![]() ![]() Of course, the longer lived substance will remain radioactive for a much longer time. It is obvious, that the longer the half-life, the greater the quantity of radionuclide needed to produce the same activity. The following figure illustrates the amount of material necessary for 1 curie of radioactivity. This amount of material can be calculated using λ, which is the decay constant of certain nuclide: The relationship between half-life and the amount of a radionuclide required to give an activity of one curie is shown in the figure. If the decay constant (λ) is given, it is easy to calculate the half-life, and vice-versa. Where ln 2 (the natural log of 2) equals 0.693. The relationship can be derived from decay law by setting N = ½ N o. There is a relation between the half-life (t 1/2) and the decay constant λ. In calculations of radioactivity one of two parameters ( decay constant or half-life), which characterize the rate of decay, must be known. Radioactive material with a short half life is much more radioactive but will obviously lose its radioactivity rapidly. Notice that short half lives go with large decay constants. Table of examples of half lives and decay constants. , where N (number of particles) is the total number of particles in the sample, A (total activity) is the number of decays per unit time of a radioactive sample, m is the mass of remaining radioactive material. (Number of nuclei) N = N.e -λt (Activity) A = A.e -λt (Mass) m = m.e -λt The radioactive decay law can be derived also for activity calculations or mass of radioactive material calculations: No matter how long or short the half life is, after seven half lives have passed, there is less than 1 percent of the initial activity remaining. Radioactive material with a short half life is much more radioactive (at the time of production) but will obviously lose its radioactivity rapidly. Half lives range from millionths of a second for highly radioactive fission products to billions of years for long-lived materials (such as naturally occurring uranium). In 14 more days, half of that remaining half will decay, and so on. If a radioisotope has a half-life of 14 days, half of its atoms will have decayed within 14 days. The half-life is the amount of time it takes for a given isotope to lose half of its radioactivity. The rate of nuclear decay is also measured in terms of half-lives. The radioactive decay of certain number of atoms (mass) is exponential in time. This constant probability may vary greatly between different types of nuclei, leading to the many different observed decay rates. This constant is called the decay constant and is denoted by λ, “lambda”. When loading the fuel, the detectors provide an adequate signal to detectors so they can detect incorrect loading patterns.The radioactive decay law states that the probability per unit time that a nucleus will decay is a constant, independent of time. Some utilities use a neutron source, others rely on spent fuel activity. The problem with the californium source is that it will "burn out" if left in the reactor during power operations. Note that you have to irradiate the antimony to "charge" the source.Ī third option, which is usually only used in the first cycle when all the fuel is fresh, is a californium source that has a high spontaneous fission rate. The high energy gammas react with the beryllium to create neutrons. The antimony is irradiated during the power cycle and decays emitting high energy gammas. The second way is to use a neutron source. You can also get spontaneous fissions from higher actinides that have build up. These can come from a number of reaction including spontaneous fission, gamma/neutron reactions, etc. The first way uses the fact that you have quite a bit of exposed/burned fuel that emit neutrons. There are two ways commonly used to "start" the chain reaction in operating nuclear power plants. ![]()
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