Radioactivity. Basic law of radioactive decay

The history of the study of radioactivity began on March 1, 1896, when a famous French scientist accidentally discovered a strangeness in the radiation of uranium salts. It turned out that the photographic plates located in the same box with the sample were overexposed. This was led to by the strange, highly penetrating radiation possessed by uranium. This property was found in the heaviest elements, completing periodic table. It was given the name "radioactivity".

Enter the characteristics of radioactivity

This process is the spontaneous transformation of an atom of an isotope of an element into another isotope with the simultaneous release of elementary particles (electrons, nuclei of helium atoms). The transformation of atoms turned out to be spontaneous, not requiring the absorption of energy from the outside. The main quantity characterizing the process of energy release during the process is called activity.

The activity of a radioactive sample is the probable number of decays of a given sample per unit time. The international unit of measurement is called the becquerel (Bq). 1 becquerel is the activity of a sample in which, on average, 1 decay occurs per second.

A=λN, where λ is the decay constant, N is the number of active atoms in the sample.

There are α, β, γ decays. The corresponding equations are called displacement rules:

Time interval in radioactivity

The moment of particle disintegration cannot be determined for this particular atom. For him, this is more of an “accident” than a pattern. The energy release characterizing this process is defined as the activity of the sample.

It has been noticed that it changes over time. Although individual elements demonstrate a surprising constancy in the degree of emission, there are substances whose activity decreases several times over a fairly short period of time. Amazing variety! Is it possible to find a pattern in these processes?

It has been established that there is a time during which exactly half of the atoms of a given sample undergo decay. This time interval is called the “half-life.” What is the point of introducing this concept?

half-life?

It seems that in a time equal to the period, exactly half of all active atoms of a given sample decay. But does this mean that within two half-lives all active atoms will completely decay? Not at all. After a certain moment, half of the radioactive elements remain in the sample, after the same period of time, another half of the remaining atoms decay, and so on. In this case, the radiation remains long time, significantly exceeding the half-life. This means that active atoms are retained in the sample regardless of radiation

Half-life is a value that depends solely on the properties of a given substance. The value of the quantity has been determined for many known radioactive isotopes.

Table: “Half-life of the decay of individual isotopes”

Name	Designation	Type of decay	Half life
			0.001 seconds


		beta, gamma
		alpha, gamma
		alpha, gamma	4.5 billion years

The half-life was determined experimentally. During laboratory studies, activity is measured repeatedly. Since laboratory samples are of minimal size (the safety of the researcher is paramount), the experiment is carried out at different time intervals, repeating many times. It is based on the pattern of changes in the activity of substances.

In order to determine the half-life, the activity of a given sample is measured at certain periods of time. Taking into account the fact that this parameter is related to the number of decayed atoms, using the law of radioactive decay, the half-life is determined.

Example definition for an isotope

Let the number of active elements of the isotope under study at a given time be equal to N, the time interval during which the observation is carried out t 2 - t 1, where the start and end times of the observation are quite close. Let us assume that n is the number of atoms that decayed in a given time interval, then n = KN(t 2 - t 1).

In this expression, K = 0.693/T½ is the proportionality coefficient, called the decay constant. T½ is the half-life of the isotope.

Let's take the time interval as one. In this case, K = n/N indicates the fraction of the isotope nuclei present that decay per unit time.

Knowing the value of the decay constant, the decay half-life can also be determined: T½ = 0.693/K.

It follows that per unit time, not a certain number of active atoms decay, but a certain fraction of them.

Law of Radioactive Decay (LDC)

The half-life is the basis of the ZRR. The pattern was derived by Frederico Soddi and Ernest Rutherford based on the results of experimental studies in 1903. It is surprising that repeated measurements, carried out using instruments that were far from perfect, under the conditions of the early twentieth century, led to an accurate and reasonable result. It became the basis of the theory of radioactivity. Let us derive a mathematical notation for the law of radioactive decay.

Let N 0 be the number of active atoms at a given time. After the time interval t, N elements will remain undecayed.

By a time equal to the half-life, exactly half of the active elements will remain: N=N 0 /2.

After another half-life, the following remain in the sample: N=N 0 /4=N 0 /2 2 active atoms.

After a time equal to another half-life, the sample will retain only: N=N 0 /8=N 0 /2 3 .

