The fission of the uranium nucleus. Chain reaction. Process description

The division of the 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 division began a new era - the "atomic age". The potential of its possible use and the ratio of risk to benefit from its application not only gave rise to many sociological, political, economic and scientific achievements, but also serious problems. Even from a purely scientific point of view, the nuclear fission process created a large number of puzzles and complications, and its full theoretical explanation is a matter of the future.

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The binding energies (per nucleon) for different nuclei differ. The heavier ones have a lower binding energy than those located in the middle of the periodic table.

This means that heavy nuclei, for which the atomic number is greater than 100, are advantageously divided into two smaller fragments, thereby releasing the energy that is converted into the kinetic energy of the fragments. This process is called the splitting of the atomic nucleus.

In accordance with the stability curve, which shows the dependence of the number of protons on the number of neutrons for stable nuclides, heavier nuclei prefer a larger number of neutrons (in comparison with 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 over part of the allocated energy. The study of the fission of the nucleus of the uranium atom showed that 3-4 neutrons are released at this time: ²³⁸ U → ¹⁴⁵ La + 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 the splitting is usually about 50. However, the reason for this is not yet fully understood.

The binding energies of ²³⁸ U, ¹⁴⁵ La and ⁹⁰ Br are equal to 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 division

The processes of spontaneous splitting are known in nature, but they are very rare. The average lifetime of this process is about ^10-17 years, and, for example, the average lifetime of the alpha decay of the same radionuclide is about 10 ¹¹ years.

The reason for this is that in order to split into two parts, the core must first be deformed (stretched) 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 drop of liquid 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, spontaneous fission of the nucleus of the uranium atom occurs, the fragments must overcome this barrier by quantum tunneling. The barrier value is about 6 MeV, as in the case of alpha decay, but the probability of tunneling of the α particle is much larger than the much heavier product of atom splitting.

Forced splitting

Much more likely is the induced fission of the uranium nucleus. In this case, the mother nucleus is irradiated with neutrons. If the parent absorbs it, they bind, releasing the binding energy in the form of vibrational energy, which can exceed 6 MeV, necessary to overcome the potential barrier.

Where the energy of the 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 the atom. In the case of ²³⁸ U, the binding energy of the additional neutrons is short of about 1 MeV. This means that the fission of the uranium nucleus is induced only by a neutron with kinetic energy greater than 1 MeV. On the other hand, the isotope ²³⁵ U has one unpaired neutron. When a nucleus absorbs an additional one, it forms a pair with it, and as a result of this pairing an additional binding energy appears. This is sufficient to free up the amount of energy necessary for the core to overcome the potential barrier and the isotope division occurs when colliding with any neutron.

Beta decay

Despite the fact that three or four neutrons are emitted during the fission reaction, the fragments still contain more neutrons than their stable isobars. This means that fragments of the cleavage are, as a rule, unstable with respect to beta decay.

For example, when the fission of the uranium nucleus is ²³⁸ U, the stable isobar with A = 145 is neodymium ¹⁴⁵ Nd, which means that the fragments of lanthanum ¹⁴⁵ La decompose in three stages, each time emitting an electron and antineutrinos until a stable nuclide is formed. A stable isobar with A = 90 is zirconium ⁹⁰ Zr, therefore, the splitting fragment of bromine ⁹⁰ Br decomposes into five stages of the β-decay chain.

These β-decay chains secrete additional energy, which is almost entirely carried away by electrons and antineutrinos.

Nuclear reactions: fission of uranium nuclei

Direct radiation of a neutron from the nuclide with too much of their quantity to ensure the stability of the nucleus is unlikely. Here the thing is that there is no Coulomb repulsion, and therefore the surface energy tends to hold the neutron in connection with the parent. Nevertheless, this sometimes happens. For example, the fragment of division of ⁹⁰ Br in the first stage of beta decay produces krypton-90, which can be in an excited state with sufficient energy to overcome surface energy. In this case, neutron radiation can occur directly with the formation of krypton-89. This isobar is still unstable with respect to β-decay until it becomes stable yttrium-89, so that the krypton-89 decays into three stages.

Fission of uranium nuclei: chain reaction

Neutrons emitted in the cleavage reaction can be absorbed by another parent nucleus, which then itself undergoes induced fission. In the case of uranium-238, the three neutrons that arise emerge at an energy of less than 1 MeV (the energy released upon fission of the uranium nucleus-158 MeV-basically goes over into the kinetic energy of the splitting fragments), so they can not cause further fission of this nuclide. Nevertheless, at a significant concentration of the rare isotope ²³⁵ U, these free neutrons can be captured by ²³⁵ U nuclei, which can actually cause splitting, since in this case there is no energy threshold below which the fission is not induced.

This is the principle of the chain reaction.

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 formed in stage n-1. This number will depend on how many neutrons obtained in stage n-1 are absorbed by the nucleus, which Can undergo forced division.

• If k <1, then the chain reaction will simply die out and the process will stop very quickly. This is exactly what happens in natural uranium ore, in which the concentration of ²³⁵ U is so small that the probability of absorption of one of the neutrons by this isotope is extremely insignificant.

• If k> 1, then the chain reaction will increase until all fissile material is used (atomic bomb). This is achieved by enriching the natural ore to a sufficiently high concentration of uranium-235. For a spherical sample, the value of k increases with increasing probability of neutron absorption, which depends on the radius of the sphere. Therefore, the mass U must exceed some critical mass, so that the fission of uranium nuclei (chain reaction) can occur.

• If k = 1, then a controlled reaction takes place. This is used in nuclear reactors. The process is controlled by the distribution among uranium rods of cadmium or boron, which absorb most of the neutrons (these elements have the ability to capture neutrons). The fission of the uranium core is controlled automatically by moving the rods in such a way that the value of k remains equal to unity.