Decay rate half time

Equation (8.8) shows that, after reactor shutdown, all 1135 in the reactor core decays to produce Xel35. Since the half-life of 1135 is shorter than the half-life of Xel35, xenon will be produced more rapidly than it decays. As shown in Figure xenon concentration in the core will peak at a time, tpj, the iodine has depleted to the point where the iodine decay in equation (8.6) just matches the xenon decay rate. After time the rate of xenon decay exceeds the rate of production decay and the xenon concentration in the core will... 

Since 16 = 24, four half-lives have elapsed in 18.0 h, and each half-life equals 4.50 h. The half-life of isotope B thus is 2.5 x 4.50 h = 11.25 h. Now, since 32 = 25, five half-lives must elapse before the decay rate of isotope B falls to of its original value. Thus, the time elapsed for this amount of decay is ... 

The SI unit of activity is the becquerel (Bq) 1 Bq = 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 rate of transformation 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, T r i.e., the time it takes for a specified source material to decay to half its initial activity. The activity of a radionuclide at time t may be calculated by A = A° e ° rad where A is the activity in dps, A ° is the activity at time zero, t is the time at which measured, and T" is the radiological half-life of the radionuclide. It is apparent that activity exponentially decays with time. The time when the activity of a sample of radioactivity becomes one-half its original value is the radioactive half-life and is expressed in any suitable unit of time. 

Class (3) reactions include proton-transfer reactions of solvent holes in cyclohexane and methylcyclohexane [71,74,75]. The corresponding rate constants are 10-30% of the fastest class (1) reactions. Class (4) reactions include proton-transfer reactions in trans-decalin and cis-trans decalin mixtures [77]. Proton transfer from the decalin hole to aliphatic alcohol results in the formation of a C-centered decalyl radical. The proton affinity of this radical is comparable to that of a single alcohol molecule. However, it is less than the proton affinity of an alcohol dimer. Consequently, a complex of the radical cation and alcohol monomer is relatively stable toward proton transfer when such a complex encounters a second alcohol molecule, the radical cation rapidly deprotonates. Metastable complexes with natural lifetimes between 24 nsec (2-propanol) and 90 nsec (tert-butanol) were observed in liquid cis- and tra 5-decalins at 25°C [77]. The rate of the complexation is one-half of that for class (1) reactions the overall decay rate is limited by slow proton transfer in the 1 1 complex. The rate constant of unimolecular decay is (5-10) x 10 sec for primary alcohols, bimolecular decay via proton transfer to the alcohol dimer prevails. Only for secondary and ternary alcohols is the equilibrium reached sufficiently slowly that it can be observed at 25 °C on a time scale of > 10 nsec. There is a striking similarity between the formation of alcohol complexes with the solvent holes (in decalins) and solvent anions (in sc CO2). 

In Chapter 12, the concept of half-life was used in connection with the time it took for reactants to change into products during a chemical reaction. Radioactive decay follows first order kinetics (Chapter 12). First order kinetics means that the decay rate... 

The word radioactive sounds scciry, but science and medicine are stuffed with useful, friendly applications for radioisotopes. Many of these applications are centered on the predictable decay rates of various radioisotopes. These predictable rates are characterized by half-lives. The half-life of a radioisotope is simply the amount of time it tcikes for exactly half of a sample of that isotope to decay into daughter nuclei. For excimple, if a scientist knows that a sample originally contained 42 mg of a certain radioisotope and measures 21 mg of that isotope in the sample four days later, then the half-life of that radioisotope is four days. The half-lives of radioisotopes range from seconds to billions of yecirs. 

The conventional unit of radioactivity, the curie (Ci), is equivalait to 3.7 X 10 radioactive events per second. The SI unit used for denoting the amount of radioactive material contained in a given sample of matter is the becquerel (Bq) one becquerel is that quantity of a radioactive nuclide in which there is one radioactive event per second (1 Bq = 2.7 x 10 Ci). Since radionuclides decay exponentially with time, each element at its own rate, the time required for a given quantity of a radionuclide to lose one-half of its radioactivity is call its physical half-Ufe. 

