Radioactive decay mean life

The decay constant, X, defines the probability that a particular atom will decay within a given time (X = In 2/t1/2). The half-life (t1/2) describes a time interval after which N = NJ2. The observed counting rate or activity (A) is equal to XN. Another way to describe radioactive decay is in terms of the mean life (t) of a... 

In this type of thermometry, long mean-life radioactive nuclei are used. The latter perform a J8 decay into an excited state which emits y to return to the fundamental state... 

Another isotopic anomaly, discovered in Allende inclusions, concerns magnesium, for which an intrinsically low abundance in these samples makes its isotope ratios sensitive to small effects. Certain of the inclusions show a correlation between 26Mg and 27 Al, indicating an origin of excess 26Mg from radioactive decay of 26 A1 (mean life 1 Myr), the existence of which had previously been postulated as a heat source for meteorite parent bodies (Fig. 3.32). Other short-lived activites that seem to have been alive in the early Solar System are 10Be (mean life 2.2 Myr) from a correlation of 10B with 9Be, and 41Ca (mean life 0.15 Myr) from a correlation of... 

The conceptual problems start when considering materials such as plutonium, which is a by-product of the nuclear electricity industry. Plutonium is one of the most chemically toxic materials known to humanity, and it is also radioactive. The half-life of 238Pu is so long at 4.5 x 108 years (see Table 8.2) that we say with some certainty that effectively none of it will disappear from the environment by radioactive decay and if none of it decays, then it cannot have emitted ionizing a and f) particles, etc. and, therefore, cannot really be said to be a radioactive hazard. Unfortunately, the long half-life also means that the 238Pu remains more-or-less for ever to pollute the environment with its lethal chemistry. 

Because a diffusion profile does not end abruptly (except for some special cases), it is necessary to quantify the meaning of diffusion distance. To do so, examine Equation 3-40a. Define the distance at which the concentration is halfway between Co and to be the mid-distance of diffusion, Xmid- The concept of Xmid is similar to that of half-life ti/2 for radioactive decay. From the definition, Xmid can be solved from the following ... 

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... 

As these superheavy elements get heavier, they become less stable the nuclei sit around for progressively shorter times before undergoing radioactive decay. Plutonium-239 has a half-life of 24,000 years, which means that it takes this long for half the atoms in a sample of Pu to decay. Califomium-249 (element 98) has a half-life of350 years mendelevium-258 (lOl), fifty-one days seaborgium-266 (106) twenty-one seconds. Isotope 272 of element 111 has a fleeting existence with a half-life of 1.5 milliseconds, and that of isotope 277 of element 112, made in 1996, is less than a third of a millisecond. This is one reason why it becomes increasingly hard to make and see these superheavy elements. ... 

Another parameter that is used to describe the decay of a radioactive species is the mean life (x), which is the average life expectancy of a radioactive atom. The mean life is defined as... 

Thus, the mean life is equal to the reciprocal of the decay constant and is longer than the half-life by a factor of Vo.693- The activity of a radionuclide is reduced by a factor of Ve during each mean life. The decay of a radioactive nuclide can be discussed in terms of half-life or mean life, and you will see both in the cosmochemistry literature. We will use the half-life in this chapter because this formulation is used more often in chronology applications. Discussions of galactic chemical evolution and the age of the elements (Chapter 9) are often done in terms of mean life. 

The abundances of radioactive isotopes over time in the galaxy can be modeled based on the above considerations. With an approximately constant production rate, the abundance of a stable nuclide will grow and will be proportional to the time over which it has been produced. In contrast, the abundance of a radionuclide will reach a steady state between production and decay in about eight mean lifetimes. (We will use mean life (t) instead of... 

You know that radioactive decay is first-order, so it is necessary only to find the rate constant for decay, from which the half-life may be calculated by means of Equation 15-11. To make the first-order plot, first convert cpm to log cpm to get... 

