Nuclear division-- the process of splitting an atomic nucleus into two nuclei with similar masses, called fission fragments. As a result of fission, other reaction products can also arise: light nuclei (mainly alpha particles), neutrons and gamma rays. Fission can be spontaneous (spontaneous) and forced (as a result of interaction with other particles, primarily with neutrons). Fission of heavy nuclei -- exothermic process, as a result of which a large amount of energy is released in the form of kinetic energy of reaction products, as well as radiation. Nuclear fission serves as a source of energy in nuclear reactors and nuclear weapons.
In 1938, German scientists O. Gann and F. Strassmann discovered that when uranium is irradiated with neutrons, elements are formed from the middle periodic table- barium and lanthanum, which laid the foundation for practical use nuclear energy.
The fission of heavy nuclei occurs through the capture of neutrons. In this case, new particles are emitted and the binding energy of the nucleus, transferred to the fission fragments, is released.
Physicists A. Meitner and O. Frisch explained this phenomenon by the fact that the uranium nucleus that has captured a neutron is divided into two parts, called fragments. There are more than two hundred division options, for example:
- 235U + 1 n > 139 Xe + 95 Sr + 2 1 n.
- 92 0 54 38 0
In this case, 200 MeV of energy is released per nucleus of the uranium isotope 235 U.
Most of this energy comes from fragment nuclei, the rest comes from the kinetic energy of fission neutrons and radiation energy.
To synthesize similarly infected protons, it is necessary to overcome Coulomb repulsive forces, which is possible at sufficiently high velocities of colliding particles. Prerequisites for the synthesis of helium nuclei from protons are available in the interior of stars. On the ground thermonuclear reaction fusion was carried out during experimental thermonuclear explosions.
Since for heavy nuclei the ratio of the number of neutrons and protons N/Z is ? 1.6, and for lighter nuclei - fragments it is close to unity, the fragments at the moment of their occurrence are overloaded with neutrons, in order to transition to a stable state, they emit secondary neutrons. The emission of secondary neutrons is an important feature of the fission reaction of heavy nuclei, therefore secondary neutrons are also called fission neutrons. When each uranium nucleus fissions, 2-3 fission neutrons are emitted. Secondary neutrons can cause new fission events, which makes it possible to fission chain reaction- a nuclear reaction in which the particles causing the reaction are formed as products of this reaction. The chain reaction is characterized neutron multiplication factor k, equal to the ratio of the number of neutrons at a given stage of the reaction to their number at the previous stage. If k< 1, цепная реакция не возникает (или прекращается), при k >1 there is a developing chain reaction, the number of divisions increases like an avalanche and the reaction can become explosive. At k=1, a self-sustaining reaction occurs, in which the number of neutrons remains constant. This is exactly the chain reaction that occurs in nuclear reactors.
The multiplication coefficient depends on the nature of the fissile substance, and for a given isotope - on its quantity, as well as on the size and shape core- the space in which the chain reaction occurs. Not all neutrons that have enough energy for nuclear fission participate in a chain reaction - some of them “get stuck” in the nuclei of non-fissile impurities, which are always present in the core, and some leave the core, the dimensions of which are finite, before being captured by any nucleus (neutron leakage). The minimum dimensions of the core at which a chain reaction is possible are called critical dimensions, and the minimum mass of fissile substances located in a system of critical sizes is called critical mass. So, in a piece of pure uranium 92 235 U, each neutron captured by the nucleus causes fission with the emission of an average of 2.5 secondary neutrons, but if the mass of such uranium is less than 9 kg, then most of the neutrons fly out without causing fission, so that a chain reaction does not arise. Therefore, substances whose nuclei are capable of fission are stored in the form of pieces isolated from each other, less than a critical mass. If several such pieces are quickly and tightly connected so that their total mass exceeds the critical mass, an avalanche-like multiplication of neutrons will begin, and the chain reaction will acquire an uncontrollable explosive character. This is what the device is based on. atomic bomb.
In addition to the fission reaction of heavy nuclei, there is another way to release intranuclear energy - the fusion reaction of light nuclei. The amount of energy released during the fusion process is so great that at a high concentration of interacting nuclei, it may be sufficient to cause a chain thermonuclear reaction. In this process, the rapid thermal motion of nuclei is supported by the energy of the reaction, and the reaction itself is supported by thermal movement. To achieve the required kinetic energy, the temperature of the reactant must be very high (107 - 108 K). At this temperature, the substance is in a state of hot, fully ionized plasma, consisting of atomic nuclei and electrons. Completely new opportunities are opening up for humanity with the implementation of the thermonuclear reaction of fusion of light elements. One can imagine three ways to carry out this reaction:
- 1) a slow thermonuclear reaction that spontaneously occurs in the depths of the Sun and other stars;
- 2) a fast self-sustaining thermonuclear reaction of an uncontrolled nature, occurring during the explosion of a hydrogen bomb;
- 3) controlled thermonuclear reaction.