By the time n half-lives have passed, N=N 0 /2 n active particles will remain in the sample. In this expression, n=t/T½: the ratio of the research time to the half-life.

ZRR has a slightly different mathematical expression, more convenient in solving problems: N=N 0 2 - t/ T½.

The pattern allows us to determine, in addition to the half-life, the number of atoms of the active isotope that have not decayed at a given time. Knowing the number of atoms of the sample at the beginning of observation, after some time it is possible to determine the lifetime of this preparation.

The formula of the law of radioactive decay helps to determine the half-life only if certain parameters are available: the number of active isotopes in the sample, which is quite difficult to find out.

Consequences of the law

The ZPP formula can be written using the concepts of activity and mass of drug atoms.

Activity is proportional to the number of radioactive atoms: A=A 0 .2 -t/T. In this formula, A 0 is the activity of the sample at the initial moment of time, A is the activity after t seconds, T is the half-life.

The mass of a substance can be used in a pattern: m=m 0 .2 -t/T

Over any equal period of time, absolutely the same proportion of radioactive atoms present in a given preparation decays.

Limits of applicability of the law

The law is statistical in every sense, defining the processes occurring in the microcosm. It is clear that the half-life of radioactive elements is a statistical value. The probabilistic nature of events in atomic nuclei suggests that an arbitrary nucleus can fall apart at any moment. It is impossible to predict an event; you can only determine its probability at a given time. As a consequence, the half-life is meaningless:

for a single atom;
for a sample of minimum mass.

Atom lifetime

The existence of an atom in its original state can last a second, or maybe millions of years. There is also no need to talk about the lifetime of this particle. By introducing a value equal to the average lifetime of atoms, we can talk about the existence of atoms of a radioactive isotope and the consequences of radioactive decay. The half-life of the nucleus of an atom depends on the properties of the given atom and does not depend on other quantities.

Is it possible to solve the problem: how to find the half-life, knowing the average lifetime?

The formula for the relationship between the average lifetime of an atom and the decay constant is no less helpful in determining the half-life.

τ= T 1/2 /ln2= T 1/2 /0.693=1/ λ.

In this notation, τ is the average lifetime, λ is the decay constant.

Use of half-life

The use of ZRR to determine the age of individual samples became widespread in research at the end of the twentieth century. The accuracy of dating fossil artifacts has improved so much that it can provide insights into life spans dating back millennia BC.

Fossil organic samples are based on changes in the activity of carbon-14 (a radioactive isotope of carbon) present in all organisms. It enters a living organism in the process of metabolism and is contained in it in certain concentration. After death, metabolism environment stops. The concentration of radioactive carbon falls due to natural decay, and activity decreases proportionally.

If there is such a value as the half-life, the formula for the law of radioactive decay helps determine the time from the moment the organism ceases to function.

Radioactive transformation chains

Radioactivity studies were carried out in laboratory conditions. The amazing ability of radioactive elements to remain active for hours, days and even years could not but surprise physicists at the beginning of the twentieth century. Research, for example, on thorium, was accompanied by an unexpected result: in a closed ampoule, its activity was significant. At the slightest breath she fell. The conclusion was simple: the transformation of thorium is accompanied by the release of radon (gas). All elements during the process of radioactivity are transformed into a completely different substance, differing in both physical and chemical properties. This substance, in turn, is also unstable. Currently, three series of similar transformations are known.

Knowledge of such transformations is extremely important in determining the time of inaccessibility of zones contaminated during atomic and nuclear research or disasters. The half-life of plutonium - depending on its isotope - ranges from 86 years (Pu 238) to 80 million years (Pu 244). The concentration of each isotope gives an idea of the period of disinfection of the territory.

The most expensive metal

It is known that in our time there are metals that are much more expensive than gold, silver and platinum. These include plutonium. Interestingly, plutonium created during the process of evolution does not occur in nature. Most elements are obtained in laboratory conditions. Operation of plutonium-239 nuclear reactors gave him the opportunity to become extremely popular these days. Obtaining sufficient quantities of this isotope for use in reactors makes it practically priceless.

Plutonium-239 is obtained under natural conditions as a consequence of a chain of transformations of uranium-239 into neptunium-239 (half-life - 56 hours). A similar chain makes it possible to accumulate plutonium in nuclear reactors. The rate of appearance of the required amount exceeds the natural one billions of times.

