Nuclear reactions: simple and clear. Nuclear reaction

§ 3.13 Nuclear reactions and mass defect

1. Reactions are possible in the presence of high temperatures and high electromagnetic fields

2. The passage of processes due to neutrons, which do not require large magnetic fields and high temperatures

Nucleosynthesis. The phenomenon of nucleosynthesis was studied by a scientist Burbidge.

At the moment of the formation of the Universe there was mixture of electron particles.

Due to the interaction of protons and neutrons, hydrogen And helium, and in the following proportions: 2/3 – N, 1/3 – He.

All other elements were formed from hydrogen.

The sun consists of helium and hydrogen (10-20 million ºС).

There are hotter stars (more than 150 million ºС). In the depths of these planets formed carbon, oxygen, nitrogen, sulfur and magnesium.

Other elements were created in supernova explosions (uranium and heavier ones).

Throughout the Universe, helium and hydrogen are the most common (3/4 hydrogen and 1/4 helium).

○ The most common elements on Earth:

§7 “Wave-particle (dual) theory”

In 1900 M. Planck put forward a theory: absolutely black body also emits energy, but emits it in portions (quanta).

● Electron-magnetic field quantum is photon.

○ Wave nature of the photon:

- diffraction(deviation of light from a straight direction, or the ability to bend around obstacles)

- interference(wave interaction in which waves can overlap each other and either enhance or cancel each other)

1.Intensify

2.Intensity decreases

3.Repaid

○ Corpuscular nature of the photon:

● Photo effect– the phenomenon of emission of electrons by a substance under the influence of electromagnetic radiation.

Stoletov studied the laws of the photocell.

An explanation of the photoelectric effect has been given Einstein within the framework of corpuscular theory.

A photon hitting an electron transfers part of its energy.

● Compton effect– if X-ray radiation is directed at a substance, it is scattered by the electrons of the substance. This scattered radiation will have a longer wavelength than the incident radiation. The difference depends on the scattering angle.

E = hυ

h – bar

υ – radiation frequency

●Photon – wave packet.

Mathematically, the wave-particle duality is expressed in L. de Broglie's equation:

λ = h / (m · v) = h / P

P– impulse

This dualism is a universal theory; it can be distributed to all types of matter.

○ Examples:

Electron

m e = 9.1 10 -28 Gv ~ 10 8 cm/sλ ~ 10 -8 cm

flying ball

m= 50 gv~ 25 cm/sλ ~ 10 -32 cm

1) The Uncertainty Principle[IN. Heisenberg] – it is impossible to simultaneously accurately determine the coordinate of a particle and its momentum.

∆q · ∆ p ≥ h / 2

∆q – uncertainty of any coordinate

∆p – momentum uncertainty

∆E · ∆ t ≥ h / 2

∆E – particle energy

∆t – uncertainty of time

2) The principle of complementarity[N. Bohr] - obtaining experimental information about some quantities that describe a microobject is inevitably associated with the loss of information about other quantities, additional to the first.

3) Principle of causality(a consequence of the uncertainty principle) – a principle of classical physics. There is a cause-and-effect relationship between natural phenomena. The principle of causality does not apply to objects of the microworld.

4) Identity principle– it is impossible to experimentally study identical microparticles.

5) Principle of correspondence- any more general theory, being a development of the classical theory, does not completely reject it, but indicates the boundaries of its application.

6) Superposition principle– the resulting effect is the sum of the effects caused by each phenomenon separately.

● Schrödinger equation– the basic equation of quantum mechanics.

● Wave function[Ψ] is a function of both coordinates and time.

E = E kin. + U

U – potential energy

E kin . = (m v 2 ) / 2 = p 2 / 2m

E=p 2 / 2m + U

E Ψ = ( p 2 / 2 m + U ) · Ψ

(Ψ 2 · d · v) shows where and in what state the corresponding particle is located.

Effective cross section of nuclear reactions .