An uncontrolled thermonuclear reaction is a hydrogen bomb, the explosion of which occurs as a result of nuclear interaction:
D + D -> He3 + n; D + D -> T + r; T + D -> He4 + n,
leading to the synthesis of the helium isotope He3, containing two protons and one neutron in the nucleus, and ordinary helium He4, containing two protons and two neutrons in the nucleus. Here n is a neutron, and p is a proton, D is deuterium and T is tritium.
He began experiments on irradiating uranium with slow neutrons from a radium-beryllium source. The purpose of these experiments, which served as an impetus for numerous similar experiments carried out in other laboratories, was the discovery of transuranic elements unknown at that time, which were supposed to be obtained as a result of the decay of uranium isotopes formed during the capture of neutrons. New radioactive products were indeed found, but further research showed that the radiochemical properties of many of the “new transuranium elements” were different from expected ones. The study of these unusual products continued until 1939, when radiochemists Hahn and Strassmann proved that the new activities did not belong to heavy elements, but to atoms of average weight. The correct interpretation of the unusual nuclear process was given in the same year by Meitner and Frisch, who proposed that an excited uranium nucleus splits into two fragments of approximately equal mass. Based on the analysis of the binding energies of the elements periodic table They came to the conclusion that each fission event should release a very large amount of energy, several tens of times greater than the energy released during decay. This was confirmed by the experiments of Frisch, who registered pulses from fission fragments in the ionization chamber, and Joliot, who showed, based on measurements of the paths of fragments, that the latter have high kinetic energy.
From Fig. 1 it is clear that nuclei with A = 40-120 have the greatest stability, i.e. located in the middle of the periodic table. The processes of combination (synthesis) of light nuclei and fission of heavy nuclei are energetically favorable. In both cases, the final nuclei are located in the region of values of A where the specific binding energy is greater than the specific binding energy of the initial nuclei. Therefore, these processes must occur with the release of energy. Using data on specific binding energies, it is possible to estimate the energy that is released in one fission event. Let a nucleus with mass number A 1 = 240 be divided into two equal fragments with A 2 = 120. In this case, the specific binding energy of the fragments, compared to the specific binding energy of the initial nucleus, increases by 0.8 MeV (from 1 to 7.6 MeV for a nucleus with A 1 = 240 to 2 8.4 MeV for a nucleus with A 2 = 120). In this case, energy must be released
E = A 1 1 - 2A 2 2 = A 1 ( 2 - 1)240(8.4-7.6) MeV 200 MeV.
. Elementary theory of fission
Let us calculate the amount of energy released during the fission of a heavy nucleus. Let us substitute into (f.2) the expressions for the binding energies of nuclei (f.1), assuming A 1 = 240 and Z 1 = 90. Neglecting the last term in (f.1) due to its smallness and substituting the values of the parameters a 2 and a 3 ,we get
From this we obtain that fission is energetically favorable when Z 2 /A > 17. The value of Z 2 /A is called the fissibility parameter. The energy E released during fission increases with increasing Z 2 /A; Z 2 /A = 17 for nuclei in the yttrium and zirconium region. From the obtained estimates it is clear that fission is energetically favorable for all nuclei with A > 90. Why are most nuclei stable with respect to spontaneous fission? To answer this question, let's look at how the shape of the nucleus changes during fission.
During the fission process, the nucleus sequentially passes through the following stages (Fig. 2): ball, ellipsoid, dumbbell, two pear-shaped fragments, two spherical fragments. How does the potential energy of a nucleus change during different stages of fission? After fission has occurred, and the fragments are located at a distance from each other much greater than their radius, the potential energy of the fragments, determined by the Coulomb interaction between them, can be considered equal to zero.
Let us consider the initial stage of fission, when the nucleus, with increasing r, takes the form of an increasingly elongated ellipsoid of revolution. At this stage of division, r is a measure of the deviation of the nucleus from the spherical shape (Fig. 3). Due to the evolution of the shape of the nucleus, the change in its potential energy is determined by the change in the sum of the surface and Coulomb energies E" n + E" k. It is assumed that the volume of the nucleus remains unchanged during the deformation process. In this case, the surface energy E"n increases, as the surface area of the nucleus increases. The Coulomb energy E"k decreases, as the average distance between nucleons increases. Let the spherical core, as a result of a slight deformation characterized by a small parameter, take the shape of an axially symmetric ellipsoid. It can be shown that the surface energy E" n and the Coulomb energy E" k vary as follows depending on:
In the case of small ellipsoidal deformations, the increase in surface energy occurs faster than the decrease in Coulomb energy.