Energy Applications

We can talk a lot about the shortcomings of nuclear energy and about the “oddities” of humanity, which uses almost any discovery to destroy its own kind. The discovery of plutonium-239, which is capable of taking part in, made it possible to use it as a source of peaceful energy. Uranium-235, which is an analogue of plutonium, is extremely rare on Earth; isolating it from it is much more difficult than obtaining plutonium.

Age of the Earth

Radioisotope analysis of isotopes of radioactive elements gives a more accurate idea of the lifetime of a particular sample.

Using the chain of transformations "uranium - thorium" contained in earth's crust, makes it possible to determine the age of our planet. The percentage of these elements on average over the entire earth's crust is the basis of this method. According to the latest data, the age of the Earth is 4.6 billion years.

LABORATORY WORK No. 19

STUDYING THE LAW OF RADIOACTIVE DECAY

AND METHODS OF PROTECTION AGAINST RADIOACTIVE RADIATION

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

Job Objectives : 1) determination of linear absorption coefficients 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 means : Windows computer.

THEORETICAL PART

Introduction

Composition of the atomic nucleus

The nucleus of any atom consists of two types of particles - protons and neutrons. A 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 its mass is almost the same as that of the proton. Neutrons and protons, which are two constituent elements of the atomic nucleus, are collectively called nucleons. The number of protons in a nucleus (or 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 called the mass number. 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 nuclei of some chemical elements into the nuclei of other elements emitting radioactive radiation.

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

Radioactive transformations occur spontaneously. The speed of their flow is not affected by changes in temperature and pressure, the presence of electric and magnetic fields, the type of chemical compound of a 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 escape 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).

A distinction is made between natural and artificial radioactivity.

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

Four main types of radioactivity are possible and actually 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 .

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

During the process of radioactive decay, a nucleus can emit not only the particles that are part of it, but also new particles that are born during the decay process. Processes of this kind are b- and g-decays.

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

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

Z X A ® Z +1 Y A + e - + .

It must be emphasized that the electron emitted during b - decay is not related to 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 a 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 a neutrino. In this case, as in positron decay, one of the protons turns into a neutron:

e - + Z X A ® Z -1 Y A +n.

G-radiation includes electromagnetic waves, the length of which is significantly less than the interatomic distances:

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

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 a nucleus with the emission of g - radiation is in many ways reminiscent of the emission of photons by excited atoms. Like an atom, the 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, only some probabilistic judgments can be made about this event. For a large collection of radioactive nuclei, a statistical law can be obtained that expresses the dependence of undecayed nuclei on time.

Let the nuclei decay within a sufficiently short time interval. This number is proportional to the time interval, as well as the total number of radioactive nuclei:

, (1)

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

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

(2)

Potentiating expression (3), we have

This is it 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 a more active element.

In practice, instead of the decay constant, another characteristic of a radioactive isotope is more often used - half life . This is the time during which half of the radioactive nuclei decay. Naturally, this definition is valid for sufficiently large number cores. Figure 1 shows how using curves 1 and 2 you can find the half-lives of nuclei: draw a straight line parallel to the abscissa axis through the ordinate point 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.

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 established that during radioactive decay He nuclei (α-particles), electrons (β-particles) and hard electromagnetic radiation(γ-rays).

In 1934, decay with the emission of positrons (β + -decay) was discovered, and in 1940, a new type of radioactivity was discovered - spontaneous fission of nuclei: a fissioning 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. Thus, there are the following types radioactive decay: α-decay; -decay; - decay; e - capture.

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

Atomic nuclei are made up of protons and neutrons, which have a general name - nucleons. The number of protons in the nucleus determines chemical properties atom and is denoted Z (serial number element). Number of nucleons in the kernel 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, but physical properties can vary greatly. To designate isotopes, use the symbol of a chemical element with two indices: A Z X. The lower index is the serial number, the upper index is the mass number. Often the subscript is omitted because it is indicated by the element's symbol itself.

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 carbon isotope 12 C is stable, but the isotope 14 C is radioactive.

Radioactive decay is a statistical phenomenon. The ability of an isotope to decay is characterized by the decay constant λ.

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

Let us denote the number N of radioactive decay nuclei at time t, dN 1 - the number of nuclei decaying during time dt. Since the number of nuclei in matter is huge, the law is satisfied large numbers. The probability of nuclear decay in a short time dt is found by the formula dP = λdt. The frequency is equal to the probability: d N 1 / N = dP = λdt. d N 1 / N = λdt- a formula that determines the number of decayed nuclei.