Unlike most chemical reactions, in which starting substances taken in stoichiometric quantities react with each other completely, nuclear reaction causes only a small fraction of all bombarding particles falling on the target. This is explained by the fact that the nucleus occupies a negligible part of the volume atom , so the probability of an incident particle passing through the target encountering a nucleus atom very small. The Coulomb potential barrier between the incident particle and the nucleus (if they have the same charge) also prevents nuclear reactions . For quantities. characteristics of the probability of nuclear reactions use the concept of effective section a. It characterizes the probability of the transition of two colliding particles to a certain final state and is equal to the ratio of the number of such transitions per unit time to the number of bombarding particles passing per unit time through a unit area perpendicular to the direction of their movement. The effective cross-section has the dimension of area and is comparable in order of magnitude to the cross-sectional area atomic nuclei (about 10 -28 m2). Previously, a non-system unit of effective section was used - barn (1 barn = 10 -28 m 2).
Real values for various nuclear reactions vary widely (from 10 -49 to 10 -22 m2). The value depends on the nature of the bombarding particle, its energy, and, especially to a large extent, on the properties of the irradiated nucleus. In case of nuclear irradiation neutrons with varying energy neutrons one can observe the so-called resonant capture neutrons , which is characterized by a resonant cross section. Resonant capture is observed when the kinetic energy neutron is close to the energy of one of the stationary states of the compound nucleus. The cross section corresponding to the resonant capture of a bombarding particle can exceed the non-resonant cross section by several orders of magnitude.
If a bombarding particle is capable of causing a nuclear reactions through several channels, then the sum of the effective cross sections of various processes occurring with a given irradiated nucleus is often called the total cross section.
Effective cross sections of nuclear reactions for different kernels isotopes k.-l. elements are often very different from each other. Therefore, when using the mixture isotopes for the implementation of nuclear reactions it is necessary to take into account the effective cross sections for each nuclide taking into account its prevalence in the mixture isotopes
Nuclear outputs reactions
Nuclear Reaction Yields -number ratio acts of nuclear reactions to the number of particles falling per unit area (1 cm 2) of the target usually does not exceed 10 -6 -10 -3. For thin targets (simplistically, a target can be called thin if, when passing through it, the flow of bombarding particles does not noticeably weaken), the nuclear yield reactions is proportional to the number of particles falling on 1 cm 2 of the target surface, the number of nuclei contained in 1 cm 2 of the target, as well as the value of the effective cross section of the nuclear reactions . Even when using such a powerful source of incident particles as a nuclear reactor, within 1 hour it is usually possible to obtain when carrying out nuclear reactions under the influence of neutrons no more than a few mg atoms containing new kernels. Usually the mass of a substance obtained in one or another nuclear reactions , significantly less.

Bombarding particles.
To implement nuclear reactions use neutrons n, protons p, deuterons d, tritons t, particles, heavy ions (12 C, 22 Ne, 40 Ar, etc.), electrons e and quanta. Sources neutrons (see Neutron sources) during nuclear reactions serve: mixtures of metal Be and a suitable emitter, for example. 226 Ra (so-called ampoule sources), neutron generators, nuclear reactors. Because in most cases nuclear reactions are higher for neutrons with low energies (thermal neutrons ), then before directing the flow neutrons at the target, they are usually slowed down using paraffin, graphite and other materials. In case of slow neutrons basic. process for almost all nuclei - radiation capture - nuclear reaction type because the Coulomb barrier of the nucleus prevents the escape protons and particles. Under the influence neutron fission chain reactions .
When used as bombarding particles protons , deuterons, etc., flow carrying a positive charge, the bombarding particle is accelerated to high energies (from tens of MeV to hundreds of GeV) using various accelerators. This is necessary so that a charged particle can overcome the Coulomb potential barrier and enter the irradiated nucleus. When irradiating targets with positively charged particles, max. nuclear outputs reactions are achieved using deuterons. This is due to the fact that the binding energy proton and neutron in the deuteron is relatively small, and accordingly, the distance between proton and neutron .
When deuterons are used as bombarding particles, only one nucleon often penetrates into the irradiated nucleus - proton or neutron , the second nucleon of the deuteron nucleus flies further, usually in the same direction as the incident deuteron. High effective cross sections can be achieved when conducting nuclear reactions between deuterons and light nuclei at relatively low energies of incident particles (1-10 MeV). Therefore nuclear reactions with the participation of deuterons can be carried out not only by using deuterons accelerated at an accelerator, but also by heating a mixture of interacting nuclei to a temperature of about 10 7 K. Such nuclear reactions called thermonuclear. Under natural conditions, they occur only in the interior of stars. On Earth thermonuclear reactions involving deuterium, deuterium and tritium, deuterium and lithium etc. carried out with explosions thermonuclear (hydrogen) bombs.
For particles, the Coulomb barrier for heavy nuclei reaches ~25 MeV. Equally probable nuclear reactions and Nuclear Products reactions usually radioactive, for nuclear reactions - usually stable kernels.
For the synthesis of new superheavy chemicals. elements are important nuclear reactions , occurring with the participation of heavy particles accelerated in accelerators ions (22 Ne, 40 Ar, etc.). For example, on nuclear reactions m.b. synthesis carried out fermia. For nuclear reactions with heavy ions typical big number output channels. For example, when bombarding 232 Th nuclei ions 40 Ar produces Ca, Ar, S, Si, Mg, Ne nuclei.
To implement nuclear reactions under the influence of quanta, high-energy quanta (tens of MeV) are suitable. Quanta with lower energies experience only elastic scattering from nuclei. Nuclear flowing under the influence of incident quanta reactions called photonuclear, these reactions reach 10 30 m 2.
Although electrons have a charge opposite to the charge of the nuclei, penetration electrons into the nucleus is possible only in cases where nuclei are irradiated using electrons , the energy of which exceeds tens of MeV. To obtain such electrons betatrons and other accelerators are used.
Nuclear research reactions provide a variety of information about the internal structure of nuclei. Nuclear reactions involving neutrons make it possible to obtain a huge amount of energy in nuclear reactors. As a result of nuclear fission reactions driven by neutrons a large number of different radionuclides , which can be used, in particular in chemistry like isotope tracers. In some cases nuclear reactions allow you to receivelabeled compounds. Nuclear reactions are the basis activation analysis. Using nuclear reactions synthesis of artificial chemicals has been carried out. elements ( technetium, promethium, transuranic elements, transactinoids).

