Radioactive decay equations mean life

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 ... 

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... 

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 ... 

The same arguments may be used in the case that a neutron death is accompanied also by the prompt production of delayed neutron emitters. Each delayed neutron emitter decays according to the radioactive decay law with mean life r and emits a neutron coincident with its decay. The resulting equations are... 

In most practical situations, the number of radioactive atoms present is exceedingly high and the probability of detection very small. This means that the number of decays detected n decays or C counts) is very much smaller than the number of radioactive atoms present N). (Exceptions to this general situation, when the efficiency of detection and probability of particle emission are very high and when the count period is comparable to the half-life of the nuclide, are discussed in Section 5.7.) In fact, if we assume the detection efficiency to be subsumed into / , it makes no difference to the statistics whether we consider number of decays or number of counts detected and from now on we can take n and C as equivalent. Under these circumstances, various mathematical approximations can be made to Equation (5.18) which lead to a new form for the probability distribution. 

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