The solution to the equation is: , - the formula is called the law of radioactive decay: The number of radioactive nuclei decreases with time according to an exponential law.

Here N is the number of undecayed nuclei at time t; N o - the initial number of undecayed nuclei; λ is the radioactive decay constant.

In practice, it is not the decay constant that is used λ , and the quantity called half-life T.

Half-life (T) is the time during which half of the radioactive nuclei decay.

Law of radioactive decay through period half-life (T) has the form:

The relationship between half-life and decay constant is given by the formula: T = ln(2/λ) = 0.69/λ

The half-life can be either very long or very short.

To assess the degree of activity of a radioactive isotope, a quantity called activity is used.

Activity number of nuclei of a radioactive drug decaying per unit time: A = dN decay /dt

The SI unit of activity is 1 becquerel (Bq) = 1 disintegration/s - the activity of a drug in which 1 disintegration occurs in 1 s. A larger unit of activity is 1 rutherford (Rd) = Bq. An off-system unit of activity is often used - the curie (Ci), equal to the activity of 1 g of radium: 1 Ci = 3.7 Bq.

Over time, activity decreases according to the same exponential law according to which the radionuclide itself decays:

= .
In practice, the formula is used to calculate activity:

A = = λN = 0.693 N/T.

If we express the number of atoms through mass and mass, then the formula for calculating activity will take the form: A = = 0.693 (μT)

where is Avogadro's number; μ - molar mass.

1. Radioactivity. The basic law of radioactive decay. Activity.

2. Main types of radioactive decay.

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

4. Natural and artificial radioactivity. Radioactive series.

5. Use of radionuclides in medicine.

6. Accelerators of charged particles and their use in medicine.

7. Biophysical basis of the action of ionizing radiation.

8. Basic concepts and formulas.

9. Tasks.

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

Firstly, all living things are constantly exposed to natural background radiation, which constitute cosmic radiation, radiation from radioactive elements located in the surface layers of the earth’s crust, and radiation from elements entering 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. The basic law of radioactive decay. Activity

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

Atomic nuclei consist of protons and neutrons, which have a general name - nucleons. The number of protons in the nucleus determines the chemical properties of the atom and is denoted by Z (this is serial number chemical element). The number of nucleons in a nucleus is called mass number and denote A. Nuclei with the same atomic number and different mass numbers are called isotopes. All isotopes of one chemical element have identical chemical properties. Physical properties isotopes can vary greatly. To designate isotopes, use the symbol of a chemical element with two indices: A Z X. The lower index is the serial number, the upper index is the mass number. Often the subscript is omitted because it is indicated by the element's symbol itself. 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 carbon isotope 12 C is stable, but the isotope 14 C is radioactive.

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

Decay constant- 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 law of radioactive decay.

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

In practice, instead decay constantλ another quantity is often used, called half-life.

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

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

The graph of dependence (33.4) is shown in Fig. 33.1.

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

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

Table 33.1. Half-lives for some elements

For evaluation degree of radioactivity isotope use a special quantity called activity.

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

The SI unit of activity is becquerel(Bq), 1 Bq corresponds to one decay event per second. In practice, more

childish non-systemic unit of activity - curie(Ci), equal to the activity of 1 g 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 various types radioactive decay, and γ-rays are a by-product of these processes. In addition, γ-rays accompany more complex nuclear transformations, which are not considered here.

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

The α-decay scheme is written as

where X, Y are the symbols of the mother and daughter nuclei, respectively. When writing α-decay, you can write “He” instead of “α”.

During this decay, the atomic number Z of the element decreases by 2, and the mass number A decreases 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. The general property of complex microobjects is that they have discrete set energy states. This also applies to kernels. Therefore, γ-radiation from excited nuclei has a discrete spectrum. Consequently, the energy spectrum of α-particles is discrete.

The energy of emitted α-particles for almost all α-active isotopes lies in the range of 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 beta decay is distributed randomly between the beta particle and the neutrino. 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 of 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 electron β - decay scheme is written in the form

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

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

2. Positronicβ + -decay involves 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 produce ionizing particles, but it does accompanied by X-ray radiation. This radiation occurs when the space vacated by the absorption of an internal electron is filled by an electron from the outer orbit.

