Lesson summary "Fission of uranium nuclei. Chain reaction." Nuclear fission reactions

Nuclear fission reactions- fission reactions, which consist in the fact that a heavy nucleus, under the influence of neutrons, and, as it later turned out, other particles, is divided into several lighter nuclei (fragments), most often into two nuclei of similar mass.

A feature of nuclear fission is that it is accompanied by the emission of two or three secondary neutrons, called fission neutrons. Since for medium nuclei the number of neutrons is approximately equal to the number of protons ( N/Z ≈ 1), and for heavy nuclei the number of neutrons significantly exceeds the number of protons ( N/Z ≈ 1.6), then the resulting fission fragments are overloaded with neutrons, as a result of which they release fission neutrons. However, the emission of fission neutrons does not completely eliminate the overload of fragment nuclei with neutrons. This causes the fragments to become radioactive. They can undergo a series of β - -transformations, accompanied by the emission of γ quanta. Since β - decay is accompanied by the transformation of a neutron into a proton, then after a chain of β - transformations the ratio between neutrons and protons in the fragment will reach a value corresponding to a stable isotope. For example, during the fission of a uranium nucleus U

U+ n → Xe + Sr +2 n(265.1)

fission fragment Xe, as a result of three acts of β - decay, turns into the stable isotope of lanthanum La:

Heh → Cs → Ba → La.

Fission fragments can be diverse, so reaction (265.1) is not the only one leading to the fission of U.

Most fission neutrons are emitted almost instantly ( t≤ 10 –14 s), and part (about 0.7%) is emitted by fission fragments some time after fission (0.05 s ≤ t≤ 60 s). The first of them are called instant, second – lagging. On average, each fission event produces 2.5 neutrons. They have a relatively wide energy spectrum ranging from 0 to 7 MeV, with an average energy of about 2 MeV per neutron.

Calculations show that nuclear fission must also be accompanied by the release of a large amount of energy. In fact, the specific binding energy for medium-mass nuclei is approximately 8.7 MeV, while for heavy nuclei it is 7.6 MeV. Consequently, when a heavy nucleus divides into two fragments, an energy equal to approximately 1.1 MeV per nucleon should be released.

The theory of fission of atomic nuclei (N. Bohr, Ya. I. Frenkel) is based on the droplet model of the nucleus. The nucleus is considered as a drop of electrically charged incompressible liquid (with a density equal to nuclear and obeying the laws of quantum mechanics), the particles of which, when a neutron hits the nucleus, enter into oscillatory motion, as a result of which the nucleus is torn into two parts, scattering with enormous energy.

The probability of nuclear fission is determined by the energy of the neutrons. For example, if high-energy neutrons cause fission of almost all nuclei, then neutrons with an energy of several mega-electron-volts cause fission only of heavy nuclei ( A>210), Neutrons having activation energy(the minimum energy required to carry out a nuclear fission reaction) of the order of 1 MeV, causes fission of the nuclei of uranium U, thorium Th, protactinium Pa, plutonium Pu. Thermal neutrons fission the nuclei of U, Pu, and U, Th (the last two isotopes do not occur in nature, they are obtained artificially).

Secondary neutrons emitted during nuclear fission 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 fission chain reaction is characterized by multiplication factor k neutrons, which is equal to the ratio of the number of neutrons in a given generation to their number in the previous generation. A necessary condition for the development of a fission chain reaction is requirement k ≥ 1.

It turns out that not all secondary neutrons produced cause subsequent nuclear fission, which leads to a decrease in the multiplication factor. Firstly, due to the finite dimensions core(the space where a valuable reaction occurs) and the high penetrating ability of neutrons, some of them will leave the active zone before being captured by any nucleus. Secondly, some neutrons are captured by nuclei of non-fissile impurities, which are always present in the core. In addition, along with fission, competing processes of radiative capture and inelastic scattering can take place.

The multiplication coefficient depends on the nature of the fissile substance, and for a given isotope, on its quantity, as well as the size and shape of the active zone. The minimum dimensions of the core at which a chain reaction is possible are called critical sizes. The minimum mass of fissile material located in a system of critical dimensions required to implement chain reaction, called critical mass.