In the region of heavy nuclei 2E n > E k the sum of the surface and Coulomb energies increases with increasing . From (f.4) and (f.5) it follows that at small ellipsoidal deformations, an increase in surface energy prevents further changes in the shape of the nucleus, and, consequently, fission. Expression (f.5) is valid for small values (small deformations). If the deformation is so great that the core takes the shape of a dumbbell, then surface tension forces, like Coulomb forces, tend to separate the core and give the fragments a spherical shape. At this fission stage, an increase in strain is accompanied by a decrease in both Coulomb and surface energies. Those. with a gradual increase in the deformation of the nucleus, its potential energy passes through a maximum. Now r has the meaning of the distance between the centers of future fragments. As the fragments move away from each other, the potential energy of their interaction will decrease, since the Coulomb repulsion energy Ek decreases. The dependence of the potential energy on the distance between the fragments is shown in Fig. 4. The zero level of potential energy corresponds to the sum of the surface and Coulomb energies of two non-interacting fragments.
The presence of a potential barrier prevents the instantaneous spontaneous fission of nuclei. In order for a nucleus to instantly split, it must be given an energy Q exceeding the height of the barrier H. The maximum potential energy of a fissile nucleus is approximately equal to
e 2 Z 1 Z 2 /(R 1 +R 2), where R 1 and R 2 are the radii of the fragments. For example, when a gold nucleus is divided into two identical fragments, e 2 Z 1 Z 2 /(R 1 + R 2) = 173 MeV, and the amount of energy E released during fission () is equal to 132 MeV. Thus, when a gold nucleus fissions, it is necessary to overcome a potential barrier of about 40 MeV.
The higher the barrier height H, the lower the ratio of Coulomb and surface energy E to /E p in the initial nucleus. This ratio, in turn, increases with increasing divisibility parameter Z 2 /A (). The heavier the nucleus, the lower the height of the barrier H ,
since the fissibility parameter increases with increasing mass number:
 |
Those. According to the droplet model, there should be no nuclei with Z 2 /A > 49 in nature, since they spontaneously fission almost instantly (within a characteristic nuclear time of the order of 10 -22 s). The possibility of the existence of atomic nuclei with Z 2 /A > 49 (“island of stability”) is explained by the shell structure. The dependence of the shape, height of the potential barrier H and fission energy E on the value of the fission parameter Z 2 /A is shown in Fig. 5.
The energy E released during fission increases with increasing Z 2 /A. The value of Z 2 /A = 17 for 89 Y (yttrium). Those. fission is energetically favorable for all nuclei heavier than yttrium. Why are most nuclei resistant to spontaneous fission? To answer this question, it is necessary to consider the division mechanism.
During the process of fission, the shape of the nucleus changes. The core sequentially passes through the following stages (Fig. 7.1): ball, ellipsoid, dumbbell, two pear-shaped fragments, two spherical fragments. How does the potential energy of the nucleus change at different stages of fission?
Initial core with magnification r takes the form of an increasingly elongated ellipsoid of revolution. In this case, due to the evolution of the shape of the nucleus, the change in its potential energy is determined by the change in the sum of the surface and Coulomb energies E p + E k. In this case, the surface energy increases as the surface area of the nucleus increases. The Coulomb energy decreases as the average distance between protons increases. If, under slight deformation, characterized by a small parameter , the original core has taken the shape of an axially symmetric ellipsoid, the surface energy E" p and the Coulomb energy E" k as functions of the deformation parameter change as follows:
In ratios (7.4–7.5) E n and E k are the surface and Coulomb energies of the initial spherically symmetric nucleus.
In the region of heavy nuclei 2E p > E k and the sum of the surface and Coulomb energies increases with increasing . From (7.4) and (7.5) it follows that at small deformations, an increase in surface energy prevents further changes in the shape of the nucleus, and, consequently, fission.
Relationship (7.5) is valid for small deformations. If the deformation is so great that the core takes the shape of a dumbbell, then the surface and Coulomb forces tend to separate the core and give the fragments a spherical shape. Thus, with a gradual increase in the deformation of the nucleus, its potential energy passes through a maximum. A graph of changes in the surface and Coulomb energies of the nucleus depending on r is shown in Fig. 7.2.
The presence of a potential barrier prevents the instantaneous spontaneous fission of nuclei. In order for a nucleus to split, it needs to impart an energy Q that exceeds the height of the fission barrier H. The maximum potential energy of a fissioning nucleus E + H (for example gold) into two identical fragments is ≈ 173 MeV, and the amount of energy E released during fission is 132 MeV . Thus, when a gold nucleus fissions, it is necessary to overcome a potential barrier of about 40 MeV.
The height of the fission barrier H is greater, the lower the ratio of Coulomb and surface energy E to /E p in the initial nucleus. This ratio, in turn, increases with increasing division parameter Z 2 /A (7.3). The heavier the nucleus, the lower the height of the fission barrier H, since the fission parameter, assuming that Z is proportional to A, increases with increasing mass number:
| E k /E p = (a 3 Z 2)/(a 2 A) ~ A. | (7.6) |
Therefore, heavier nuclei generally need to impart less energy to cause nuclear fission.
