That allows you to determine the law of radioactive decay. Law of radioactive decay

kernel models.

In nuclear theory, a model approach is used based on the analogy of the properties of atomic nuclei with the properties, for example, of a liquid drop, the electron shell of an atom, etc.: respectively, nuclear models are called drop, shell, etc. Each of the models describes only a certain set of properties of the nucleus and cannot give its complete description.

drip model(N. Bor, Ya. I. Frenkel, 1936) is based on the analogy in the behavior of nucleons in the nucleus and molecules in a liquid drop. In both cases, the forces are short-range and tend to saturate. The droplet model explained the mechanism of nuclear reactions and especially nuclear fission reactions, but failed to explain the increased stability of some nuclei.

According to shell model , the nucleons in the nucleus are distributed over discrete energy levels (shells) filled with nucleons according to the Pauli principle, and the stability of the nuclei is associated with the filling of these levels. It's believed that nuclei with completely filled shells are the most stable, they are called magical are nuclei containing 2, 8, 20, 28, 50, 82, 126 protons or neutrons. There are also doubly magic cores , in which both the number of protons and the number of neutrons are magic - this is , and they are especially stable. The shell model of the nucleus made it possible to explain the spins and magnetic moments of nuclei, the different stability of atomic nuclei, and the periodicity of their properties.

With the accumulation of experimental data, the following arose: generalized kernel model (synthesis of drop and shell models), optical model of the nucleus (explains the interaction of nuclei with incident particles), etc.

z:\Program Files\Physicon\Open Physics 2.5 part 2\design\images\Fwd_h.gifz:\Program Files\Physicon\Open Physics 2.5 part 2\design\images\Bwd_h.gifRadioactivity

Almost 90% of the known 2500 atomic nuclei are unstable. An unstable nucleus spontaneously transforms into other nuclei with the emission of particles. This property of nuclei is called radioactivity . In this way, radioactivity is the ability of some atomic nuclei to spontaneously (spontaneously) transform into other nuclei with emission various kinds radiation and elementary particles . The phenomenon of radioactivity was discovered in 1896 by the French physicist Henri Becquerel, who discovered that uranium salts emit unknown radiation that can penetrate through barriers that are opaque to light and cause blackening of the photographic emulsion. Two years later, French physicists Marie and Pierre Curie discovered the radioactivity of thorium and discovered two new radioactive elements - polonium and radium.

Distinguish natural radioactivity(observed in unstable isotopes that exist in nature) and artificial(observed in isotopes synthesized by nuclear reactions in the laboratory). There is no fundamental difference between them.

Radioactive radiation is of three types: α -, β - and γ -radiation. α - and β -rays in a magnetic field experience deviations in opposite sides, and β -beams deviate much more. γ -rays in a magnetic field do not deviate at all (Fig. 1).

Picture 1.

Scheme of the experiment for the detection of α-, β- and γ-radiation. K - lead container, P - radioactive preparation, F - photographic plate, AT- a magnetic field.

α -radiation- this is a stream of α-particles - helium nuclei has the lowest penetrating power (0.05 mm) and high ionizing power;

β rays- this is a flow of electrons, they have a lower ionizing ability, but a greater penetrating one (≈ 2 mm);

γ rays are shortwave electromagnetic radiation with extremely short wavelength λ< 10 –10 м является потоком частиц – γ-квантов. Обладают наибольшей проникающей способностью. Они способны проходить через слой свинца толщиной 5–10 см.

Law radioactive decay

The theory of radioactive decay is based on the assumption that radioactive decay is a spontaneous process that obeys the laws of statistics. The probability of nuclear decay per unit time, equal to the fraction of nuclei decaying in 1 s, is called radioactive decay constant λ. Number of cores dN disintegrated in a very short period of time dt proportional to the total number of radioactive nuclei N(undecayed nuclei) and time interval dt:

The value of λN is called activity (decay rate): А = λN = . The SI unit of activity is the becquerel (Bq). Until now, in nuclear physics, an off-system unit of activity is also used - curie (Ci): 1Ci \u003d 3.7 10 10 Bq.

The “–” sign indicates that the total number of radioactive nuclei decreases during the decay process. Separating the variables and integrating,

where N 0 - initial number undecayed nuclei (at time t= 0); N - number undecayed nuclei at the time t. It can be seen that the number of undecayed nuclei decreases exponentially with time. During the time τ = 1/λ, the number of undecayed nuclei will decrease by e≈ 2.7 times. The value τ is called average life time radioactive nucleus.

Another quantity characterizing the intensity of radioactive decay is half-life T - this is the period of time during which, on average, the number of undecayed nuclei is halved.

The half-life is the main quantity that characterizes the rate of radioactive decay. The shorter the half-life, the more intense the decay.

The law of radioactive decay can be written in another form, using the number 2 as the base, and not e:

Rice. 2 illustrates the law of radioactive decay.

Figure 2. Law of radioactive decay.

Radioactivity is used to date archaeological and geological finds by the concentration of radioactive isotopes (radiocarbon method, which is as follows: an unstable carbon isotope occurs in the atmosphere due to nuclear reactions caused by cosmic rays. A small percentage of this isotope is found in the air along with the usual stable isotope. Plants and other organisms consume carbon from the air, and they accumulate both isotopes in the same proportion as in the air.After the death of plants, they cease to consume carbon and the unstable isotope, as a result of β-decay, gradually turns into nitrogen with a half-life of 5730 years. measurements of the relative concentration of radioactive carbon in the remains of ancient organisms can determine the time of their death).