The speed of development of chain reactions is different. Let T - average time

life of one generation, and N- the number of neutrons in a given generation. In the next generation their number is equal kN,T. e. increase in the number of neutrons per generation dN = kN – N = N(k – 1). The increase in the number of neutrons per unit time, i.e., the rate of growth of the chain reaction,

. (266.1)

Integrating (266.1), we obtain

,

Where N 0 is the number of neutrons at the initial moment of time, and N- their number at a time t. N determined by the sign ( k- 1). At k>1 is coming developing reaction, the number of fissions continuously increases and the reaction can become explosive. At k=1 goes self-sustaining reaction in which the number of neutrons does not change over time. At k <1 идет fading reaction

Chain reactions include controlled and uncontrollable ones. The explosion of an atomic bomb, for example, is an uncontrolled reaction. To prevent an atomic bomb from exploding during storage, U (or Pu) in it is divided into two parts distant from each other with masses below critical. Then, with the help of an ordinary explosion, these masses come closer together, the total mass of the fissile substance becomes greater than the critical one and an explosive chain reaction occurs, accompanied by the instant release of a huge amount of energy and great destruction. The explosive reaction begins due to available neutrons from spontaneous fission or neutrons from cosmic radiation. Controlled chain reactions occur in nuclear reactors.

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:

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

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 (NFPs) are a complex mixture of more than 200 radioactive isotopes of 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

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

Uranium nuclei fission occurs in the following way: First, a neutron hits the nucleus, like a bullet hitting an apple. In the case of an apple, a bullet would either make a hole in it or blow it into pieces. When a neutron enters the nucleus, it is captured by nuclear forces. The neutron is known to be neutral, so it is not repelled by electrostatic forces.

How does a uranium nucleus fission occur?

So, having entered the nucleus, the neutron disturbs the equilibrium, and the nucleus is excited. It stretches out to the sides like a dumbbell or an infinity sign: ∞ . Nuclear forces, as is known, act at a distance commensurate with the size of the particles. When the nucleus is stretched, the effect of nuclear forces becomes insignificant for the outer particles of the “dumbbell,” while electrical forces act very powerfully at such a distance, and the nucleus is simply torn into two parts. In this case, two or three more neutrons are emitted.

Fragments of the nucleus and released neutrons scatter at great speed in different directions. The fragments are slowed down quite quickly by the environment, but their kinetic energy is enormous. It is converted into internal energy of the environment, which heats up. In this case, the amount of energy released is enormous. The energy obtained from the complete fission of one gram of uranium is approximately equal to the energy obtained from burning 2.5 tons of oil.

Chain reaction of fission of several nuclei

We looked at the fission of one uranium nucleus. During fission, several (usually two or three) neutrons are released. They fly apart at great speed and can easily get into the nuclei of other atoms, causing a fission reaction in them. This is a chain reaction.

That is, the neutrons obtained as a result of nuclear fission excite and force other nuclei to fission, which in turn themselves emit neutrons, which continue to stimulate further fission. And so on until fission of all uranium nuclei in the immediate vicinity occurs.

In this case, a chain reaction can occur avalanche-like, for example, in the event of an atomic bomb explosion. The number of nuclear fissions increases exponentially in a short period of time. However, a chain reaction can also occur with attenuation.

The fact is that not all neutrons meet nuclei on their way, which they induce to fission. As we remember, inside a substance the main volume is occupied by the void between the particles. Therefore, some neutrons fly through all matter without colliding with anything along the way. And if the number of nuclear fissions decreases over time, then the reaction gradually fades.

Nuclear reactions and critical mass of uranium

What determines the type of reaction? From the mass of uranium. The greater the mass, the more particles the flying neutron will meet on its path and the greater the chance of getting into the nucleus. Therefore, a “critical mass” of uranium is distinguished - this is the minimum mass at which a chain reaction is possible.

The number of neutrons produced will be equal to the number of neutrons that fly out. And the reaction will proceed at approximately the same speed until the entire volume of the substance is produced. This is used in practice in nuclear power plants and is called a controlled nuclear reaction.

The fission of uranium nuclei was discovered in 1938 by German scientists O. Hahn and F. Strassmann. They were able to establish that when uranium nuclei are bombarded with neutrons, elements of the middle part of the periodic table are formed: barium, krypton, etc. The correct interpretation of this fact was given by the Austrian physicist L. Meitner and the English physicist O. Frisch. They explained the appearance of these elements by the decay of uranium nuclei that captured a neutron into two approximately equal parts. This phenomenon is called nuclear fission, and the resulting nuclei are called fission fragments.

see also

1. Vasiliev A. Uranium fission: from Klaproth to Hahn // Quantum. - 2001. - No. 4. - P. 20-21,30.

Droplet model of the nucleus

This fission reaction can be explained based on the droplet model of the nucleus. In this model, the core is considered as a drop of electrically charged incompressible fluid. In addition to the nuclear forces acting between all nucleons of the nucleus, protons experience additional electrostatic repulsion, as a result of which they are located at the periphery of the nucleus. In an unexcited state, the forces of electrostatic repulsion are compensated, so the nucleus has a spherical shape (Fig. 1, a).