The height of the fission barrier vanishes at 2E p – E k = 0 (7.5). In this case
2E p /E k = 2(a 2 A)/(a 3 Z 2),
Z 2 /A = 2a 2 /(a 3 Z 2) ≈ 49.
Thus, according to the droplet model, nuclei with Z 2 /A > 49 cannot exist in nature, since they must spontaneously split into two fragments almost instantly within a characteristic nuclear time of the order of 10–22 s. The dependences of the shape and height of the potential barrier H, as well as the fission energy on the value of the parameter Z 2 /A are shown in Fig. 7.3.
Rice. 7.3. Radial dependence of the shape and height of the potential barrier and fission energy E at different values of the parameter Z 2 /A. The value E p + E k is plotted on the vertical axis.
Spontaneous fission of nuclei with Z 2 /A< 49,
для которых высота барьера H
не равна нулю, с точки зрения классической физики невозможно. Однако в квантовой
механике такое деление возможно за счет туннельного эффекта – прохождения
осколков деления через потенциальный барьер. Оно носит название спонтанного
деления. Вероятность спонтанного деления растет с увеличением параметра деления
Z 2 /A,
т. е. с уменьшением высоты барьера деления. В целом период спонтанного деления
уменьшается при переходе от менее тяжелых ядер к более тяжелым от
T 1/2 >10 21 years for 232 Th to 0.3 s for 260 Rf.
Forced fission of nuclei with Z 2 /A< 49
может быть вызвано их возбуждением фотонами, нейтронами, протонами, дейтронами,
a частицами и другими частицами, если вносимая в
ядро энергия достаточна для преодоления барьера деления.
The minimum value of the excitation energy of a compound nucleus E* formed during neutron capture is equal to the neutron binding energy in this nucleus ε n. Table 7.1 compares the barrier height H and the neutron binding energy ε n for the Th, U, and Pu isotopes formed after neutron capture. The binding energy of a neutron depends on the number of neutrons in the nucleus. Due to the pairing energy, the binding energy of an even neutron is greater than the binding energy of an odd neutron.
Table 7.1
Fission barrier height H, neutron binding energy ε n
| Isotope | Fission barrier height H, MeV | Isotope | Neutron binding energy ε n |
|---|---|---|---|
| 232 Th | 5.9 | 233 Th | 4.79 |
| 233U | 5.5 | 234 U | 6.84 |
| 235U | 5.75 | 236 U | 6.55 |
| 238 U | 5.85 | 239U | 4.80 |
| 239 Pu | 5.5 | 240 Pu | 6.53 |
A characteristic feature of fission is that the fragments, as a rule, have different masses. In the case of the most probable fission of 235 U, the mass ratio of the fragments is on average ~ 1.5. The mass distribution of fragments from the fission of 235 U by thermal neutrons is shown in Fig. 7.4. For the most probable fission, the heavy fragment has a mass number of 139, the light one - 95. Among the fission products there are fragments with A = 72 - 161 and Z = 30 - 65. The probability of fission into two fragments of equal mass is not zero. When 235 U is fissioned by thermal neutrons, the probability of symmetric fission is approximately three orders of magnitude less than in the case of the most probable fission into fragments with A = 139 and 95.
Asymmetric division is explained by the shell structure of the nucleus. The nucleus strives to split in such a way that the main part of the nucleons of each fragment forms the most stable magical skeleton.
The ratio of the number of neutrons to the number of protons in the 235 U nucleus N/Z = 1.55, while for stable isotopes with a mass number close to the mass number of fragments, this ratio is 1.25 − 1.45. Consequently, fission fragments turn out to be heavily overloaded with neutrons and must be
β - radioactive. Therefore, fission fragments undergo successive β - decays, and the charge of the primary fragment can change by 4 − 6 units. Below is a typical chain of radioactive decays of 97 Kr, one of the fragments formed during the fission of 235 U:
The excitation of fragments, caused by a violation of the ratio of the number of protons and neutrons, characteristic of stable nuclei, is also removed due to the emission of prompt fission neutrons. These neutrons are emitted by moving fragments in a time less than ~ 10 -14 s. On average, 2–3 prompt neutrons are emitted in each fission event. Their energy spectrum is continuous with a maximum of about 1 MeV. The average energy of a prompt neutron is close to 2 MeV. The emission of more than one neutron in each fission event makes it possible to obtain energy through a nuclear fission chain reaction.
With the most probable fission of 235 U by thermal neutrons, a light fragment (A = 95) acquires a kinetic energy of ≈ 100 MeV, and a heavy fragment (A = 139) acquires a kinetic energy of about 67 MeV. Thus, the total kinetic energy of the fragments is ≈ 167 MeV. The total fission energy in this case is 200 MeV. Thus, the remaining energy (33 MeV) is distributed among other fission products (neutrons, electrons and antineutrinos from β-decay fragments, γ-radiation from fragments and their decay products). The distribution of fission energy between the various products during the fission of 235 U by thermal neutrons is given in Table 7.2.
