The decay equation

Radioactive decay is a first order process. The rate of decay is directly proportional to the number of atoms of radionuclide present in the source, i.e. the activity. A, is directly proportional to the number of atoms, V, of nuclide present  

The proportionality constant, X, is called the decay constant and has the units of reciprocal time (e.g. s, h , etc.). The reciprocal of the decay constant is the mean lifetime, t, of the radionuchde, the average time which an atom can be expected to exist before its nucleus decays  

This time represents a decay of the source by a factor of e (i.e. 2.718). It is more convenient and meaningful to refer to the half-life, the radionuchde - the time during 

The year has alternative definitions, and there is a move towards standardizing on the day as the unit for quoting long half-hves. Equation (1.7) leads to the more commonly used decay equation relating number of atoms N,) at time (t) and half-life (tif ) - 

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Taking the derivatives and comparing with the decay equation, we obtain... 

Because there is a double decay involved in parent P disintegration, the decay equation corresponding to the general formula of equation 11.83 reads as follows ... 

Although the above /tth-order expressions are quite simple they are general enough to embrace many of the decay equations used to date [see Szepe and Levenspiel (1968)]. 

The decay (ot- and p-decay) of an unstable nuclide can be described by the decay equation (first-order reaction) ... 

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... 

B is formed by j5-decay of A and, due to the recoil, it gets a high kinetic energy. B itself should be radioactive, since otherwise it is not possible to determine analytically the yields of the products of B. The situation is different in the case of decay of tritium nuclide. The decay (equation 70) ... 

It takes about 10 y for just half the samarium-149 in nature to decay by alpha-particle emission. Write the decay equation, and find the isotope that is produced by the reaction. 

Comparison of the above exponential to the decay equation y = yoe, /r reveals that... 

A radioactive san le may contain several different radioactive nuclides which are not genetically related. The decay of each nuclide follows the decay equations of the previous section. The detector measures a certain amount of the radioactivity of each species so that... 

The V represents the antineutrino v is the neutrino. Neutrino and antineutrino emissions serve to balance the energy and rotation before and after decay. Neutrinos have no charge and little mass as a result, they interact to a vanishingly small degree with matter and are difficult to detect without elaborate apparatus. The neutrino (or antineutrino) must be included in the decay equation to conserve energy, angular momentum, and spin. The neutron, proton, beta particle, and neutrino all have a nuclear spin of 1 /2. A fuller discussion of this topic is in nuclear chemistry texts such as Choppin et al. (1995). 

The fission process releases the large amounts of energy used in nuclear reactors and weapons and also several neutrons. The number of these neutrons depends on both the process and the fissioning atom, as indicated in the decay equations above. When the number of neutrons exceeds one per fission and the energy of the neutrons is suitably moderated to induce further fission, a chain reaction is induced that can be used for energy production. 

Thus, for a nondeactivating catalyst, the nature of the solid presence (fixed or fluidized, or even moving as found by Sadana and Doraiswamy, 1971) is of no consequence, as long as the fluid flow patterns are the same, plug flow in this case. It is only when the catalyst is subject to decay that the performances of the reactors differ, and then the nature of the decay equation plays a significant role in determining the conversions achievable. 

Because this radionuclide is not found in nature, its decay is an example of induced or artificial radioactivity. When decays, it emits a particle having the mass of an electron and a charge equal to that of an electron, except that it is positive. This positive electron is called a positron, and it is represented by the symbol Je. The decay equation is... 

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