Question

If 23592U released only 1.5 neutrons per fission on average (instead of 2.5), would a chain reaction be possible? If so, how would the chain reaction be different than if 3 neutrons were released per fission?

Answer 1

Solution:

In the fission of 23592U there are, on the average, 2.5 neutrons released per fission. The fact that the fission of 23592U releases on the average ,2.5 neutrons, makes it possible for a self-sustaining series of fissions to occur . Each neutron released by the fission process can initiate another fission reaction, resulting in the release of still more neutrons. These neutrons initiate more fission reactions, and the process results in a self-sustaining chain reaction. Suppose a different element is being fissioned and , on the average only 1.0 neutron is released per fission. If a small fraction of the thermal neutrons absorbed by the nuclei does not produce a fission a self-sustaining chain reaction cannot be produced using this element. Since each fission produces only one neutron the product of a fission reaction can at best, initiate only one more fission reaction. However, since a small fraction of the thermal neutrons absorbed by the nuclei does not produce a fission, at some point, the absorbed neutron will not produce a fission and, since there are no other neutrons to initiate a fission, the process will eventually stop.

Much more energy is released when a uranium 23592U nucleus fissions than when a carbon 126C atom in coal is combined with oxygen during the coal-burning process. It is true that the mass of the uranium nucleus is about 20 times greater than that of a carbon nucleus (235/12 = 20). But even 20 carbon atoms, when burned, release much less energy than a single 23592U nucleus releases when it fissions. In fact, they release about 2 million times less energy. Thus, the mass of coal needed is about 2 million times greater than the mass of uranium.

Nuclear fission occurs when a massive nucleus captures a slow moving neutron and is split into two less-massive fragments that have a greater binding energy per nucleon than the massive parent nucleus. Since the binding energy per nucleon of the daughter nuclei is greater than that of the parent nucleus, energy is released. It appears primarily as kinetic energy of the fission products.

Nuclear fusion occurs when two low-mass nuclei with relatively small binding energies per nucleon combine or "fuse" into a single, more massive nucleus that has a greater binding energy per nucleon. Since the binding energy per nucleon of the more massive nucleus is greater than that of the parent nuclei, a substantial amount of energy is released. The energy released per nucleon in a fusion reaction is greater than that released in a fission reaction. Therefore, for a given mass of fuel, a fusion reaction will yield more energy than a fission reaction.

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