po, an a-emitter having a half-life of 1.6 x lO " s, that are of most concern. Polonium-218 decays to lead-214 [15067-28A] a p-emitter haviag = 27 min, which decays to bismuth-214 [14733-03-0], a p-emitter haviag... 

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... 

Nucleus Radioactive decay product y-Ray energy, keV T - 1/2 Production... 

Safety. A large inventory of radioactive fission products is present in any reactor fuel where the reactor has been operated for times on the order of months. In steady state, radioactive decay heat amounts to about 5% of fission heat, and continues after a reactor is shut down. If cooling is not provided, decay heat can melt fuel rods, causing release of the contents. Protection against a loss-of-coolant accident (LOCA), eg, a primary coolant pipe break, is required. Power reactors have an emergency core cooling system (ECCS) that comes into play upon initiation of a LOCA. 

Wastes. Nuclear reactors produce unique wastes because these materials undergo radioactive decay and in so doing emit harmhil radiation. 

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

The simplest model of time-dependent behavior of a neutron population in a reactor consists of the point kinetics differential equations, where the space-dependence of neutrons is disregarded. The safety of reactors is greatly enhanced inherently by the existence of delayed neutrons, which come from radioactive decay rather than fission. The differential equations for the neutron population, n, and delayed neutron emitters, are... 

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). 

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. 

Table 4. Properties of Stable Particles Associated With Radioactive Decay...

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