Among the radioactive processes are: 1) decay; 2) β-decay (including electron capture); 3) γ-decay; 4) spontaneous fission of heavy nuclei; 5) proton radioactivity - the nucleus emits one or two protons (Flerov, USSR, 1963).

Radioactive decay occurs according to the displacement rules:

Alpha decay. Alpha decay is the spontaneous transformation of an atomic nucleus, which is called the parent nucleus into another (daughter) nucleus, while emitting α -particle - the nucleus of a helium atom.

An example of such a process is α - decay of radium:

α - the decay of nuclei in many cases is accompanied by γ -radiation.

beta decay. If α - decay is typical for heavy nuclei, then β - decay - for almost all. At β -decay charge number Z increases by one, and the mass number A remains unchanged.

Three types of β-decay are known: 1) e electronic

+

Where - antineutrino - antiparticle in relation to the neutrino.

- electron neutrino (small neutron) - a particle with zero mass and charge. Due to the absence of a charge and mass in a neutrino, this particle interacts very weakly with the atoms of matter, so it is extremely difficult to detect it in an experiment. This particle was discovered only in 1953. Currently, it is known that there are several varieties of neutrinos. Participates (except gravitational) only in weak interaction.

2) positron β+-disintegration, in which they fly out of the nucleus positron and neutrinos.

+

Positron is a particle-twin of an electron, differing from it only in the sign of the charge. (The existence of the positron was predicted by the outstanding physicist P. Dirac in 1928. A few years later, the positron was discovered in cosmic rays).

3)Electronic capture (K - capture) - the nucleus captures the orbital electron K - shells .

+

Gamma decay. The process is intranuclear and emission occurs not by the mother, but by the daughter nucleus. Unlike α - and β -decays γ -decay is not associated with a change in the internal structure of the nucleus and is not accompanied by a change in the charge or mass numbers.

(Radioactive radiation of all kinds has a very strong biological effect on living organisms, which consists in the processes of excitation and ionization of atoms and molecules that make up living cells. Under the action of ionizing radiation, complex molecules and cellular structures, resulting in radiation damage to the body) .

(The inert, colorless, radioactive gas radon can pose a serious health hazard to humans. Radon is a product α -decay of radium and has a half-life T= 3.82 days. It may accumulate in enclosed spaces. Once in the lungs, radon emits α -particles and turns into polonium, which is not a chemically inert substance. This is followed by a chain of radioactive transformations of the uranium series. The average person receives 55% of ionizing radiation from radon and only 11% from medical services. The contribution of cosmic rays is about 8%.

Nuclear reactions

A nuclear reaction is the process of interaction of an atomic nucleus with another nucleus or elementary particle, accompanied by a change in the composition and structure of the nucleus and the release of secondary particles or γ-quanta.

Symbolically, one can write : X + a → Y + b or X (a, b) Y, where X, Y– initial and final nuclei; a and b bombarding and emitted particles.

During nuclear reactions, several conservation laws: momentum, energy, angular momentum, charge, spin. In addition to these classical conservation laws, the so-called conservation law holds true in nuclear reactions. baryon charge (i.e. the number of nucleons - protons and neutrons). A number of other conservation laws specific to nuclear physics and elementary particle physics also hold.

Classification of nuclear reactions:

1) by the nature of the particles involved in them - reactions under the action of neutrons; charged particles; γ – quanta;

2) according to the energy of the particles that cause them - reactions at low, medium and high energies;

3) according to the type of nuclei involved in them;

4) by the nature of the ongoing nuclear transformations - reactions with the emission of neutrons; charged particles; capture reactions.

Nuclear reactions are accompanied by energy transformations. energy output nuclear reaction is called the quantity

where ∑ M i is the sum of the masses of the particles involved in the nuclear reaction;

∑M k is the sum of masses of formed particles. Value Δ M called mass defect. Nuclear reactions can proceed with the release ( Q> 0) - exothermic or with energy absorption ( Q < 0) - эндотермические.

There are two fundamental various ways release of nuclear energy.

1. Fission of heavy nuclei . A fission reaction is a process in which an unstable nucleus is divided into two large fragments of comparable masses.

In 1939, the German scientists O. Hahn and F. Strassmann discovered the fission of uranium nuclei. Uranium occurs in nature in the form of two isotopes: (99.3%) and (0.7%).

Of primary interest to nuclear power is the nuclear fission reaction. As a result of nuclear fission initiated by a neutron, new neutrons arise that can cause fission reactions of other nuclei. The fission of a uranium nucleus releases energy of the order of 210 MeV per uranium atom. With the complete fission of all the nuclei contained in 1 g of uranium, the same energy is released as during the combustion of 3 tons of coal or 2.5 tons of oil.

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

Figure 2. Scheme of the development of a chain reaction

For a chain reaction to occur, it is necessary that the so-called neutron multiplication factor was more than one. In other words, there should be more neutrons in each subsequent generation than in the previous one. A device that maintains a controlled nuclear fission reaction is called nuclear (or atomic ) reactor .

