| MadSci Network: Physics |
First some terminology, from the Glossary of terms in Nuclear Science and Technology, American Nuclear Society, 1986. - Critical size: The minimum physical dimensions of a reactor core or an assembly than can be made critical for a specified geometrical arrangement and material composition. - Criticality: The condition of being critical. - Criticality factor: The effective multiplication factor. And, from page 149 of Nuclear Reactor Engineering, Samuel Glasstone and Alexander Sesonske, Van Nostrand Reinhold Company, 1981 - The effective multiplication factor of a system of finite size is given by k = (rate of neutron production)/(rate of neutron absorption and leakage) If k is less than 1, the system is subcritical - neutrons are being absorbed or leaking from the system faster than they are being produced. If k is greater than 1, the system is supercritical - neutrons are being produced faster than they are being removed, by either absorption or leakage. The requirement for criticality in a finite system is that k=1 in the absence of an extraneous source of neutrons. How can the critical mass of uranium be determined? Given the effective multiplication factor, k, is 1; the critical size or mass can be determined from a consideration of the rates of production, absorption, and leakage of neutrons. Those considerations can become very involved. See, for instance, the pages immediately following page 149 of Nuclear Reactor Engineering (cited above). Note that the criticality of uranium varies significantly for different configurations (ratios of uranium-235 to other uranium isotopes, and presence of neutron reflectors and moderators). Neutron reflectors scatter some neutrons back into the system under consideration and moderators slow neutrons down. For instance, the critical mass for a solid sphere of uranium-235 is much greater than the mass of uranium-235 needed to attain criticality when mixed with a moderator. That is because moderators slow neutrons down to speeds (energies) at which the neutron is more likely to cause fission of uranium-235. Are all elements heavier than iron capable of fission, given enough mass? Yes, but... Every element could be said to have a probability of fissioning dependent upon the energy of the neutron or other particle used to cause fission. But, for most elements the probability of fission is nill, neglecting other exotic collison processes which are not considered in determining critical mass. Critical mass, in the context of your question, only pertains to fissionable materials. The most common fissionable atoms are uranium-233, uranium-235, and plutonium-239. Thorium-232 and uranium-238 are also fissionable, but require higher energy neutrons than are required for the other fissionable atoms. Thanks for your question, sid.
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