Gamma radiation has an electromagnetic nature and represents photons with a wavelengthλ ≤ 10 -10 m.

Gamma radiation is not an independent species 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 ability.

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 causes in tissues. The ability of a particle to ionize depends on both its type and its energy. As a particle moves deeper into matter, it loses its energy. This process is called ionization inhibition.

For quantitative characteristics For the interaction of a charged particle with matter, several quantities are used:

Once the particle's energy drops below the ionization energy, its ionizing effect ceases.

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

Let's look at some characteristic features 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 linear ionization density on the path traveled by an α-particle in the medium

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

Electrons formed during the ionization process, as a rule, move away from the α-particle track 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 interacting particles.

Interaction Characteristics 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

Like α particles, the ionization ability of β particles increases with decreasing energy.

Gamma radiation

Absorption γ -radiation by matter obeys an exponential law similar to the law of absorption of X-ray radiation:

The main processes responsible for absorption γ -radiation are the photoelectric effect and Compton scattering. In this case, a relatively small quantity free electrons (primary ionization), which have very high energy. They cause processes of secondary ionization, which is incomparably higher than the primary one.

33.4. Natural and artificial

radioactivity. Radioactive series

Terms natural And artificial radioactivity are conditional.

Natural called the radioactivity of isotopes existing 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 under the influence of solar radiation.

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

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

Natural radioactivity

IN initial period to study radioactivity, researchers could only use natural radionuclides (radioactive isotopes) contained in earth rocks in sufficient quantities large quantities: 232 Th, 235 U, 238 U. Three radioactive series begin with these radionuclides, ending with stable isotopes Pb. Subsequently, a series was discovered starting with 237 Np, with the final stable nucleus 209 Bi. In Fig. Figure 33.4 shows the row starting with 238 U.

Rice. 33.4. Uranium-radium series

Elements of this series are the main source of internal human radiation. 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 meat reindeer. 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 the dose of natural radiation received by humans. Formed in the earth's crust, this gas seeps into the atmosphere and enters 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%). This element comes from the soil through the root system of 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 in the protective effect of the atmosphere. Sources of natural background radiation are listed in Table. 33.4.

Table 33.4. Component of natural radioactive background

33.5. Use of radionuclides in medicine

Radionuclides are 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 based on the selective accumulation of certain chemical elements by individual organs. Iodine, for example, is concentrated in the 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- use of high-energy γ-radiation (60 Co source) to destroy deep-lying tumors. To prevent superficial tissues and organs from being subjected to harmful effects, exposure to ionizing radiation is carried out in different sessions in different directions.

2. Alpha therapy- therapeutic use of α-particles. These particles have a significant linear ionization density and are absorbed by even a small layer of air. Therefore therapeutic

The use of alpha rays is possible through direct contact with the surface of the organ or when administered internally (using a needle). For surface exposure, radon therapy (222 Rn) is used: exposure to the skin (baths), digestive organs (drinking), and respiratory organs (inhalation).

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 influence of neutrons, emit α -particles. After this, the diseased organ is irradiated with a stream of neutrons. In this way α -particles are formed directly inside the organ on which they should have a destructive effect.

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

Table 33.5. Characteristics of isotopes

33.6. Charged 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 produced.

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

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-rays are obtained by directing a beam of particles to a special target, which is the source of X-rays. This radiation differs from the X-ray tube by significantly higher quantum energy.

Synchrotron X-rays occurs during the acceleration of electrons in ring accelerators - synchrotrons. Such radiation has a high degree of directionality.

The direct effect of fast particles is associated with their high penetrating ability. Such particles pass through superficial 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 destroy 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 basis 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 of a biological system, resulting in their ionization and excitation. The duration of this stage is 10 -16 -10 -13 s.

2. Physico-chemical stage consists of various kinds reactions leading to the redistribution of 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 changes 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 various functional disorders, to premature cell death as a result of the action of apoptotic mechanisms or due to necrosis. Damage received at the biological stage can be inherited.

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

Let us note the general patterns of the biological stage:

Large disturbances with low absorbed energy (a lethal dose of radiation for humans causes the body to heat up by only 0.001°C);

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

Characterized by a hidden, latent period;

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;

Detrimental effect on tissues of an adult organism in which there is division;

Similarity of radiation changes with the pathology of early aging.