After the \(~^(235)_(92)U\) nucleus captures a neutron, an intermediate nucleus \(~(^(236)_(92)U)^*\) is formed, which is in an excited state. In this case, the neutron energy is evenly distributed among all nucleons, and the intermediate nucleus itself is deformed and begins to vibrate. If the excitation is small, then the nucleus (Fig. 1, b), freeing itself from excess energy by emitting γ -quantum or neutron, returns to a stable state. If the excitation energy is sufficiently high, then the deformation of the core during oscillations can be so great that a constriction is formed in it (Fig. 1, c), similar to the constriction between two parts of a bifurcating drop of liquid. Nuclear forces acting in a narrow waist can no longer withstand the significant Coulomb force of repulsion of parts of the nucleus. The waist breaks, and the core breaks up into two “fragments” (Fig. 1, d), which fly off in opposite directions.

uran.swf Flash: Uranium fission Enlarge Flash Fig. 2.

Currently, about 100 different isotopes with mass numbers from about 90 to 145 are known, resulting from the fission of this nucleus. Two typical fission reactions of this nucleus are:

\(~^(235)_(92)U + \ ^1_0n \ ^(\nearrow)_(\searrow) \ \begin(matrix) ^(144)_(56)Ba + \ ^(89)_( 36)Kr + \ 3^1_0n \\ ^(140)_(54)Xe + \ ^(94)_(38)Sr + \ 2^1_0n \end(matrix)\) .

Note that nuclear fission initiated by a neutron produces new neutrons that can cause fission reactions in other nuclei. Fission products of uranium-235 nuclei can also be other isotopes of barium, xenon, strontium, rubidium, etc.

When the nuclei of heavy atoms fission (\(~^(235)_(92)U\)), very large energy is released - about 200 MeV during the fission of each nucleus. About 80% of this energy is released as kinetic energy of fragments; the remaining 20% ​​comes from the energy of radioactive radiation from fragments and the kinetic energy of prompt neutrons.

An estimate of the energy released during nuclear fission can be made using the specific binding energy of nucleons in the nucleus. Specific binding energy of nucleons in nuclei with mass number A≈ 240 of the order of 7.6 MeV/nucleon, while in nuclei with mass numbers A= 90 – 145 specific energy is approximately 8.5 MeV/nucleon. Consequently, the fission of a uranium nucleus releases energy of the order of 0.9 MeV/nucleon, or approximately 210 MeV per uranium atom. The complete fission of all nuclei contained in 1 g of uranium releases the same energy as the combustion of 3 tons of coal or 2.5 tons of oil.

see also

1. Varlamov A.A. Droplet model of the nucleus //Quantum. - 1986. - No. 5. - P. 23-24

Chain reaction

Chain reaction- a nuclear reaction in which the particles causing the reaction are formed as products of this reaction.

When a uranium-235 nucleus fissions, which is caused by a collision with a neutron, 2 or 3 neutrons are released. Under favorable conditions, these neutrons can hit other uranium nuclei and cause them to fission. At this stage, from 4 to 9 neutrons will appear, capable of causing new decays of uranium nuclei, etc. Such an avalanche-like process is called a chain reaction. A diagram of the development of a chain reaction of fission of uranium nuclei is shown in Fig. 3.

reakcia.swf Flash: chain reaction Enlarge Flash Fig. 4.

Uranium occurs in nature in the form of two isotopes \[~^(238)_(92)U\] (99.3%) and \(~^(235)_(92)U\) (0.7%). When bombarded by neutrons, the nuclei of both isotopes can split into two fragments. In this case, the fission reaction \(~^(235)_(92)U\) occurs most intensely with slow (thermal) neutrons, while the nuclei \(~^(238)_(92)U\) react fission only with fast neutrons with energies of the order of 1 MeV. Otherwise, the excitation energy of the resulting nuclei \(~^(239)_(92)U\) turns out to be insufficient for fission, and then nuclear reactions occur instead of fission:

\(~^(238)_(92)U + \ ^1_0n \to \ ^(239)_(92)U \to \ ^(239)_(93)Np + \ ^0_(-1)e\ ) .

