Half-life for radioactivity

Values in parentheses refer to the isotope of longest known half-life for radioactive elements. 

The half-life for radioactive nuclei varies significantly from one species to another. E.g. has the Uranium-... 

You relate the half-life for radioactive decay, ti/2, to the decay constant k by the equation... 

Such a product occurs often and is a fixture of many mass transfer correlations. The quantity ka is very similar to the rate constant of a first-order reversible reaction with an equilibrium constant equal to unity. This particular problem is similar to the calculation of a half-life for radioactive decay. 

The activity in a 10.00-mL sample of radioactive wastewater containing fgSr was found to be 9.07 X 10 disintegrations/s. What is the molar concentration of 3gSr in the sample The half-life for fgSr is 28.1 years. 

All radioactive isotopes decay with a characteristic half-life. For example, Fe decays with a half-life of 45 days, while Cu decays with a half-life of 12.6 hours. As a result of the decay, signature high-energy photons or y rays are emitted from a given radioisotope. Thus, Fe emits two prominent y rays at 1099 and 1292 keV, " Na emits at 1368 and 2754 keV, and Zn emits at 1115 keV. Compilations of y rays used in NAA can be found in y-ray tables. 

The actinoid elements (or actinides An) constitute a series of 14 elements which are formed by the progressive filling of the 5/ electron shell and follow actinium in the periodic table (atomic numbers 90-103). All of the isotopes of the actinide elements are radioactive and only four of the primordial isotopes, Th, and " " Pu, have a sufficient long half-life for there to be any of these left in nature. 

Tracers have been used to label fluids in order to track fluid movement and monitor chemical changes of the injected fluid. Radioactive materials are one class of commonly used tracers. These tracers have several drawbacks. One drawback is that they require special handling because of the danger posed to personnel and the environment. Another drawback is the alteration by the radioactive materials of the natural isotope ratio indigenous to the reservoir— thereby interfering with scientific analysis of the reservoir fluid characteristics. In addition, the half life of radioactive tracers tends to be either too long or too short for practical use. 

The discovery of two new elements started a frenetic race to find more. Actinium was soon unearthed (Debierne 1900) and many other substances were isolated from U and Th which also seemed to be new elements. One of these was discovered somewhat fortuitously. Several workers had noticed that the radioactivity of Th salts seemed to vary randomly with time and they noticed that the variation correlated with drafts in the lab, appearing to reflect a radioactive emanation which could be blown away from the surface of the Th. This Th-emanation was not attracted by charge and appeared to be a gas, °Rn, as it turns out, although Rutherford at first speculated that it was Th vapor. Rutherford swept some of the Th-emanation into a jar and repeatedly measured its ability to ionize air in order to assess its radioactivity. He was therefore the first to report an exponential decrease in radioactivity with time, and his 1900 paper on the subject introduced the familiar equation dN/dt = - iN, as well as the concept of half-lives (Rutherford 1900a). His measured half-life for the Th emanation of 60 seconds was remarkably close to our present assessment of 55.6 seconds for °Rn. 

The natural cosmic ray background and the environmental radioactivity set a lower limit on measurable counting rates and thus the minimum number of radioactive atoms in the sample. This minimum number increases linearly with the half-life. For 14C the number of atoms present in a sample is given by ... 

The half-life of radioactive decay or of a chemical reaction is the length of time required for exactly half the material under study to be consumed, e.g. by chemical reaction or radioactive decay. We often give the half-life the symbol t /2, and call it tee half. 

Excretion - The plasma half-life for trospium following oral administration is approximately 20 hours. After administration of oral trospium, the majority of the dose (85.2%) was recovered in feces and a smaller amount (5.8%) was recovered in urine 60% of the radioactivity excreted in urine was unchanged trospium. The mean renal clearance for trospium (29.07 L/h) is 4-fold higher than average glomerular filtration rate, indicating that active tubular secretion is a major route of elimination for trospium. There may be competition for elimination with other compounds that also are renally eliminated. 

Number of atoms of radioactive 87Rb and daughter 87Sr as a function of time in units of half-life. For each half-life the number of radioactive 87Rb atoms drops by a factor of two as the 87Rb atoms decay to 87Sr. After 10 half-lives, the parent isotope is effectively gone. 

Following oral administration of radiolabeled furosemide, excretion was reported to be almost complete within 3 days in rats (96-98%) and dogs (98-99%). Rat urine contained 40-50% of the parent drug, 30% 4-chloro-5-sulfamoyl-anthranilic acid, and four unidentified metabolites that accounted for the rest of the administered radioactivity. In contrast, urine of dog and monkey contained 85% unmetabolized furosemide, 7% 4-chloro-5-sulfamoyl-anthranilic acid, and the remainder was due to unidentified metabolites. Following intramuscular injection of 5 mg furosemide/kg bw in cattle, the half-life for plasma elimination was estimated at 4.3 h. In contrast, the half-life of furosemide in cattle was reported to be less than 1 h following intravenous administration. 

A variety of radioactive isotopes is available having gamma rays diller-ing in penetrating ability, and with half-lives varying from a few minutes to many years. Radioactive iodine with an 8 day half-life and radioactive bromine with a l -day half-life were used for most tests. Radiation from these isotopes passes easily through the walls of pipe found in the oil field. 

The half-life, defined in the previous section and listed for each isotope in Table 6.1, is an important property when designing experiments using radioisotopes. Using an isotope with a short half-life (for example, 24Na with ty2 = 15 hr) is difficult because the radioactivity lost during the course of the experiment is significant. Quantitative measurements made before and after the experiment must be corrected for this loss of activity. Radioactive phosphorus, 32P, an isotope of significant value in biochemical research, has a relatively short half-life (14 days), so if quantitative measurements are made they must be corrected as described in Equations 6.7 and 6.8. More information about the choice of a radioisotope in an experiment, the detec-... 

Radiochemistry involves the application of the basic ideas of inorganic, organic, physical, and analytical chemistry to the manipulation of radioactive material. However, the need to manipulate radioactive materials imposes some special constraints (and features) upon these endeavors. The first of these features is the number of atoms involved and the solution concentrations. The range of activity levels in radiochemical procedures ranges from pCi to MCi. For the sake of discussion, let us assume an activity level, D, typical of radiotracer experiments of 1 p,Ci (= 3.7 x 104 dis/s = 3.7 x 104 Bq), of a nucleus with mass number A 100. If we assume a half-life for this radionuclide of 3 d, the number of nuclei present can be calculated from the equation... 

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. 

Half-Life. For the radioactive nuclides this time period corresponds to that during which loss by disintegration of 50% of the nuclide occurs. The units of time are designated by year (yr), day (d),hour (h), minute (min), and second (s). 

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