History of the discovery of fission of uranium nuclei

Droplet model of the nucleus

After a nucleus captures a neutron, an intermediate nucleus 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 ? -quantum or neutron, returns to a stable state. If the excitation energy is sufficiently high, then the deformation of the core during vibrations can be so great that a waist is formed in it (Fig. 1, c), similar to the waist 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.
Currently, about 100 different isotopes with mass numbers from about 90 to 145 are known, resulting from the fission of this nucleus. Two typical reactions divisions of this nucleus have the form:
.
Note that nuclear fission initiated by a neutron produces new neutrons that can cause fission reactions in other nuclei. The fission products of uranium-235 nuclei can also be other isotopes of barium, xenon, strontium, rubidium, etc.
When the nuclei of heavy atoms () are fissioned, 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 is 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.

Nuclear chain reaction

Nuclear chain reaction - a sequence of singlenuclear reactions , each of which is caused by a particle that appeared as a reaction product at the previous step in the sequence. An example of a nuclear chain reaction is the chain reactionnuclear fission heavy elements, in which the main number of fission events is initiatedneutrons , obtained from nuclear fission in the previous generation.

Uranium occurs in nature in the form of two isotopes: (99.3%) and (0.7%). When bombarded by neutrons, the nuclei of both isotopes can split into two fragments. In this case, the fission reaction occurs most intensely with slow (thermal) neutrons, while nuclei enter into a fission reaction only with fast neutrons with an energy of the order of 1 MeV. Otherwise, the excitation energy of the formed nuclei
turns out to be insufficient for fission, and then nuclear reactions occur instead of fission:
.
Uranium isotope ? -radioactive, half-life 23 minutes. The neptunium isotope is also radioactive, with a half-life of about 2 days.
.

The plutonium isotope is relatively stable, with a half-life of 24,000 years. The most important property plutonium is that it fissions under the influence of neutrons in the same way as. Therefore, with the help a chain reaction can be carried out.
The scheme discussed above chain reaction 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

A nuclear reactor is a device in which controllednuclear chain reaction , accompanied by the release of energy. The first nuclear reactor was built in December 1942 in the USA under the leadership of E.Fermi . In Europe, the first nuclear reactor was launched in December 1946 in Moscow under the leadership of I.V.Kurchatova . By 1978, there were already about a thousand nuclear reactors operating in the world. various types. The components of any nuclear reactor are:core With nuclear fuel , usually surrounded by a neutron reflector,coolant , chain reaction control system, radiation protection, remote control system. The main characteristic of a nuclear reactor is its power. Power at 1 Meth corresponds to a chain reaction in which 3 10 16 acts of fission into 1 occur sec.