Table 7.2
Fission energy distribution 235 U thermal neutrons
Nuclear fission products (NFP) are a complex mixture of more than 200 radioactive isotopes 36 elements (from zinc to gadolinium). Most of the activity comes from short-lived radionuclides. Thus, 7, 49 and 343 days after the explosion, the activity of PYD decreases by 10, 100 and 1000 times, respectively, compared to the activity one hour after the explosion. The yield of the most biologically significant radionuclides is given in Table 7.3. In addition to PYN, radioactive contamination is caused by radionuclides of induced activity (3 H, 14 C, 28 Al, 24 Na, 56 Mn, 59 Fe, 60 Co, etc.) and the undivided part of uranium and plutonium. The role of induced activity during thermonuclear explosions is especially great.
Table 7.3
The release of some fission products from a nuclear explosion
| Radionuclide | Half life | Output per division, % | Activity per 1 Mt, 10 15 Bq |
|---|---|---|---|
| 89 Sr | 50.5 days. | 2.56 | 590 |
| 90 Sr | 29.12 years | 3.5 | 3.9 |
| 95 Zr | 65 days | 5.07 | 920 |
| 103 Ru | 41 days | 5.2 | 1500 |
| 106 Ru | 365 days | 2.44 | 78 |
| 131 I | 8.05 days | 2.9 | 4200 |
| 136 Cs | 13.2 days | 0.036 | 32 |
| 137 Cs | 30 years old | 5.57 | 5.9 |
| 140 Ba | 12.8 days | 5.18 | 4700 |
| 141 Cs | 32.5 days. | 4.58 | 1600 |
| 144 Cs | 288 days | 4.69 | 190 |
| 3 H | 12.3 years | 0.01 | 2.6·10 -2 |
During nuclear explosions in the atmosphere, a significant part of the precipitation (up to 50% for ground explosions) falls near the test area. Some radioactive substances are retained in the lower part of the atmosphere and, under the influence of the wind, move over long distances, remaining at approximately the same latitude. Staying in the air for about a month, radioactive substances gradually fall to Earth during this movement. Most of the radionuclides are emitted into the stratosphere (to a height of 10–15 km), where they are globally dissipated and largely disintegrated.
Various structural elements of nuclear reactors have been highly active for decades (Table 7.4)
Table 7.4
Specific activity values (Bq/t uranium) of the main fission products in fuel elements removed from the reactor after three years of operation
| Radionuclide | 0 | 1 day | 120 days | 1 year | 10 years | |
|---|---|---|---|---|---|---|
| 85 Kr | 5. 78· 10 14 | 5. 78· 10 14 | 5. 66· 10 14 | 5. 42· 10 14 |
4. 7· 10 14 |
3. 03· 10 14 |
| 89 Sr | 4. 04· 10 16 | 3. 98· 10 16 | 5. 78· 10 15 | 2. 7· 10 14 |
1. 2· 10 10 |
|
| 90 Sr | 3. 51· 10 15 | 3. 51· 10 15 | 3. 48· 10 15 | 3. 43· 10 15 |
3. 26· 10 15 |
2. 75· 10 15 |
| 95 Zr | 7. 29· 10 16 | 7. 21· 10 16 | 1. 99· 10 16 | 1. 4· 10 15 | 5. 14· 10 11 | |
| 95 Nb | 7. 23· 10 16 | 7. 23· 10 16 | 3. 57· 10 16 | 3. 03· 10 15 | 1. 14· 10 12 | |
| 103 Ru | 7. 08· 10 16 | 6. 95· 10 16 | 8. 55· 10 15 | 1. 14· 10 14 | 2. 97· 10 8 | |
| 106 Ru | 2. 37· 10 16 | 2. 37· 10 16 | 1. 89· 10 16 | 1. 19· 10 16 | 3. 02· 10 15 | 2. 46· 10 13 |
| 131 I | 4. 49· 10 16 | 4. 19· 10 16 | 1. 5· 10 12 | 1. 01· 10 3 | ||
| 134 Cs | 7. 50· 10 15 | 7. 50· 10 15 | 6. 71· 10 15 | 5. 36· 10 15 | 2. 73· 10 15 | 2. 6· 10 14 |
| 137 Cs | 4. 69· 10 15 | 4. 69· 10 15 | 4. 65· 10 15 | 4. 58· 10 15 | 4. 38· 10 15 | 3. 73· 10 15 |
| 140 Ba | 7. 93· 10 16 | 7. 51· 10 16 | 1. 19· 10 14 | 2. 03· 10 8 | ||
| 140 La | 8. 19· 10 16 | 8. 05· 10 16 | 1. 37· 10 14 | 2. 34· 10 8 | ||
| 141 Ce | 7. 36· 10 16 | 7. 25· 10 16 | 5. 73· 10 15 | 3. 08· 10 13 | 5. 33· 10 6 | |
| 144 Ce | 5. 44· 10 16 | 5. 44· 10 16 | 4. 06· 10 16 | 2. 24· 10 16 | 3. 77· 10 15 | 7. 43· 10 12 |
| 143 PM | 6. 77· 10 16 | 6. 70· 10 16 | 1. 65· 10 14 | 6. 11· 10 8 | ||
| 147 PM | 7. 05·10 15 | 7. 05· 10 15 | 6. 78· 10 15 | 5. 68· 10 15 |
3. 35· 10 14 |
The study of the interaction of neutrons with matter led to the discovery of a new type of nuclear reactions. In 1939, O. Hahn and F. Strassmann investigated the chemical products resulting from the bombardment of uranium nuclei by neutrons. Barium was found among the reaction products - chemical element with a mass much less than the mass of uranium. The problem was solved by German physicists L. Meitner and O. Frisch, who showed that when neutrons are absorbed by uranium, the nucleus splits into two fragments:
Where k > 1.