The first nuclear reactor was built in 1942 in the USA under the direction of E. Fermi. In our country, the first reactor was built in 1946 under the leadership of I.V. Kurchatov.

2. thermonuclear reactions . The second way to release nuclear energy is associated with fusion reactions. During the fusion of light nuclei and the formation of a new nucleus, a large amount of energy should be released. Fusion reactions of light nuclei are called thermonuclear reactions as they can only flow at very high temperatures. Calculation of the temperature required for this T leads to a value of the order of 10 8 -10 9 K. At this temperature, the substance is in a completely ionized state, which is called plasma .

Implementation controlled thermonuclear reactions will give humanity a new environmentally friendly and practically inexhaustible source of energy. However, obtaining ultrahigh temperatures and confining plasma heated to a billion degrees is the most difficult scientific and technical task on the way to the implementation of controlled thermal nuclear fusion. One way to solve it is to contain hot plasma in a limited volume by strong magnetic fields. This method was proposed by our compatriots theoretical physicists A.D. Sakharov (1921-1989), I.E. Tamm (1895-1971) and others. technical performance thermonuclear reactors. One of them - Tokamak-10, first created in 1975 at the Institute of Atomic Energy. I.V. Kurchatov. Recently, new modifications are being built fusion reactors. Managed thermonuclear fusion- this is major problem modern natural science, with the solution of which, as expected, a new promising path for the development of energy will open.

At this stage in the development of science and technology, only uncontrolled fusion reaction in a hydrogen bomb. The high temperature required for nuclear fusion is achieved here by detonating a conventional uranium or plutonium bomb.

Thermonuclear reactions play an extremely important role in the evolution of the universe. The radiation energy of the Sun and stars is of thermonuclear origin.z:\Program Files\Physicon\Open Physics 2.5 part 2\design\images\buttonModel_h.gifz:\Program Files\Physicon\Open Physics 2.5 part 2\design\images\buttonModel_h.gifz :\Program Files\Physicon\Open Physics 2.5 part 2\design\images\buttonModel_h.gif

The term "radioactivity", which got its name from the Latin words "radio" - "I radiate" and "activus" - "active", means the spontaneous transformation of atomic nuclei, accompanied by the emission of gamma radiation, elementary particles or lighter nuclei. At the heart of all known to science types of radioactive transformations are the fundamental (strong and weak) interactions of the particles that make up the atom. A previously unknown type of penetrating radiation emitted by uranium was discovered in 1896 by the French scientist Antoine Henri Becquerel, and the concept of “radioactivity” was introduced into wide use at the beginning of the 20th century by Marie Curie, who, studying the invisible rays emitted by some minerals, managed to isolate pure radioactive element - radium.

Differences between radioactive transformations and chemical reactions

The main feature of radioactive transformations is that they occur spontaneously, while chemical reactions in any case require some kind of external influence. In addition, radioactive transformations proceed continuously and are always accompanied by the release of a certain amount of energy, which depends on the strength of the interaction of atomic particles with each other. Neither temperature, nor the presence of electric and magnetic fields, nor the use of the most efficient chemical catalyst, nor pressure, nor the aggregate state of a substance affects the rate of reactions inside atoms. Radioactive transformations do not depend on any external factor and can neither be accelerated nor slowed down.

Law of radioactive decay

The intensity of radioactive decay, as well as its dependence on the number of atoms and time, is expressed in the Law of Radioactive Decay, discovered by Ernest Rutherford and Frederick Soddy in 1903. In order to come to certain conclusions, which later found their reflection in the new law, scientists conducted the following experiment: they separated one of the radioactive products and studied its independent activity separately from the radioactivity of the substance from which it was isolated. As a result, it was found that the activity of any radioactive products, regardless of the chemical element, decreases exponentially over time. Based on this, scientists concluded that the rate of radioactive transformation is always proportional to the number of systems that have not yet undergone transformation.

The formula for the Law of Radioactive Decay is as follows:

according to which the number of decays -dN that occurred over a period of time dt (a very short interval) is proportional to the number of atoms N. In the formula of the Law of radioactive decay there is another important value - the decay constant (or the reciprocal of the half-life) λ, which characterizes the probability of nuclear decay per unit of time.

What chemical elements are radioactive?

Atomic instability chemical elements- this is rather an exception than a pattern; for the most part, they are stable and do not change over time. However, there is a certain group of chemical elements, the atoms of which are more prone to decay than others and, when decaying, radiate energy, and also emit new particles. The most common chemical elements are radium, uranium and plutonium, which have the ability to turn into other elements with simpler atoms (for example, uranium turns into lead).

It was formulated after the phenomenon of radioactivity was discovered by Becquerel in 1896. It consists in the unpredictable transition of some types of nuclei to others, while they emit various particles and elements. The process is natural when it manifests itself in isotopes existing in nature, and artificial, in cases where they are obtained in the nucleus that decays, is considered the parent, and the resulting one is the child. In other words, the basic law of radioactive decay involves an arbitrary natural process of transformation of one nucleus into another.