In the core of a nuclear reactor there is nuclear fuel, a chain reaction of nuclear fission occurs and energy is released. State Nuclear reactor is characterized by an effective coefficient Kef neutron multiplication or reactivity r:

R = (K? - 1)/K eff. (1)

If TO ef > 1, then the chain reaction increases over time, the nuclear reactor is in a supercritical state and its reactivity r > 0; If TO ef < 1 , then the reaction dies out, the reactor is subcritical, r< 0; при TO ? = 1, r = 0, the reactor is in a critical state, a stationary process is in progress and the number of fissions is constant over time. To initiate a chain reaction when starting a nuclear reactor, a neutron source (a mixture of Ra and Be, 252 Cf) is usually introduced into the core etc.), although this is not necessary, since spontaneous fission of nuclei uranium and cosmic rays provide a sufficient number of initial neutrons for the development of a chain reaction at TO ef > 1.

Most nuclear reactors use 235 U as a fissile substance. . If the core, other than nuclear fuel (natural or enriched Uranus), contains a neutron moderator (graphite, water and other substances containing light nuclei, seeNeutron moderation ), then the main part of divisions occurs under the influencethermal neutrons (thermal reactor ). Natural gas can be used in a thermal neutron nuclear reactor Uranus , not enriched 235 U (these were the first nuclear reactors). If there is no moderator in the core, then the bulk of fissions is caused by fast neutrons with energy x n > 10 kev(fast reactor ). Intermediate neutron reactors with energies of 1-1000 are also possible ev.

By design, nuclear reactors are divided into heterogeneous reactors , in which nuclear fuel is distributed discretely in the core in the form of blocks, between which there is a neutron moderator, andhomogeneous reactors , in which the nuclear fuel and moderator are a homogeneous mixture (solution or suspension). Blocks with nuclear fuel in a heterogeneous nuclear reactor are calledfuel elements (fuel rods) form a regular lattice; the volume per fuel rod is called a cell. Based on the nature of their use, nuclear reactors are divided into power reactors andresearch reactors . Often one nuclear reactor performs several functions .

In Criticality Conditions, a Nuclear Reactor has the form:

TO ef = K ? ? P = 1, (1)

Where 1 - P is the probability of neutron release (leakage) from the core of the Nuclear Reactor, TO ? - the neutron multiplication factor in an infinitely large core, determined for thermal nuclear reactors by the so-called “four factor formula”:

TO? =neju. (2)

Here n is the average number of secondary (fast) neutrons produced during fission of the 235 U nucleus thermal neutrons, e is the multiplication factor for fast neutrons (increase in the number of neutrons due to fission of nuclei, mainly nuclei 238 U , fast neutrons); j is the probability that a neutron will not be captured by a nucleus 238 U during the slowdown process, u is the probability that a thermal neutron will cause fission. The value h = n/(l + a) is often used, where a is the ratio of the radiation capture cross section s p to the fission cross section s d.

Condition (1) determines the size of the Nuclear Reactor. For example, for a nuclear reactor made of natural uranium and graphite n = 2.4. e » 1.03, eju » 0.44, from where TO? =1.08. This means that for TO ? > 1 necessary P<0,93, что соответствует (как показывает теория Ядерного реактора) размерам активной зоны Ядерный реактор ~ 5-10 m. The volume of a modern nuclear power reactor reaches hundreds m 3 and is determined mainly by heat removal capabilities, and not by criticality conditions. The volume of the active zone of a Nuclear Reactor in a critical state is called the critical volume of the Nuclear Reactor, and the mass of fissile material is called the critical mass. A nuclear reactor with fuel in the form of solutions of salts of pure fissile isotopes in water and with a water neutron reflector have the lowest critical mass. For 235 U this mass is 0.8 kg, For 239 Pu - 0,5 kg. 251 has the smallest critical mass Cf (theoretically 10 g). Critical parameters of a graphite nuclear reactor with natural uranium: mass of uranium 45 T, graphite volume 450 m 3 . To reduce neutron leakage, the core is given a spherical or nearly spherical shape, for example, a cylinder with a height on the order of the diameter or a cube (the smallest surface-to-volume ratio).

The value of n is known for thermal neutrons with an accuracy of 0.3% (Table 1). As the energy x n of the neutron that caused fission increases, n increases according to the law: n = n t + 0.15x n (x n in Mev), where n t corresponds to fission by thermal neutrons.