33.8. Basic concepts and formulas

Continuation of the table

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 the 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 the growing tree? The half-life of radon is T = 5570 years.

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

After how many years will activity in these places 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 Chernobyl disaster zone, 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. To determine the blood volume of an animal, the following method is used. A small volume of blood is taken from the animal, red blood cells are separated from the plasma and placed in a solution with radioactive phosphorus, which is assimilated by the red blood cells. The labeled red blood cells are reintroduced into the animal's circulatory system, and after some time the activity of the blood sample is determined.

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

Under radioactive decay, or just disintegration, understand the natural radioactive transformation of nuclei, which occurs spontaneously. An atomic nucleus undergoing radioactive decay is called maternal, the emerging core - subsidiaries.

The theory of radioactive decay is based on the assumption that radioactive decay is a spontaneous process that obeys the laws of statistics. Since individual radioactive nuclei decay independently of each other, we can assume that the number of nuclei d N, decayed on average during the time interval from t to t + dt, proportional to the time period dt and number N undecayed nuclei at the time t:

where is a constant for a given radioactive substance quantity called radioactive decay constant; the minus sign indicates that total number radioactive nuclei decreases during the decay process.

By separating the variables and integrating, i.e.

(256.2)

where is the initial number of undecayed nuclei (at the time t = 0), N- number of undecayed nuclei at a time t. Formula (256.2) expresses law of radioactive decay, according to which the number of undecayed nuclei decreases exponentially with time.

The intensity of the radioactive decay process is characterized by two quantities: the half-life and the average lifetime of the radioactive nucleus. Half life- the time during which the initial number of radioactive nuclei is halved on average. Then, according to (256.2),

Half-lives for naturally radioactive elements range from ten millionths of a second to many billions of years.

Total life expectancy dN cores is equal to . Having integrated this expression over all possible t(i.e. from 0 to ) and dividing by the initial number of cores, we get average life time radioactive nucleus:

(taken into account (256.2)). Thus, the average lifetime of a radioactive nucleus is the reciprocal of the radioactive decay constant.

Activity A nuclide (common name atomic nuclei that differ in the number of protons Z and neutrons N) V radioactive source is the number of decays that occur with the nuclei of a sample in 1 s:

(256.3)

The SI unit of activity is becquerel(Bq): 1 Bq - activity of a nuclide, at which one decay event occurs in 1 s. Still in nuclear physics An off-system unit of activity of a nuclide in a radioactive source is also used - curie(Ci): 1 Ci = 3.7×10 10 Bq. Radioactive decay occurs in accordance with the so-called displacement rules, allowing us to establish which nucleus arises as a result of the decay of a given parent nucleus. Offset rules:

For -decay

(256.4)

For -decay

(256.5)

where is the mother nucleus, Y is the symbol of the daughter nucleus, is the helium nucleus (-particle), is the symbolic designation of the electron (its charge is –1 and its mass number is zero). The displacement rules are nothing more than a consequence of two laws that apply during radioactive decays - the conservation of electric charge and the conservation of mass number: the sum of the charges (mass numbers) of the resulting nuclei and particles is equal to the charge (mass number) of the original nucleus.

Nuclei resulting from radioactive decay can, in turn, be radioactive. This leads to the emergence chains, or row, radioactive transformations ending with a stable element. The set of elements that form such a chain is called radioactive family.

From the displacement rules (256.4) and (256.5) it follows that the mass number during -decay decreases by 4, but does not change during -decay. Therefore, for all nuclei of the same radioactive family, the remainder when dividing the mass number by 4 is the same. Thus, there are four different radioactive families, for each of which the mass numbers are given by one of the following formulas:

A = 4n, 4n+1, 4n+2, 4n+3,

Where n- whole positive number. Families are named by the longest-lived (with the longest half-life) “ancestor”: the families of thorium (from), neptunium (from), uranium (from) and sea anemone (from). The final nuclides, respectively, are , , , , i.e. the only family of neptunium (artificially radioactive nuclei) ends with a nuclide Bi, and all the rest (naturally radioactive nuclei) are nuclides Pb.

