Fission of a nucleus is the splitting of a heavy atom into two fragments of approximately equal mass, accompanied by the release of a large amount of energy.
The discovery of nuclear fission began a new era - the "atomic age". The potential of its possible use and the ratio of risk to benefit from its use have not only generated many sociological, political, economic and scientific achievements, but also serious problems. Even from a purely scientific point of view, the process of nuclear fission has created a large number of puzzles and complications, and a complete theoretical explanation of it is a matter of the future.
Sharing is profitable
The binding energies (per nucleon) differ for different nuclei. Heavier ones have lower binding energies than those located in the middle of the periodic table.
This means that heavy nuclei with an atomic number greater than 100 benefit from dividing into two smaller fragments, thereby releasing energy thatconverted into kinetic energy of fragments. This process is called the splitting of the atomic nucleus.
According to the stability curve, which shows the dependence of the number of protons on the number of neutrons for stable nuclides, heavier nuclei prefer more neutrons (compared to the number of protons) than lighter ones. This suggests that along with the splitting process, some "spare" neutrons will be emitted. In addition, they will also take on some of the released energy. The study of nuclear fission of the uranium atom showed that 3-4 neutrons are released: 238U → 145La + 90 Br + 3n.
The atomic number (and atomic mass) of the fragment is not equal to half the atomic mass of the parent. The difference between the masses of atoms formed as a result of splitting is usually about 50. However, the reason for this is not yet fully understood.
The binding energies of 238U, 145La and 90Br are 1803, 1198 and 763 MeV, respectively. This means that as a result of this reaction, the fission energy of the uranium nucleus is released, equal to 1198 + 763-1803=158 MeV.
Spontaneous fission
Processes of spontaneous splitting are known in nature, but they are very rare. The average lifetime of this process is about 1017 years, and, for example, the average lifetime of alpha decay of the same radionuclide is about 1011 years.
The reason for this is that in order to split into two parts, the kernel mustfirst undergo deformation (stretch) into an ellipsoidal shape, and then, before the final splitting into two fragments, form a “neck” in the middle.
Potential barrier
In the deformed state, two forces act on the core. One of them is the increased surface energy (the surface tension of a liquid drop explains its spherical shape), and the other is the Coulomb repulsion between fission fragments. Together they produce a potential barrier.
As in the case of alpha decay, in order for the spontaneous fission of the uranium atom nucleus to occur, the fragments must overcome this barrier using quantum tunneling. The barrier is about 6 MeV, as in the case of alpha decay, but the probability of tunneling of an α particle is much greater than that of a much heavier atom fission product.
Forced splitting
Much more likely is induced fission of the uranium nucleus. In this case, the parent nucleus is irradiated with neutrons. If the parent absorbs it, they bind, releasing binding energy in the form of vibrational energy that can exceed the 6 MeV required to overcome the potential barrier.
Where the energy of an additional neutron is insufficient to overcome the potential barrier, the incident neutron must have a minimum kinetic energy in order to be able to induce the splitting of an atom. In the case of 238U bond energy additionalneutrons are missing about 1 MeV. This means that fission of the uranium nucleus is induced only by a neutron with a kinetic energy greater than 1 MeV. On the other hand, the isotope 235U has one unpaired neutron. When the nucleus absorbs an additional one, it forms a pair with it, and as a result of this pairing, additional binding energy appears. This is enough to release the amount of energy necessary for the nucleus to overcome the potential barrier and the isotope fission occurs upon collision with any neutron.
Beta Decay
Despite the fact that the fission reaction emits three or four neutrons, the fragments still contain more neutrons than their stable isobars. This means that fission fragments are generally unstable against beta decay.
For example, when uranium fission occurs 238U, the stable isobar with A=145 is neodymium 145Nd, which means that the lanthanum fragment 145La decays in three stages, each time emitting an electron and an antineutrino, until a stable nuclide is formed. The stable isobar with A=90 is zirconium 90Zr, so the splitting fragment bromine 90Br decays in five stages of the β-decay chain.
These β-decay chains release additional energy, almost all of which is carried away by electrons and antineutrinos.
Nuclear reactions: fission of uranium nuclei
Direct radiation of a neutron from a nuclide with tooa large number of them to ensure the stability of the kernel is unlikely. The point here is that there is no Coulomb repulsion and so the surface energy tends to keep the neutron in bond with the parent. However, this sometimes happens. For example, the fission fragment 90Br in the first stage of beta decay produces krypton-90, which can be in an excited state with enough energy to overcome the surface energy. In this case, the emission of neutrons can occur directly with the formation of krypton-89. This isobar is still unstable to β decay until it changes to stable yttrium-89, so krypton-89 decays in three steps.
Uranium fission: chain reaction
Neutrons emitted in a fission reaction can be absorbed by another parent nucleus, which then itself undergoes induced fission. In the case of uranium-238, the three neutrons that are produced come out with an energy of less than 1 MeV (the energy released during the fission of the uranium nucleus - 158 MeV - is mainly converted into the kinetic energy of the fission fragments), so they cannot cause further fission of this nuclide. However, with a significant concentration of the rare isotope 235U, these free neutrons can be captured by nuclei 235U, which can indeed cause fission, since in this case, there is no energy threshold below which fission is not induced.
This is the chain reaction principle.
Types of nuclear reactions
Let k be the number of neutrons produced in a sample of fissile material at stage n of this chain, divided by the number of neutrons produced at stage n - 1. This number will depend on how many neutrons are produced at stage n - 1, are absorbed by the nucleus, which may undergo forced fission.
• If k < is 1, then the chain reaction will simply fizzle out and the process will stop very quickly. This is exactly what happens in natural uranium ore, in which the concentration of 235U is so low that the probability of absorption of one of the neutrons by this isotope is extremely negligible.
• If k > 1, then the chain reaction will grow until all the fissile material is used (atomic bomb). This is achieved by enriching natural ore to obtain a sufficiently high concentration of uranium-235. For a spherical sample, the value of k increases with an increase in the neutron absorption probability, which depends on the radius of the sphere. Therefore, the mass of U must exceed some critical mass in order for the fission of uranium nuclei (a chain reaction) to occur.
• If k=1, then a controlled reaction takes place. This is used in nuclear reactors. The process is controlled by distributing cadmium or boron rods among the uranium, which absorb most of the neutrons (these elements have the ability to capture neutrons). The fission of the uranium nucleus is controlled automatically by moving the rods so that the value of k remains equal to one.