During the fission of a uranium nucleus, a thermal neutron with an energy of ~0.1 eV releases an energy of ~200 MeV. The essential point is that this process is accompanied by the appearance of neutrons capable of causing the fission of other uranium nuclei - fission chain reaction . Thus, one neutron can give rise to a branched chain of nuclear fissions, and the number of nuclei participating in the fission reaction will increase exponentially. Prospects for using the fission chain reaction have opened up in two directions:
· controlled nuclear fission reaction– creation of nuclear reactors;
· runaway nuclear fission reaction- creation of nuclear weapons.
In 1942, the first nuclear reactor. In the USSR, the first reactor was launched in 1946. Currently, thermal and electrical energy produced in hundreds of nuclear reactors operating in different countries around the world.
As can be seen from Fig. 4.2, with increasing value A specific binding energy increases up to A» 50. This behavior can be explained by a combination of forces; The binding energy of an individual nucleon increases if it is attracted not by one or two, but by several other nucleons. However, in elements with mass number values greater A» 50 specific binding energy gradually decreases with increasing A. This is due to the fact that nuclear attractive forces are short-range, with a radius of action on the order of the size of an individual nucleon. Outside this radius, electrostatic repulsion forces predominate. If two protons are separated by more than 2.5 × 10 - 15 m, then the forces of Coulomb repulsion rather than nuclear attraction prevail between them.
A consequence of this behavior of the specific binding energy depending on A is the existence of two processes - nuclear fusion and fission . Let's consider the interaction of an electron and a proton. When a hydrogen atom is formed, an energy of 13.6 eV is released and the mass of the hydrogen atom is 13.6 eV less than the sum of the masses of a free electron and a proton. Similarly, the mass of two light nuclei exceeds the mass after their combination on D M. If you connect them, they will merge releasing energy D Ms 2. This process is called nuclear fusion . The mass difference can exceed 0.5%.
If a heavy nucleus splits into two lighter nuclei, their mass will be 0.1% less than the mass of the parent nucleus. Heavy nuclei tend to division into two lighter nuclei with the release of energy. The energy of an atomic bomb and a nuclear reactor represents the energy , released during nuclear fission . Hydrogen bomb energy is the energy released during nuclear fusion. Alpha decay can be considered as a highly asymmetric fission in which the parent nucleus M splits into a small alpha particle and a large residual nucleus. Alpha decay is possible only if the reaction
weight M turns out to be greater than the sum of the masses and the alpha particle. All cores with Z> 82 (lead) .At Z> 92 (uranium) alpha decay half-lives turn out to be significantly longer than the age of the Earth, and such elements do not occur in nature. However, they can be created artificially. For example, plutonium ( Z= 94) can be obtained from uranium in a nuclear reactor. This procedure has become common and costs only 15 dollars per 1 g. So far, it has been possible to obtain elements up to Z= 118, however at a much higher price and, as a rule, in negligible quantities. One can hope that radiochemists will learn to obtain, albeit in small quantities, new elements from Z> 118.
If a massive uranium nucleus could be divided into two groups of nucleons, then these groups of nucleons would rearrange themselves into nuclei with a stronger bond. During the restructuring process, energy would be released. Spontaneous nuclear fission is permitted by the law of conservation of energy. However, the potential barrier to fission reactions in naturally occurring nuclei is so high that the probability of spontaneous fission is much less than the probability of alpha decay. The half-life of 238 U nuclei relative to spontaneous fission is 8×10 15 years. This is more than a million times the age of the Earth. If a neutron collides with a heavy nucleus, it can move to a higher energy level near the top of the electrostatic potential barrier, resulting in an increased probability of fission. A nucleus in an excited state can have a significant angular momentum and acquire an oval shape. Areas on the periphery of the nucleus penetrate the barrier more easily because they are partially already behind the barrier. For an oval-shaped nucleus, the role of the barrier is further weakened. When a nucleus or slow neutron is captured, states are formed with very short lifetimes relative to fission. The difference in mass between the uranium nucleus and typical fission products is such that, on average, the fission of uranium releases an energy of 200 MeV. The rest mass of the uranium nucleus is 2.2×10 5 MeV. About 0.1% of this mass is converted into energy, which is equal to the ratio of 200 MeV to the value of 2.2 × 10 5 MeV.