§ 257. Laws of decay

Currently, more than two hundred active nuclei are known, mainly heavy ( A > 200, Z> 82). Only a small group of -active nuclei occur in areas with A= 140 ¸ 160 ( rare earths). -Decomposition obeys the displacement rule (256.4). An example of -decay is the decay of an isotope of uranium with the formation Th:

The velocities of particles emitted during decay are very high and range for different nuclei from 1.4 × 10 7 to 2 × 10 7 m/s, which corresponds to energies from 4 to 8.8 MeV. According to modern concepts, -particles are formed at the moment of radioactive decay when two protons and two neutrons moving inside the nucleus meet.

Particles emitted by a specific nucleus usually have a certain energy. More subtle measurements, however, have shown that the energy spectrum of -particles emitted by a given radioactive element exhibits a “fine structure”, that is, several groups of -particles are emitted, and within each group their energies are practically constant. The discrete spectrum of -particles indicates that atomic nuclei have discrete energy levels.

-decay is characterized by a strong relationship between half-life and energy E flying particles. This relationship is determined empirically Geiger-Nattall law(1912) (D. Nattall (1890-1958) - English physicist, H. Geiger (1882-1945) - German physicist), which is usually expressed as a connection between mileage(the distance traveled by a particle in a substance before it comes to a complete stop) - particles in the air and the radioactive decay constant:

(257.1)

Where A And IN- empirical constants, . According to (257.1), the shorter the half-life of a radioactive element, the greater the range, and therefore the energy of the particles emitted by it. The range of particles in the air (at normal conditions) is several centimeters; in denser media it is much smaller, amounting to hundredths of a millimeter (-particles can be detained with an ordinary sheet of paper).

Rutherford's experiments on the scattering of -particles on uranium nuclei showed that -particles up to an energy of 8.8 MeV experience Rutherford scattering on nuclei, i.e., the forces acting on -particles from the nuclei are described by Coulomb's law. This type of scattering of -particles indicates that they have not yet entered the region of action of nuclear forces, i.e., we can conclude that the nucleus is surrounded by a potential barrier, the height of which is not less than 8.8 MeV. On the other hand, -particles emitted by uranium have an energy of 4.2 MeV. Consequently, -particles fly out from the -radioactive nucleus with an energy noticeably lower than the height of the potential barrier. Classical mechanics could not explain this result.

An explanation for -decay is given by quantum mechanics, according to which the escape of an -particle from the nucleus is possible due to the tunnel effect (see §221) - the penetration of an -particle through a potential barrier. There is always a non-zero probability that a particle with an energy less than the height of the potential barrier will pass through it, i.e., indeed, particles can fly out of a radioactive nucleus with an energy less than the height of the potential barrier. This effect is entirely due to the wave nature of -particles.

The probability of a particle passing through a potential barrier is determined by its shape and is calculated based on the Schrödinger equation. In the simplest case of a potential barrier with rectangular vertical walls (see Fig. 298, A) the transparency coefficient, which determines the probability of passing through it, is determined by the previously discussed formula (221.7):

Analyzing this expression, we see that the transparency coefficient D the longer (therefore, the shorter the half-life) the smaller in height ( U) and width ( l) the barrier is in the path of the -particle. In addition, with the same potential curve, the greater the energy of the particle, the smaller the barrier to its path. E. Thus, the Geiger-Nattall law is qualitatively confirmed (see (257.1)).

§ 258. -Disintegration. Neutrino

The phenomenon of -decay (in the future it will be shown that there is and (-decay) obeys the displacement rule (256.5)

and is associated with the release of an electron. We had to overcome a number of difficulties with the interpretation of decay.

First, it was necessary to substantiate the origin of the electrons emitted during the decay process. The proton-neutron structure of the nucleus excludes the possibility of an electron escaping from the nucleus, since there are no electrons in the nucleus. The assumption is that electrons fly out not from the nucleus, but from electron shell, is untenable, since then optical or x-ray radiation should be observed, which is not confirmed by experiments.

Secondly, it was necessary to explain the continuity of the energy spectrum of emitted electrons (the energy distribution curve of -particles typical for all isotopes is shown in Fig. 343).

How can active nuclei, which have well-defined energies before and after decay, emit electrons with energy values from zero to a certain maximum? That is, the energy spectrum of emitted electrons is continuous? The hypothesis that during β-decay electrons leave the nucleus with strictly defined energies, but as a result of some secondary interactions they lose one or another share of their energy, so that their original discrete spectrum turns into a continuous one, was refuted by direct calorimetric experiments. Since the maximum energy is determined by the difference in the masses of the mother and daughter nuclei, then decays in which the electron energy< , как бы протекают с нарушением закона сохранения энергии. Н. Бор даже пытался обосновать это нарушение, высказывая предположение, что закон сохранения энергии носит статистический характер и выполняется лишь в среднем для большого числа элементарных процессов. Отсюда видно, насколько принципиально важно было разрешить это затруднение.