Table 1. - Values ​​n and h) for thermal neutrons (according to data for 1977)

During the operation of a nuclear reactor, a change in the composition of the fuel occurs due to the accumulation of fission fragments in it and the formationtransuranic elements , mainly isotopes Pu . The effect of fission fragments on the reactivity of a nuclear reactor is called poisoning (for radioactive fragments) and slagging (for stable ones). Poisoning is caused mainly by 135 Xe which has the largest neutron absorption cross section (2.6 10 6 barn). Its half-life T 1/2 = 9.2 hours, the fission yield is 6-7%. Main part 135 Xe is formed as a result of the decay of 135 ] (Shopping center = 6,8 h). When poisoned, Cef changes by 1-3%. Large absorption cross section 135 Xe and the presence of intermediate isotope 135 I lead to two important phenomena: 1) to an increase in concentration 135 Xe and, consequently, to a decrease in the reactivity of the Nuclear Reactor after its shutdown or reduction in power (“iodine pit”). This forces an additional reserve of reactivity in the regulatory bodies or makes short-term stops and power fluctuations impossible. Depth and duration iodine wells depend on the neutron flux Ф: at Ф = 5·10 13 neutron/cm 2? sec duration iodine pits ~ 30 h, and the depth is 2 times greater than the stationary change TO ef caused by poisoning 135 Xe . 2) Due to poisoning, spatiotemporal oscillations of the neutron flux F, and therefore the power of the Nuclear Reactor, can occur. These oscillations occur when F> 10 13 neutrons/cm 2? sec and large sizes of the Nuclear Reactor. Oscillation periods ~ 10 h.

The number of different stable fragments resulting from nuclear fission is large. There are fragments with large and small absorption cross sections compared to the absorption cross section of the fissile isotope. The concentration of the former reaches saturation during the first few days of operation of the Nuclear Reactor (mainly 149 Sm , changing Keff by 1%). The concentration of the latter and the negative reactivity they introduce increase linearly with time.

The formation of transuranium elements in a nuclear reactor occurs according to the following schemes:

Here 3 means neutron capture, the number under the arrow is the half-life.

Accumulation of 239 Pu (nuclear fuel) at the beginning of the operation of a nuclear reactor occurs linearly in time, and the faster (with a fixed burnup of 235 U ), the less enrichment uranium. Then the concentration is 239 Pu tends to a constant value, which does not depend on the degree of enrichment, but is determined by the ratio of neutron capture cross sections 238 U and 239 Pu . Characteristic time to establish equilibrium concentration 239 Pu ~ 3/ F years (F in units 10 13 neutrons/ cm 2 ?sec). Isotopes 240 Pu, 241 Pu reach equilibrium concentration only when the fuel is re-burned in a nuclear reactor after regeneration of nuclear fuel.

Nuclear fuel burnup is characterized by the total energy released in a nuclear reactor per 1 T fuel. For nuclear reactors operating on natural uranium, maximum burnup ~ 10 GW?day/t(heavy water nuclear reactors). In a nuclear reactor with weakly enriched uranium (2-3% 235 U ) burnout ~ 20-30 is achieved GW-day/t. In a fast neutron nuclear reactor - up to 100 GW-day/t. Burnout 1 GW-day/t corresponds to the combustion of 0.1% nuclear fuel.

When nuclear fuel burns out, the reactivity of a nuclear reactor decreases (in a nuclear reactor using natural uranium at small burnups there is some increase in reactivity). Replacement of burnt fuel can be carried out immediately from the entire core or gradually along the fuel rods so that the core contains fuel rods of all ages - a continuous overload mode (intermediate options are possible). In the first case, a nuclear reactor with fresh fuel has excess reactivity that must be compensated. In the second case, such compensation is needed only during initial startup, before entering continuous overload mode. Continuous reloading makes it possible to increase the burnup depth, since the reactivity of a nuclear reactor is determined by the average concentrations of fissile nuclides (fuel elements with a minimum concentration of fissile nuclides are unloaded). Table 2 shows the composition of the recovered nuclear fuel (in kg) Vpressurized water reactor power 3 Gvt. The entire core is unloaded simultaneously after the Nuclear Reactor has been operating for 3 years and "excerpts" 3 years(F = 3?10 13 neutron/cm 2?sec). Starting roster: 238 U - 77350, 235 U - 2630, 234 U - 20.

Table 2. - Composition of the unloaded fuel, kg