Why do some nuclei undergo radioactive decay while others do not Why, for instance, does a carbon-24 nucleus, with six protons and eight neutrons, spontaneously emit a /3 particle, whereas a carbon-23 nucleus, with six protons and seven neutrons, is stable indefinitely Before answering these questions, it s important to define what we mean by "stable." In the context of nuclear chemistry, we ll use the word stable to refer to isotopes whose half-lives can be measured, even if that half-life is only a fraction of a second. We ll call those isotopes that decay too rapidly for their half-lives to be measured unstable, and those isotopes that do not undergo radioactive decay nonradioactive, or stable indefinitely. 

An additional (and commonly misunderstood concept) is the mean life x,which is the average life of a certain group of radioactive atoms that is mathematically also derived from the decay constant X as... 

We present hereby some investigation results. Non-sorbing activity ( I, H) spreads as a passive admixture. In the time course, those radionuclides leave almost entirely the storage area, including by means of radioactive decay ( H). Tritium, due to its short half-life, even at the nearest control place (240 m from the storage), reaches the level of 5 10 IL only in the variant of maximum hydraulic gradient. 

The number of radioactive atoms present and hence the rate of disintegration decreases to one-half in one half-life, to one-quarter in two half-lives, to one-eighth in three half-lives, and so on. The half-life is characteristic of any particular radioisotope. Another useful quantity is the mean life or the average life of a radionuclide which is the reciprocal of the decay constant, = 1/A,. 

There are 280 naturally occurring nuclides that make up the 83 stable and long-lived elements. These are all the elements up to Bi with Z = 83, except for unstable Tc (Z = 43) and Pm (Z = 61) that only have short-lived isotopes, but the long-lived Th and U bring the total back to 83. Here long-lived or short-lived is with respect to the half-life of an isotope against radioactive decay and the age of the solar system. Long-lived means then an element is still present in measurable quantities since the solar system formed 4.6 Gyr ago, and radioactive isotopes with half-lives above 0.6 Gyr usually qualify... 

Although there is continual deposition of Pb to the salt-marsh surface, the quantity of excess " Pb that accumulates beneath a unit surface area (the standing crop) is finite due to radioactive decay. As Pb deposition proceeds, the standing crop in a closed system will increase only until its decay rate equals the depositional flux of Pb thereafter a steady state exists. At steady-state, the Pb flux F may be calculated from the standing crop Q and the mean life t of Pb ... 

Half-Life of Radioactive Decay Decay rates are also commonly expressed in terms of the fraction of nuclei that decay over a given time interval. The half-life (fi/i) of a nuclide is the time it takes for half the nuclei present in a sample to decay. The number of nuclei remaining is halved after each half-life. Thus, half-life has the same meaning for a nuclear change as for a chemical change (Section 16.4). Figure 23.4 shows the decay of carbon-14, which has a half-life of 5730 years, in terms of number of C nuclei remaining ... 

Understand why radioactive decay is a first-order process and the meaning of half-life convert among units of radioactivity, and calculate specific activity, decay constant, half-life, and number of nuclei estimate the age of an object from its specific activity ( 23.2) (SPs 23.4, 23.5) (EPs 23.17-23.30)... 

Aii radioactive decay processes foiiow first-order kinetics. What does this mean What happens to the rate of radioactive decay as the number of nuciides is haived Write the first-order rate law and the integrated first-order rate law. Define the terms in each equation. What is the half-life equation for radioactive decay processes How does the half-life depend on how many nuclides are present Are the half-life and rate constant k directly related or inversely related ... 

A radioactive nucleus which emits a particle to become transformed to another nucleus is described as decaying to that nucleus. Such a radioactive event is called radioactive decay. Radionuclides decay at different rates. Some can decay in millionths of a second, others take millions of years. Decay is independent of all the variables which affect chemical reactions such as temperature, pressure, and concentration. This poses particular difficulty with regard to the disposal of nuclear wastes. The rate of radioactive decay is characterized by the loss of a constant percent per unit time, not a constant number of moles per unit time. We therefore characterize the decay rate by specifying the time required for 50 percent of the original material to decay. This period of time is called the half-life, given the symbol, tj/j- The constant percent change means that 50 percent will be lost during the first half-life, 50 percent of what is left after the first half-life will decay over the second half-life, etc. 

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