Radioactive decay definition

Since effects of radioactive decay on the molar mass can be neglected, q>bas Sr can be replaced with an excellent precision by expressed through equation (1.3.2) as a function of mass fractions / and concentrations CSr requires... 

A simple way to characterize the rate of a reaction is the time it takes for the concentration to change from the initial value to halfway between the initial and final (equilibrium). This time is called the half-life of the reaction. The half-life is often denoted as ti/z. The longer the half-life, the slower the reaction. The half-life is best applied to a first-order reaction (especially radioactive decay), for which the half-life is independent of the initial concentration. For example, using the decay of " Sm as an example, [ Sm] = [ Sm]o exp( kt) (derived above). Now, by definition,... 

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 ... 

According to this definition the lifetime is the time required for the luminescence intensity to drop from 1(0) to /t = I (0)/e it should not be confused with the half-life often used for radioactive decays, this being the time t j2 required to decrease the intensity of emission from 1(0) to I (0)/2. 

The unstable nuclei in a radioactive sample do not all decay simultaneously. Instead, the decay of a given nucleus is an entirely random event. Consequently, studies of radioactive decay events require the use of statistical methods. With these methods, one may observe a large number of radioactive nuclei and predict with fair assurance that, after a given length of time, a definite fraction of them will have disintegrated but not which ones or when. 

Many of these effects of radioactive decay can be treated quantitatively using G values. Historically, the G value was defined as the number of molecules or species decomposed or formed per 100 eV of absorbed energy. A newer (SI) definition of the G value is the number of moles of molecules or species formed or decomposed per Joule of energy absorbed. (Note that 1 mol/J = 9.76 x 106 molecules/100 eV.) The G values depend on the radiation and the medium being irradiated and its physical state. Table 19.1 shows some typical G values for the irradiation of neutral liquid water. 

Radioactive contamination Contamination with radioactive matter Radioactive decay Change of unstable atomic nuclei into other stable or unstable nuclei, associated with emission of nuclear radiation Radioactive equilibria Definite ratios between the activities of mother and daughter nuclides, given by their decay constants... 

Some nuclei undergo radioactive decay by capturing an electron from the A or L shell of the atomic electron orbits. This results in the transformation of a proton to a neutron, the ejection of an unobservable neutrino of definite energy, and the emission of an x-ray where the electron vacancy of the or L shell is filled by an atomic electron from an outer orbit. Because the net change in the radionuclide species is from atomic number Z to Z — 1, similar to the nuclide change from positron emission, electron capture generally competes with all cases of positron beta decay. 

Radioactive decay involves a transition from a definite quantum state of the original nuclide to a definite quantum state of the product nuclide. The energy difference between the two quantum levels involved in the transition corresponds to the decay energy. This decay energy appears in the form of electromagnetic radiation and as the kinetic energy of the products, see Element and Nuclide Index for decay energies. 

Even complex chemical reaction mechanisms can be separated into several definite elementary reactions, i. e. the direct electronic interaction process between molecules and/or atoms when colliding. To understand the total process B-fot example the oxidation of sulfur dioxide to sulfate - it is often adequate to model and budget calculations in the climate system to describe the overall reaction, sometimes called the gross reaction, independent of whether the process A Bis going via a reaction chain A C D E. .. Z B. The complexity of mechanisms (and thereby the rate law) is significantly increased when parallel reactions occur A X beside A- C,E- X beside E F. Many air chemical processes are complex. If only one reactant (sometime called an educt) is involved in the reaction, we call it a unimolecular reaction, that is the reaction rate is proportional to the concentration of only one substance (first-order reaction). Examples are all radioactive decays, rare thermal decays (almost autocatalytic) such as PAN decomposition and all photolysis reactions, which are very important in air. The most frequent are... 

This analysis can, for example, be applied to multistep radioactive decay reactions and to isomerization reactions. In such multistep processes, every step is by definition a first-order process. An example of multistep radioactive decay is the Actinium series (see Lederer et ah, 1968), in which Bi alpha-decays to ° T1, which beta-decays to ° Pb with respective half-lives of 2.14 and 4.77 min. Therefore, in this two-step consecutive process, k J ki =/9 = 2.14/4.77 = 0.449, very close to the Acme point. Similarly, in the Radium series, Pb beta-decays to which beta-decays to Po, which then alpha-decays very rapidly (with a half-life of only 0.16 ms) to ° Pb. This multistep decay can be closely approximated by two steps, the first with a half-life of 27 min, the second with a half-life... 

Which types of radioactive decay cause the transmutation of a nuclide (Hint Review the definition of transmutation.)... 

Mendeleev s definition put into play a tacit distinction between the chemical order and the physical order, a distinction attacked by Urbain, who, along with Paneth, was one of the chemists behind lUPAC s (the International Union of Pure and Applied Chemistry) new definition of the element. Urbain was opposed to the idea that when Rutherford bombarded nitrogen or phosphorous with alpha rays he generated only a physical phenomenon, and so Urbain rejected the approach that would place radioactive isotopes in the same box in the periodic table as the non-radioactive ones. Furthermore, the phenomenon of radioactive decay demonstrated that even the idea of a simple body that lay behind Lavoisier s understanding of an element was no longer valid. Urbain interpreted radioactive decay as a form of analysis, and because simple bodies did not survive the bombardment with alpha particles, they could not be considered truly simple. Nevertheless, Mendeleev s concept of the element managed to escape this particular line of attack. Because it was a conceptual notion, an abstraction, as we have explained above, Mendeleev s element was able to resist the attacks of the most powerful instruments of modern atomic physics. 

The concept most commonly used when dealing with radioactive nuclides is activity. By definition, the activity of a number of atoms of a nuclide is the number of decay events per unit of time. The law of radioactivity tells us that this activity is equal to the decay constant times the number of atoms. 

The decay equation can also be expressed in terms of the radioactive activity (A), i.e., the number of decays per unit time per unit mass of sample. By definition, activity is the same as the decay rate, and can be written as... 

The Poisson distribution describes the results of experiments in which we count events that occur at random but at a definite average rate. Examples of the Poisson distribution include the number of emails we receive in a one-day period, the number of babies bom in a hospital in a two-day period, the number of decays of a radioactive isotope in a one-day period. 

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