Becquerel's research showed the presence of previously unknown radiation in uranium salts, which affected the photographic plate, filled the air with ions and had the property of passing through thin metal plates. The experiments of M. and P. Curie with radium and polonium confirmed the conclusion described above, and a new concept appeared in science, called the doctrine

This theory, reflecting the law of radioactive decay, is based on the assumption of a spontaneous process that is subject to statistics. Since individual nuclei decay independently of each other, it is believed that, on average, the number of decayed over a certain period of time is proportional to those that have not decayed by the end of the process. If we follow the exponential law, then the number of the latter decreases significantly.

The intensity of the phenomenon is characterized by two main properties of radiation: the period of the so-called half-life and the average calculated life span of the radioactive nucleus. The first ranges between millionths of a second and billions of years. Scientists believe that such nuclei do not age, and there is no concept of age for them.

The law of radioactive decay is based on the so-called displacement rules, and these, in turn, are a consequence of the theory of conservation and mass number. It has been experimentally established that the action magnetic field acts differently: a) the deflection of rays occurs as positively charged particles; b) as negative; c) do not show any reaction. It follows from this that there are three types of radiation.

There are the same number of varieties of the decay process itself: with the ejection of an electron; positron; absorption of one electron by the nucleus. It has been proven that nuclei corresponding to lead in their structure undergo decay with emission. The theory was called alpha decay and was formulated by G. in 1928. The second variety was formulated in 1931 by E. Fermi. His research showed that instead of electrons, some types of nuclei emit opposite particles - positrons, and this is always accompanied by the emission of a particle with zero electric charge and rest mass, neurono. The simplest example of beta decay is the transition of a neuron to a proton with a time period of 12 minutes.

These theories, considering the laws of radioactive decay, were the main ones until 1940 of the 19th century, until the Soviet physicists G. N. Flerov and K. A. Petrzhak discovered another type, during which uranium nuclei spontaneously divide into two equal particles. In 1960 two-proton and two-neutron radioactivity was predicted. But to this day, this type of decay has not been experimentally confirmed and has not been discovered. Only proton radiation was discovered, in which a proton is ejected from the nucleus.

Dealing with all these questions is quite difficult, although the law of radioactive decay itself is simple. It is not easy to understand its physical meaning and, of course, the presentation of this theory goes far beyond the limits of the physics program as a school subject.

LAB #19

STUDYING THE LAW OF RADIOACTIVE DECAY

AND WAYS OF PROTECTION AGAINST RADIOACTIVE RADIATION

Objective : 1) study of the law of radioactive decay; 2) study of the law of absorption of g- and b-rays by matter.

Work tasks : 1) determination of linear absorption coefficients of radioactive radiation various materials; 2) determination of the thickness of the half attenuation layer of these materials; 3) determination of the half-life and decay constant of a chemical element.

Supporting funds : Windows computer.

THEORETICAL PART

Introduction

The composition of the atomic nucleus

The nucleus of any atom consists of particles of two types - protons and neutrons. The proton is the nucleus of the simplest atom - hydrogen. It has a positive charge, equal in magnitude to the charge of an electron, and a mass of 1.67 × 10-27 kg. The neutron, whose existence was established only in 1932 by the Englishman James Chadwick, is electrically neutral, and the mass is almost the same as that of the proton. Neutrons and protons, which are two constituent elements of the atomic nucleus, are united by the common name of nucleons. The number of protons in a nucleus (or in a nuclide) is called the atomic number and is denoted by the letter Z. The total number of nucleons, i.e. neutrons and protons, denoted by the letter A and is called the mass number. Usually, chemical elements are usually denoted by the symbol or, where X is the symbol of the chemical element.

Radioactivity

The phenomenon of radioactivity consists in the spontaneous (spontaneous) transformation of the nuclei of some chemical elements into the nuclei of other elements with the emission of radioactive radiation..

Nuclei subject to such decay are called radioactive. Nuclei that do not undergo radioactive decay are called stable. In the process of decay, the nucleus can change both the atomic number Z and the mass number A.

Radioactive transformations proceed spontaneously. The speed of their flow is not affected by changes in temperature and pressure, the presence of electric and magnetic fields, the form chemical compound given radioactive element and its state of aggregation.

Radioactive decay is characterized by the time of its occurrence, the type and energies of the emitted particles, and when several particles are emitted from the nucleus, also by the relative angles between the directions of particle emission. Historically, radioactivity is the first nuclear process discovered by man (A. Becquerel, 1896).

Distinguish between natural and artificial radioactivity.

Natural radioactivity occurs in unstable nuclei that exist in natural conditions. Artificial is called the radioactivity of nuclei formed as a result of various nuclear reactions. There is no fundamental difference between artificial and natural radioactivity. They have common patterns.

Four main types of radioactivity are possible and indeed observed in atomic nuclei: a-decay, b-decay, g-decay, and spontaneous fission.

The phenomenon of a-decay is that heavy nuclei spontaneously emit a-particles (helium nuclei 2 H 4). In this case, the mass number of the nucleus decreases by four units, and the atomic number - by two:

Z X A ® Z -2 Y A-4 + 2 H 4.

a-particle consists of four nucleons: two neutrons and two protons.

In the process of radioactive decay, the nucleus can emit not only the particles that make up its composition, but also new particles that are born in the process of decay. Processes of this kind are b- and g-decays.

The concept of b-decay combines three types of nuclear transformations: electronic (b -) decay, positron (b +) decay and electron capture.