Energy rating,released by division,can be obtained from Weizsäcker formulas :
When a nucleus divides into two fragments, the surface energy and Coulomb energy change 
, and the surface energy increases, and the Coulomb energy decreases. Fission is possible when the energy released during fission E > 0.
.
Here A 1 = A/2, Z 1 = Z/2. From this we obtain that fission is energetically favorable when Z 2 /A> 17. Magnitude Z 2 /A called divisibility parameter . Energy E, released during division, increases with increasing Z 2 /A.
During the process of division, the nucleus changes shape - it sequentially passes through the following stages (Fig. 9.4): a ball, an ellipsoid, a dumbbell, two pear-shaped fragments, two spherical fragments.
After fission has occurred, and the fragments are located from each other at a distance much greater than their radius, the potential energy of the fragments, determined by the Coulomb interaction between them, can be considered equal to zero.
Due to the evolution of the shape of the nucleus, the change in its potential energy is determined by the change in the sum of the surface and Coulomb energies . It is assumed that the volume of the core remains unchanged during deformation. In this case, the surface energy increases as the surface area of the nucleus increases. The Coulomb energy decreases as the average distance between nucleons increases. In the case of small ellipsoidal deformations, the increase in surface energy occurs faster than the decrease in Coulomb energy.
In the region of heavy nuclei, the sum of surface and Coulomb energies increases with increasing deformation. At small ellipsoidal deformations, an increase in surface energy prevents further changes in the shape of the nucleus, and therefore fission. The presence of a potential barrier prevents the instantaneous spontaneous fission of nuclei. In order for a nucleus to instantly split, it must be given an energy exceeding the height of the fission barrier N.
Barrier height N the smaller the ratio of Coulomb and surface energy in the initial nucleus, the greater. This ratio, in turn, increases with increasing divisibility parameter Z 2 /A. The heavier the core, the lower the height of the barrier N, since the fissibility parameter increases with increasing mass number:
Heavier nuclei generally need to impart less energy to cause fission. From the Weizsäcker formula it follows that the height of the fission barrier vanishes at . Those. According to the droplet model, nuclei with should be absent in nature, since they spontaneously fission almost instantly (within a characteristic nuclear time of the order of 10–22 s). The existence of atomic nuclei with (" island of stability ") is explained by the shell structure of atomic nuclei. Spontaneous fission of nuclei with , for which the barrier height N is not equal to zero, from the point of view of classical physics it is impossible. From the point of view quantum mechanics such division is possible as a result of fragments passing through a potential barrier and is called spontaneous fission . The probability of spontaneous fission increases with increasing fissibility parameter, i.e. with decreasing fission barrier height.
Forced fission of nuclei with can be caused by any particles: photons, neutrons, protons, deuterons, α-particles, etc., if the energy they contribute to the nucleus is sufficient to overcome the fission barrier.
The masses of fragments formed during fission by thermal neutrons are not equal. The nucleus tends to split in such a way that the main part of the nucleons of the fragment forms a stable magical core. In Fig. Figure 9.5 shows the mass distribution during division. The most likely combination of mass numbers is 95 and 139.
The ratio of the number of neutrons to the number of protons in the nucleus is 1.55, while for stable elements having a mass close to the mass of fission fragments, this ratio is 1.25 - 1.45. Consequently, fission fragments are heavily overloaded with neutrons and are unstable to β-decay - radioactive.
As a result of fission, energy of ~200 MeV is released. About 80% of it comes from the energy of fragments. During one fission act more than two are formed fission neutrons with an average energy of ~2 MeV.
1 g of any substance contains 
. The fission of 1 g of uranium is accompanied by the release of ~ 9 × 10 10 J. This is almost 3 million times greater than the energy of burning 1 g of coal (2.9 × 10 4 J). Of course, 1 g of uranium is much more expensive than 1 g of coal, but the cost of 1 J of energy obtained by burning coal is 400 times higher than in the case of uranium fuel. Producing 1 kWh of energy cost 1.7 cents at coal-fired power plants and 1.05 cents at nuclear power plants.
Thanks to chain reaction nuclear fission process can be done self-sustaining . With each fission, 2 or 3 neutrons are released (Fig. 9.6). If one of these neutrons manages to cause the fission of another uranium nucleus, then the process will be self-sustaining.
A collection of fissile matter that satisfies this requirement is called critical assembly . The first such assembly, called nuclear reactor , was built in 1942 under the direction of Enrico Fermi on the grounds of the University of Chicago. The first nuclear reactor was launched in 1946 under the leadership of I. Kurchatov in Moscow. The first nuclear power plant with a capacity of 5 MW was launched in the USSR in 1954 in Obninsk (Fig. 9.7).