Table VI summarizes the sampling location and time, surface-water salinity, the measured surface-water H202 concentration, the decay rate constants, and bacterial cell counts for the five samples obtained on the transect. Although the ambient concentration of H202 remained similar throughout the transect, the decay rate decreased to give H202 half-lives of 2.5-12 h. The cell numbers were similar at all sampling locations, and the decay rate did not appear to correlate well. For some unexplained reason the increase...

When an experiment like that shown in Fig. 4 was carried out at 50°C, a similar behavior of the intermediate was observed, except that both formation and decay were six times faster. Experiments were also followed at 50°C in which 0.5 M excess P(OEt)3 was added initially, or when the intermediate rc-allyl complex was at a maximum. In the latter case, the rate of disappearance of the intermediate was essentially the same as in the control, consistent with rate-determining reductive elimination in 4 with m = 2 the rate of consumption of HCN and BD decreased abruptly, however, when excess L was added. In the experiment with L added initially, the overall rate of product formation was only about half that of the control the smaller maximum concentration of intermediate is consistent with a greater inhibiting effect of added L on the rate for formation of the intermediate than on its rate of decay. 

It is difficult to measure the half-life of a very long-lived radionuclide. Here variation in disintegration rate may not be noticeable within a reasonable length of time. In this case, the decay constant must be calculated from the absolute decay rate according to Equation (3.2). The absolute number of atoms of the radioisotope present (AO in a given sample can be calculated according to... 

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. 

In addition to X, another term used for characterizing rate of decay is half-life (ty2), the time required for half of the initial number of atoms to decay. If we substitute t = ty2 and N = Nq 2 into equation 7.5 we obtain the following equation ... 

Count the sample every two or three days for 2 weeks to confirm the 8.02-day half-life. Record sequential measurements, as in Data Table 10.1. Plot a decay curve of In net count rate vs. time. Checking the decay curve also serves as a means of determining if there are any radioactive contaminants in the sample. 

Plot the net count rates in Data Table 10.1 on a semilog graph for In net count rate vv.time (linear) in days. Draw a straight line of best fit through the points. If the last few points curve upward, try to fit 2 straight lines to the points, one for the last few points and the other to the initial points minus the count rate attributed to the lower line. Calculate the negative slope (i.e., the decay constant) for the line (or both lines). Does the line confirm the half life of 131I Estimate the uncertainty of the slope. 

The rate of radioactive decay is by convention expressed as the half-life, T1/2, defined as the time span during which a given concentration of the radioactive element atoms decays to half their initial value. T1/2 of tritium is 12.3 years. Thus, after 12.3 years one-half the initial concentration of tritium atoms is left, after 24.6 years only one-quarter is left, and so on. A radioactive decay curve of tritium is given in Fig. 10.1. Using the decay curve it is possible to determine, for example, how many years it takes for a given amount of tritium to decay to 20% of the initial amount. The answer, obtained from Fig. 10.1, is 29 years. Similarly, one can determine what percentage of an initial amount of tritium will be left after 20 years. The answer is 32% (read from Fig. 10.1). 

The radioactive emission rate is determined by the relative stability of the nuclide. One valid measure of the stability of the nuclide is its half-life. The idea is that the decay rate obeys Poisson6 statistics, and the number of radioactive nuclei at time t is n(t) = n(0) exp( t/t1/2), where fi/2 is the half-life. Appendix Table A is a complete list of all known nuclides. Table 10.1 lists some nuclides, their decay products, their half-life, and their uses. 

Radioactive half-life The time during which the decay rate of a radioactive nuclide decreases by a factor of two. 

The energy of these emissions covers a wide range of values but is typically 190 million electron volts (MeV) for fission, 17 MeV for fusion, 5 MeV for alphas, 1 MeV for gammas, and 0.5 MeV for betas. The rate of radioactive decay is expressed through the half-life, the time required for the decay rate of the unstable nuclide to decrease by a factor of two. The half-lives range from less... 

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