The phenomenon of b - decay consists in the fact that the nucleus spontaneously emits an electron e - and the lightest electrically neutral particle antineutrino, while passing into a nucleus with the same mass number A, but with an atomic number Z, but one greater:

Z X A ® Z +1 Y A + e - + .

It must be emphasized that the electron emitted during b - decay has nothing to do with orbital electrons. It is born inside the nucleus itself: one of the neutrons turns into a proton and at the same time emits an electron.

Another type of b-decay is a process in which the nucleus emits a positron e + and another lightest electrically neutral particle - a neutrino n. In this case, one of the protons turns into a neutron:

Z X A ® Z -1 Y A + e + + n.

This decay is called positron or b + decay.

The range of b-decay phenomena also includes electron capture (often also called K-capture), in which the nucleus absorbs one of the electrons of the atomic shell (usually from the K-shell), emitting neutrinos. In this case, as in positron decay, one of the protons turns into a neutron:

e - + Z X A ® Z -1 Y A + n.

To g-radiation include electromagnetic waves, the length of which is much less than the interatomic distances:

where d - has the order of 10 -8 cm. In the corpuscular picture, this radiation is a stream of particles called g-quanta. The lower limit of the energy of g-quanta

E= 2p s/l

is on the order of tens of keV. There is no natural upper limit. Modern accelerators produce quanta with energies up to 20 GeV.

The decay of the nucleus with the emission of g - radiation in many respects resembles the emission of photons by excited atoms. Like an atom, a nucleus can be in an excited state. Upon transition to a lower energy state, or ground state, the nucleus emits a photon. Since g-radiation does not carry a charge, during g-decay there is no transformation of one chemical element into another.

Basic law of radioactive decay

radioactive decay is a statistical phenomenon: it is impossible to predict when a given unstable nucleus will decay, one can only make some probabilistic judgments about this event. For a large set of radioactive nuclei, one can obtain a statistical law expressing the dependence of undecayed nuclei on time.

Let the nuclei decay in a sufficiently small time interval. This number is proportional to the time interval, and also total number radioactive nuclei:

where is the decay constant, proportional to the decay probability of a radioactive nucleus and different for different radioactive substances. The "-" sign is placed because< 0, так как число не распавшихся радиоактивных ядер убывает со временем.

We separate the variables and integrate (1) taking into account that the lower limits of integration correspond to the initial conditions (at , where is the initial number of radioactive nuclei), and the upper limits correspond to the current values ​​and :

(2)

Potentiating expression (3), we have

That's what it is basic law of radioactive decay: the number of undecayed radioactive nuclei decreases with time according to an exponential law.

Figure 1 shows decay curves 1 and 2, corresponding to substances with different decay constants (λ 1 > λ 2), but with the same initial number of radioactive nuclei. Line 1 corresponds to the more active element.

In practice, instead of the decay constant, another characteristic of a radioactive isotope is often used - half life . This is the time it takes for half of the radioactive nuclei to decay. Naturally, this definition is valid for sufficiently a large number nuclei. Figure 1 shows how curves 1 and 2 can be used to find the half-lives of nuclei: a straight line is drawn parallel to the abscissa axis through a point with ordinate , until it intersects with the curves. The abscissas of the points of intersection of the straight line and lines 1 and 2 give the half-lives T 1 and T 2.

(8)

Thus, the activity of the drug is greater, the more radioactive nuclei and the shorter their half-life. The activity of the drug decreases exponentially over time.

Activity unit - becquerel(Bq), which corresponds to the activity of the nuclide in a radioactive source, in which one decay event occurs in 1 s.

The most commonly used unit of activity is curie(Ki): 1 Ki \u003d 3.7 × 10 10 s -1, in addition to it, there is one more off-system unit of activity - rutherford(Rd): 1 Rd \u003d 10 6 Bq \u003d 10 6 s -1

To characterize the activity of a unit mass of a radioactive source, a quantity is introduced called specific mass activity and equal to the ratio of the activity of the isotope to its mass. Specific mass activity is expressed in becquerels per kilogram ().

Similar information.

1. Radioactivity. Basic law of radioactive decay. Activity.

2. The main types of radioactive decay.

3. Quantitative characteristics of the interaction of ionizing radiation with matter.

4. Natural and artificial radioactivity. radioactive rows.

5. Use of radionuclides in medicine.

6. Charged particle accelerators and their use in medicine.

7. Biophysical foundations of the action of ionizing radiation.

8. Basic concepts and formulas.

9. Tasks.

The interest of physicians in natural and artificial radioactivity is due to the following.

Firstly, all living things are constantly exposed to the natural radiation background, which is cosmic radiation, the radiation of radioactive elements that occur in the surface layers of the earth's crust, and the radiation of elements that enter the body of animals along with air and food.

Secondly, radioactive radiation is used in medicine itself for diagnostic and therapeutic purposes.

33.1. Radioactivity. Basic law of radioactive decay. Activity

The phenomenon of radioactivity was discovered in 1896 by A. Becquerel, who observed the spontaneous emission of unknown radiation from uranium salts. Soon, E. Rutherford and the Curies found that during radioactive decay, He nuclei (α-particles), electrons (β-particles) and hard electromagnetic radiation (γ-rays) are emitted.