Thirdly, it was necessary to deal with spin non-conservation during -decay. During -decay, the number of nucleons in the nucleus does not change (since the mass number does not change A), therefore the spin of the nucleus, which is equal to an integer for even A and half-integer for odd A. However, the release of an electron with spin /2 should change the spin of the nucleus by the amount /2.

The last two difficulties led W. Pauli to the hypothesis (1931) that during -decay, another neutral particle is emitted along with the electron - neutrino. The neutrino has zero charge, spin /2 and zero (or rather< 10 -4 ) массу покоя; обозначается . Впоследствии оказалось, что при - decay, it is not neutrinos that are emitted, but antineutrino(antiparticle in relation to neutrinos; denoted by ).

The hypothesis of the existence of neutrinos allowed E. Fermi to create the theory of -decay (1934), which has largely retained its significance to this day, although the existence of neutrinos was experimentally proven more than 20 years later (1956). Such a long “search” for neutrinos is associated with great difficulties due to the lack of electrical charge and mass in neutrinos. Neutrino is the only particle that does not participate in either strong or electromagnetic interactions; The only type of interaction in which neutrinos can take part is the weak interaction. Therefore, direct observation of neutrinos is very difficult. The ionizing ability of neutrinos is so low that one ionization event in the air occurs per 500 km of travel. The penetrating ability of neutrinos is so enormous (the range of neutrinos with an energy of 1 MeV in lead is about 1018 m!), which makes it difficult to contain these particles in devices.

For the experimental detection of neutrinos (antineutrinos), an indirect method was therefore used, based on the fact that in reactions (including those involving neutrinos) the law of conservation of momentum is satisfied. Thus, neutrinos were discovered by studying the recoil of atomic nuclei during -decay. If during the decay of a nucleus an antineutrino is ejected along with an electron, then the vector sum of three impulses - a recoil nucleus, an electron and an antineutrino - should be equal to zero. This has indeed been confirmed by experience. Direct detection of neutrinos became possible only much later, after the advent of powerful reactors that made it possible to obtain intense neutrino fluxes.

The introduction of neutrinos (antineutrinos) made it possible not only to explain the apparent non-conservation of spin, but also to understand the issue of continuity of the energy spectrum of ejected electrons. The continuous spectrum of -particles is due to the distribution of energy between electrons and antineutrinos, and the sum of the energies of both particles is equal to . In some decay events, the antineutrino receives more energy, in others - the electron; at the boundary point of the curve in Fig. 343, where the electron energy is equal to , all the decay energy is carried away by the electron, and the antineutrino energy is zero.

Finally, let us consider the question of the origin of electrons during -decay. Since the electron does not fly out of the nucleus and does not escape from the shell of the atom, it was assumed that the electron is born as a result of processes occurring inside the nucleus. Since during -decay the number of nucleons in the nucleus does not change, a Z increases by one (see (256.5)), then the only possibility of simultaneous implementation of these conditions is the transformation of one of the neutrons - the active nucleus into a proton with the simultaneous formation of an electron and the emission of an antineutrino:

(258.1)

This process is accompanied by the fulfillment of conservation laws electric charges, momentum and mass numbers. In addition, this transformation is energetically possible, since the rest mass of a neutron exceeds the mass of a hydrogen atom, i.e., a proton and an electron combined. This difference in mass corresponds to an energy equal to 0.782 MeV. Due to this energy, spontaneous transformation of a neutron into a proton can occur; energy is distributed between the electron and the antineutrino.

If the transformation of a neutron into a proton is energetically favorable and generally possible, then radioactive decay of free neutrons (i.e., neutrons outside the nucleus) should be observed. The discovery of this phenomenon would be a confirmation of the stated theory of decay. Indeed, in 1950, in high-intensity neutron fluxes arising in nuclear reactors, the radioactive decay of free neutrons was discovered, occurring according to scheme (258.1). The energy spectrum of the resulting electrons corresponded to that shown in Fig. 343, and the upper limit of the electron energy turned out to be equal to that calculated above (0.782 MeV).