How do you determine the critical mass of a particular radioactive element or is…

How do you determine the critical mass of a particular radioactive element or isotope? – F, United Kingdom

This questions asks how you can predict the amount of a fissionable nuclear fuel you must assemble in order for that fuel to experience self-sustaining nuclear fission chain reactions. A self-sustaining nuclear chain reaction can only occur when each fission within that material causes an average of one subsequent fission. The size, shape, and density of the nuclear fuel are important to the chain reaction because they determine how much opportunity fragments from one fission event will have at inducing subsequent events elsewhere within the fuel. A properly shaped piece of fuel that is just large enough and dense enough to experience a self-sustaining nuclear chain reaction is said to be at critical mass. Below the critical mass, the chain reaction won’t be able to sustain itself and will gradually dwindle away. Above the critical mass, the chain reaction will grow stronger exponentially. Since crossing the threshold from below critical mass to above critical mass has dramatic consequences, it can be quite important to know the point at which it occurs.

The basic calculation of critical mass is straightforward in principle, but it requires a thorough understanding of the nuclear fuel. Because you need to know how likely one nuclear fission is to cause a subsequent nuclear fission, you must know both the types of fragments you can expect from the first nuclear fission and the likelihood that each fragment will induce a subsequent fission in another atomic nucleus before that it escapes from the nuclear fuel. Because the range of possible fragments, their kinetic energies, and their paths through the nuclear fuel are so vast, an accurate calculation of critical mass is extremely complicated. As an indication of the difficulty, note that fission fragments may bounce off nuclei without inducing fission, so that you must consider bent paths as well as straight ones. Not surprisingly, the calculation of critical mass is too difficult to do exactly, even with the help of computers. In fact, one of the reasons that Germany didn’t develop nuclear weapons during World War II was that its scientists miscalculated the critical mass of a fission bomb based on enriched uranium and thought that they would need many tons of enriched uranium rather than the true critical mass of about 52 kilograms. Certain that a critical mass of enriched uranium was unattainable, they didn’t pursue the project.

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