In 1934, decay with the emission of positrons (β + -decay) was discovered, and in 1940 new type radioactivity - spontaneous fission of nuclei: a fissile nucleus falls apart into two fragments of comparable mass with the simultaneous emission of neutrons and γ -quanta. Proton radioactivity of nuclei was observed in 1982.

Radioactivity - the ability of some atomic nuclei to spontaneously (spontaneously) transform into other nuclei with the emission of particles.

Atomic nuclei are composed of protons and neutrons, which have a general name - nucleons. The number of protons in the nucleus determines Chemical properties atom and is denoted by Z (this serial number chemical element). The number of nucleons in a nucleus is called mass number and denote A. Nuclei with the same serial number and different mass numbers are called isotopes. All isotopes of one chemical element have the same Chemical properties. Physical properties isotopes can vary greatly. To designate isotopes, the symbol of a chemical element is used with two indices: A Z X. The lower index is the serial number, the upper one is the mass number. Often the subscript is omitted because the element symbol itself points to it. For example, they write 14 C instead of 14 6 C.

The ability of a nucleus to decay depends on its composition. The same element can have both stable and radioactive isotopes. For example, the 12C carbon isotope is stable, while the 14C isotope is radioactive.

Radioactive decay is a statistical phenomenon. The ability of an isotope to decay characterizes decay constantλ.

decay constant is the probability that the nucleus of a given isotope will decay per unit time.

The probability of nuclear decay in a short time dt is found by the formula

Taking into account formula (33.1), we obtain an expression that determines the number of decayed nuclei:

Formula (33.3) is called the main the law of radioactive decay.

The number of radioactive nuclei decreases with time according to an exponential law.

In practice, instead of decay constantλ often use another value called half-life.

Half life(T) - the time during which it decays half radioactive nuclei.

The law of radioactive decay using the half-life is written as follows:

Dependence graph (33.4) is shown in fig. 33.1.

The half-life can be either very long or very short (from fractions of a second to many billions of years). In table. 33.1 shows the half-lives for some elements.

Rice. 33.1. The decrease in the number of nuclei of the original substance during radioactive decay

Table 33.1. Half-lives for some elements

For rate degree of radioactivity isotopes use a special quantity called activity.

Activity - the number of nuclei of a radioactive preparation decaying per unit of time:

Unit of measure of activity in SI - becquerel(Bq), 1 Bq corresponds to one decay event per second. In practice, more

resourceful off-system unit of activity - curie(Ci) equal to the activity of 1 g of 226 Ra: 1 Ci = 3.7x10 10 Bq.

Over time, activity decreases in the same way as the number of undecayed nuclei decreases:

33.2. Main types of radioactive decay

In the process of studying the phenomenon of radioactivity, 3 types of rays emitted by radioactive nuclei were discovered, which were called α-, β- and γ-rays. Later it was found that α- and β-particles are products of two different types of radioactive decay, and γ-rays are a by-product of these processes. In addition, γ-rays also accompany more complex nuclear transformations, which are not considered here.

Alpha decay consists in the spontaneous transformation of nuclei with emissionα -particles (helium nuclei).

The α-decay scheme is written as

where X, Y are the symbols of the parent and child nuclei, respectively. When writing α-decay, instead of "α" you can write "Not".

In this decay, the atomic number Z of the element decreases by 2, and the mass number A - by 4.

During α-decay, the daughter nucleus, as a rule, is formed in an excited state and, upon transition to the ground state, emits a γ-quantum. A common property of complex micro-objects is that they have discrete set energy states. This also applies to cores. Therefore, the γ-radiation of excited nuclei has a discrete spectrum. Consequently, the energy spectrum of α-particles is also discrete.

The energy of emitted α-particles for almost all α-active isotopes lies within 4-9 MeV.

beta decay consists in the spontaneous transformation of nuclei with the emission of electrons (or positrons).

It has been established that β-decay is always accompanied by the emission of a neutral particle - a neutrino (or antineutrino). This particle practically does not interact with matter, and will not be considered further. The energy released during β-decay is distributed between the β-particle and the neutrino randomly. Therefore, the energy spectrum of β-radiation is continuous (Fig. 33.2).

Rice. 33.2. Energy spectrum of β-decay

There are two types of β-decay.

1. Electronicβ - -decay consists in the transformation of one nuclear neutron into a proton and an electron. In this case, another particle ν" appears - an antineutrino:

An electron and an antineutrino fly out of the nucleus. The scheme of electronic β - decay is written as

During electronic β-decay, the serial number of the Z-element increases by 1, the mass number A does not change.

The energy of β-particles lies in the range of 0.002-2.3 MeV.

2. Positronβ + -decay consists in the transformation of one nuclear proton into a neutron and a positron. In this case, another particle ν appears - a neutrino:

Electron capture itself does not generate ionizing particles, but it does accompanied by x-rays. This radiation occurs when the space vacated by the absorption of an inner electron is filled by an electron from an outer orbit.

Gamma radiation has an electromagnetic nature and is a photon with a wavelengthλ ≤ 10 -10 m.

Gamma radiation is not independent view radioactive decay. Radiation of this type almost always accompanies not only α-decay and β-decay, but also more complex nuclear reactions. It is not deflected by electric and magnetic fields, has a relatively weak ionizing and very high penetrating power.