Mass and you can also do supercritical . In this case, the neutrons generated during fission will cause several secondary fissions. Because neutrons travel at speeds in excess of 10 8 cm/s, a supercritical assembly can fully react (or fly apart) in less than a thousandth of a second. Such a device is called atomic bomb . A nuclear charge made of plutonium or uranium is transferred to a supercritical state, usually with the help of an explosion. The subcritical mass is surrounded by chemical explosives. When it explodes, the plutonium or uranium mass undergoes instant compression. Since the density of the sphere increases significantly, the rate of absorption of neutrons turns out to be higher than the rate of loss of neutrons due to their escape outward. This is the condition for supercriticality.
In Fig. Figure 9.8 shows a diagram of the Little Boy atomic bomb dropped on Hiroshima. The nuclear explosive in the bomb was divided into two parts, the mass of which was less than the critical mass. The critical mass required for the explosion was created by connecting both parts “by the gun method” using conventional explosives.
The explosion of 1 ton of trinitrotoluene (TNT) releases 10 9 cal, or 4 × 10 9 J. The explosion of an atomic bomb that consumes 1 kg of plutonium releases about 8 × 10 13 J of energy.
Or this is almost 20,000 times more than the explosion of 1 ton of TNT. Such a bomb is called a 20-kiloton bomb. Modern megaton bombs are millions of times more powerful than conventional TNT explosives.
The production of plutonium is based on the irradiation of 238 U with neutrons, leading to the formation of the isotope 239 U, which, as a result of beta decay, turns into 239 Np, and then after another beta decay into 239 Pu. When a low-energy neutron is absorbed, both isotopes 235 U and 239 Pu undergo fission. Fission products are characterized by stronger binding (~1 MeV per nucleon), due to which approximately 200 MeV of energy is released as a result of fission.
Every gram of plutonium or uranium consumed produces almost a gram of radioactive fission products, which have enormous radioactivity.
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Release of energy during nuclear fission. As in other nuclear reactions, the energy released during fission is equivalent to the difference in the masses of the interacting particles and the final products. Since the binding energy of a nucleon in uranium and the binding energy of one nucleon in fragments during the fission of uranium, energy must be released
Thus, during nuclear fission, enormous energy is released, the vast majority of it is released in the form of kinetic energy of fission fragments.
Distribution of fission products by mass. The uranium nucleus in most cases divides asymmetrically. Two nuclear fragments have, respectively, different speeds and different masses.
The fragments fall into two groups based on their masses; one near krypton and the other near xenon. The masses of the fragments relate to each other on average as From the laws of conservation of energy and momentum, it can be obtained that kinetic energies fragments must be inversely proportional to their masses:
The fission product yield curve is symmetrical relative to the vertical straight line passing through the point. The significant width of the maxima indicates the variety of fission paths.
Rice. 82. Distribution of uranium fission products by mass
The listed characteristics relate mainly to fission under the influence of thermal neutrons; In the case of fission under the influence of neutrons with energies of several or more, the nucleus disintegrates into two more symmetrical fragments in mass.
Properties of fission products. During the fission of a uranium atom, very many shell electrons are stripped, and the fission fragments are approximately multiply ionized positive ions, which, when passing through the substance, strongly ionize the atoms. Therefore, the ranges of fragments in the air are small and close to 2 cm.
It is easy to establish that the fragments formed during fission must be radioactive, prone to emitting neutrons. Indeed, for stable nuclei the ratio of the number of neutrons and protons varies depending on A as follows:
(see scan)
Nuclei produced by fission lie in the middle of the table and therefore contain more neutrons than is acceptable for their stability. They can be freed from excess neutrons both by decay and by directly emitting neutrons.
Delayed neutrons. One possible fission option produces radioactive bromine. In Fig. 83 shows a diagram of its decay, at the end of which there are stable isotopes
An interesting feature of this chain is that krypton can be freed from an excess neutron either due to -decay, or if it was formed in an excited state due to the direct emission of a neutron. These neutrons appear 56 seconds after fission (the lifetime is relative to the transition to an excited state, although it itself emits neutrons almost instantly.
Rice. 83. Scheme of the decay of radioactive bromine formed in an excited state during the fission of uranium
They are called delayed neutrons. Over time, the intensity of delayed neutrons decays exponentially, as with normal radioactive decay.
The energy of these neutrons is equal to the excitation energy of the nucleus. Although they make up only 0.75% of all neutrons emitted during fission, delayed neutrons play an important role in the chain reaction.
Prompt neutrons. Over 99% of neutrons are released within an extremely short time; they are called prompt neutrons.
When studying the fission process, a fundamental question arises: how many neutrons are produced in one fission event; this question is important because if their number is large on average, they can be used to fission subsequent nuclei, i.e., the possibility of creating a chain reaction arises. To resolve this issue in 1939-1940. worked in almost all the largest nuclear laboratories in the world.