Uranium isotope \(~^(238)_(92)U\) β -radioactive, half-life 23 minutes. The neptunium isotope \(~^(239)_(93)Np\) is also radioactive, with a half-life of about 2 days.

\(~^(239)_(93)Np \to \ ^(239)_(94)Pu + \ ^0_(-1)e\) .

The plutonium isotope \(~^(239)_(94)Np\) is relatively stable, with a half-life of 24,000 years. The most important property of plutonium is that it is fissile under the influence of neutrons in the same way as \(~^(235)_(92)U\). Therefore, with the help of \(~^(239)_(94)Np\) a chain reaction can be carried out.

The chain reaction diagram discussed above represents an ideal case. In real conditions, not all neutrons produced during fission participate in the fission of other nuclei. Some of them are captured by the non-fissile nuclei of foreign atoms, others fly out of the uranium (neutron leakage).

Therefore, a chain reaction of fission of heavy nuclei does not always occur and not for any mass of uranium.

Neutron multiplication factor

The development of a chain reaction is characterized by the so-called neutron multiplication factor TO, which is measured by the ratio of the number N i neutrons causing fission of the nuclei of a substance at one of the stages of the reaction, to the number N i-1 neutrons that caused fission at the previous stage of the reaction:

\(~K = \dfrac(N_i)(N_(i - 1))\) .

The multiplication coefficient depends on a number of factors, in particular on the nature and quantity of the fissile substance, and on the geometric shape of the volume it occupies. The same amount of a given substance has different meanings TO. TO maximum if the substance has a spherical shape, since in this case the loss of prompt neutrons through the surface will be minimal.

The mass of fissile material in which the chain reaction occurs with a multiplication factor TO= 1 is called critical mass. In small pieces of uranium, most neutrons fly out without hitting any nucleus.

The value of the critical mass is determined by the geometry of the physical system, its structure and external environment. Thus, for a ball of pure uranium \(~^(235)_(92)U\) the critical mass is 47 kg (a ball with a diameter of 17 cm). The critical mass of uranium can be reduced many times by using so-called neutron moderators. The fact is that neutrons produced during the decay of uranium nuclei have too high speeds, and the probability of capturing slow neutrons by uranium-235 nuclei is hundreds of times greater than fast ones. The best neutron moderator is heavy water D 2 O. When interacting with neutrons, ordinary water itself turns into heavy water.

Graphite, whose nuclei do not absorb neutrons, is also a good moderator. During elastic interaction with deuterium or carbon nuclei, neutrons are slowed down to thermal speeds.

The use of neutron moderators and a special beryllium shell, which reflects neutrons, makes it possible to reduce the critical mass to 250 g.

At the multiplication rate TO= 1 the number of fissioning nuclei is maintained at a constant level. This mode is provided in nuclear reactors.

If the mass of nuclear fuel is less than the critical mass, then the multiplication factor TO < 1; каждое новое поколение вызывает все меньшее и меньшее число делений, и реакция без внешнего источника нейтронов быстро затухает.

If the mass of nuclear fuel is greater than the critical mass, then the multiplication factor TO> 1 and each new generation of neutrons causes an increasing number of fissions. The chain reaction grows like an avalanche and has the character of an explosion, accompanied by a huge release of energy and an increase in the ambient temperature to several million degrees. This kind of chain reaction occurs when an atomic bomb explodes.

Nuclear bomb

In its normal state, a nuclear bomb does not explode because the nuclear charge in it is divided into several small parts by partitions that absorb the decay products of uranium - neutrons. The nuclear chain reaction that causes a nuclear explosion cannot be sustained under such conditions. However, if fragments of a nuclear charge are combined together, their total mass will become sufficient for a chain reaction of uranium fission to begin to develop. The result is a nuclear explosion. Moreover, the explosion power developed by a relatively small nuclear bomb is equivalent to the power released during the explosion of millions and billions of tons of TNT.

Rice. 5. Atomic bomb

2. What energy is called the energy output of the reaction? How to estimate the energy yield for a fission reaction?

3. What value characterizes the speed of a chain reaction? Write down the necessary condition for the development of a chain reaction.

4. What fission reaction is called self-sustaining? When does it occur?

5. Assess the critical core size and critical mass.

N is the concentration of nuclei. The number of collisions of a neutron with nuclei per unit time n.