33.3. Quantitative characteristics of the interaction of ionizing radiation with matter

The impact of radioactive radiation on living organisms is associated with ionization, which it induces in the tissues. The ability of a particle to ionize depends both on its type and on its energy. As the particle moves deeper into the substance, it loses its energy. This process is called ionization braking.

To quantitatively characterize the interaction of a charged particle with matter, several quantities are used:

After the energy of the particle falls below the ionization energy, it ionizing action stops.

Average linear mileage(R) of a charged ionizing particle - the path traveled by it in a substance before losing its ionizing ability.

Consider some characteristics interactions of various types of radiation with matter.

alpha radiation

The alpha particle practically does not deviate from the initial direction of its movement, since its mass is many times greater

Rice. 33.3. Dependence of the linear ionization density on the path traveled by an α-particle in a medium

the mass of the electron with which it interacts. As it penetrates deep into the substance, the ionization density first increases, and when end of run (x = R) drops sharply to zero (Fig. 33.3). This is explained by the fact that with a decrease in the speed of movement, the time that it spends near the molecule (atom) of the medium increases. In this case, the probability of ionization increases. After the energy of the α-particle becomes comparable with the energy of molecular thermal motion, it captures two electrons in the substance and turns into a helium atom.

The electrons generated during the ionization process, as a rule, move away from the track of the α-particle and cause secondary ionization.

Characteristics of the interaction of α-particles with water and soft tissues are presented in Table. 33.2.

Table 33.2. Dependence of the characteristics of interaction with matter on the energy of α-particles

beta radiation

For movement β -particles in matter are characterized by a curvilinear unpredictable trajectory. This is due to the equality of the masses of the interacting particles.

Characteristics of interaction β -particles with water and soft tissues are presented in Table. 33.3.

Table 33.3. Dependence of the characteristics of interaction with matter on the energy of β-particles

As with α particles, the ionization power of β particles increases with decreasing energy.

Gamma radiation

Absorption γ -radiation by a substance obeys an exponential law similar to the law of absorption of x-rays:

The main processes responsible for absorption γ -radiation are the photoelectric effect and Compton scattering. This produces a relatively small amount of free electrons (primary ionization), which have a very high energy. It is they who cause the processes of secondary ionization, which is incomparably higher than the primary one.

33.4. natural and artificial

radioactivity. radioactive ranks

Terms natural and artificial radioactivity are conditional.

Natural call the radioactivity of isotopes that exist in nature, or the radioactivity of isotopes formed as a result of natural processes.

For example, the radioactivity of uranium is natural. The radioactivity of carbon 14 C, which is formed in upper layers atmosphere due to solar radiation.

Artificial called the radioactivity of isotopes that arise as a result of human activities.

This is the radioactivity of all isotopes produced in particle accelerators. This also includes the radioactivity of soil, water and air, which occurs during an atomic explosion.

natural radioactivity

AT initial period the study of radioactivity, researchers could only use natural radionuclides (radioactive isotopes) contained in terrestrial rocks in sufficient in large numbers: 232 Th, 235 U, 238 U. Three radioactive series begin with these radionuclides, ending with stable Pb isotopes. Subsequently, a series starting from 237 Np was discovered, with a final stable nucleus 209 Bi. On fig. 33.4 shows a row starting with 238 U.

Rice. 33.4. Uranium-radium series

Elements of this series are the main source of internal human exposure. For example, 210 Pb and 210 Po enter the body with food - they are concentrated in fish and shellfish. Both of these isotopes accumulate in lichens and are therefore present in reindeer meat. The most significant of all natural sources of radiation is 222 Rn - a heavy inert gas resulting from the decay of 226 Ra. It accounts for about half of the dose of natural radiation received by humans. Formed in earth's crust, this gas seeps into the atmosphere and enters the water (it is highly soluble).

The radioactive isotope of potassium 40 K is constantly present in the earth's crust, which is part of natural potassium (0.0119%). From the soil, this element comes through root system plants and with plant foods (cereals, fresh vegetables and fruits, mushrooms) - into the body.

Another source of natural radiation is cosmic radiation (15%). Its intensity increases in mountainous areas due to a decrease protective effect atmosphere. Sources of natural background radiation are listed in Table. 33.4.

Table 33.4. Component of the natural radioactive background

33.5. The use of radionuclides in medicine

radionuclides called radioactive isotopes of chemical elements with a short half-life. Such isotopes do not exist in nature, so they are obtained artificially. In modern medicine, radionuclides are widely used for diagnostic and therapeutic purposes.

Diagnostic Application is based on the selective accumulation of certain chemical elements by individual organs. Iodine, for example, is concentrated in thyroid gland and calcium in the bones.

The introduction of radioisotopes of these elements into the body makes it possible to detect areas of their concentration by radioactive radiation and thus obtain important diagnostic information. This diagnostic method is called by the labeled atom method.

Therapeutic use radionuclides is based on the destructive effect of ionizing radiation on tumor cells.

1. Gamma Therapy- the use of high-energy γ-radiation (source 60 Co) for the destruction of deeply located tumors. So that superficially located tissues and organs are not subjected to a destructive effect, the effect of ionizing radiation is carried out in different sessions in different directions.

2. alpha therapy- medicinal useα-particles. These particles have a significant linear ionization density and are absorbed even by a small layer of air. Therefore, therapeutic

the use of alpha rays is possible with direct contact with the surface of the organ or with the introduction inside (with a needle). For superficial exposure, radon therapy (222 Rn) is used: exposure to the skin (baths), digestive organs (drinking), respiratory organs (inhalations).

In some cases, medicinal use α -particles is associated with the use of neutron flux. With this method, elements are first introduced into the tissue (tumor), the nuclei of which, under the action of neutrons, emit α -particles. After that, the diseased organ is irradiated with a neutron flux. In this manner α -particles are formed directly inside the organ, on which they should have a destructive effect.

Table 33.5 lists the characteristics of some radionuclides used in medicine.

Table 33.5. Isotope characterization

33.6. Particle accelerators and their use in medicine

Accelerator- an installation in which, under the influence of electric and magnetic fields, directed beams of charged particles with high energy (from hundreds of keV to hundreds of GeV) are obtained.

Accelerators create narrow beams of particles with a given energy and a small cross section. This allows you to provide directed impact on irradiated objects.

The use of accelerators in medicine

Electron and proton accelerators are used in medicine for radiation therapy and diagnostics. In this case, both the accelerated particles themselves and the accompanying X-ray radiation are used.

Bremsstrahlung X-ray obtained by directing a particle beam to a special target, which is the source of x-rays. This radiation differs from the X-ray tube by a much higher photon energy.

Synchrotron X-rays occurs in the process of accelerating electrons in ring accelerators - synchrotrons. Such radiation has a high degree of directivity.

The direct action of fast particles is associated with their high penetrating power. Such particles pass through surface tissues without causing serious damage, and have an ionizing effect at the end of their journey. By selecting the appropriate particle energy, it is possible to achieve the destruction of tumors at a given depth.

The areas of application of accelerators in medicine are shown in Table. 33.6.

Table 33.6. Application of accelerators in therapy and diagnostics

33.7. Biophysical foundations of the action of ionizing radiation

As noted above, the impact of radioactive radiation on biological systems is associated with ionization of molecules. The process of interaction of radiation with cells can be divided into three successive stages (stages).

1. physical stage consists of energy transfer radiation to molecules biological system, resulting in their ionization and excitation. The duration of this stage is 10 -16 -10 -13 s.

2. Physico-chemical the stage consists of various kinds of reactions leading to a redistribution of the excess energy of excited molecules and ions. As a result, highly active

products: radicals and new ions with a wide range of chemical properties.

The duration of this stage is 10 -13 -10 -10 s.

3. Chemical stage - this is the interaction of radicals and ions with each other and with surrounding molecules. At this stage, structural damage of various types is formed, leading to a change in biological properties: the structure and functions of membranes are disrupted; lesions occur in DNA and RNA molecules.

The duration of the chemical stage is 10 -6 -10 -3 s.

4. biological stage. At this stage, damage to molecules and subcellular structures leads to a variety of functional disorders, to premature cell death as a result of the action of apoptosis mechanisms or due to necrosis. Damage sustained on biological stage may be inherited.

The duration of the biological stage is from several minutes to tens of years.

We note the general patterns of the biological stage:

Large violations with low absorbed energy (a lethal dose of radiation for a person causes heating of the body by only 0.001 ° C);

Action on subsequent generations through the hereditary apparatus of the cell;

A latent, latent period is characteristic;

Different parts of cells have different sensitivity to radiation;

First of all, dividing cells are affected, which is especially dangerous for a child's body;

The destructive effect on the tissues of an adult organism, in which there is a division;

The similarity of radiation changes with the pathology of early aging.

33.8. Basic concepts and formulas

Table continuation

33.9. Tasks

1. What is the activity of the drug if 10,000 nuclei of this substance decay within 10 minutes?

4. The age of ancient wood samples can be approximately determined by the specific mass activity of the 14 6 C isotope in them. How many years ago was a tree cut down that was used to make an object if the specific mass activity of carbon in it is 75% of the specific mass activity of a growing tree? The half-life of radon is T = 5570 years.

9. After the Chernobyl accident, in some places soil contamination with radioactive caesium-137 was at the level of 45 Ci/km 2 .

After how many years the activity in these places will decrease to a relatively safe level of 5 Ci/km 2 . The half-life of cesium-137 is T = 30 years.

10. The permissible activity of iodine-131 in the human thyroid gland should be no more than 5 nCi. In some people who were in the area of ​​the Chernobyl disaster, the activity of iodine-131 reached 800 nCi. After how many days did activity decrease to normal? The half-life of iodine-131 is 8 days.

11. The following method is used to determine the volume of blood in an animal. A small volume of blood is taken from the animal, the erythrocytes are separated from the plasma and placed in a solution with radioactive phosphorus, which is assimilated by the erythrocytes. Labeled erythrocytes are reintroduced into the circulatory system of the animal, and after some time the activity of the blood sample is determined.

ΔV = 1 ml of this solution was injected into the blood of some animal. The initial activity of this volume was A 0 = 7000 Bq. The activity of 1 ml of blood taken from the vein of the animal a day later was equal to 38 pulses per minute. Determine the volume of the animal's blood if the half-life of radioactive phosphorus is T = 14.3 days.