Law of radioactive decay. Radioactive equilibrium

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.: accordingly, models of nuclei are called droplet, 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 drop of liquid. In both cases, the forces are short-range and are characterized by saturation. The drop model explained the mechanism of nuclear reactions and especially nuclear fission reactions, but could not explain the increased stability of some nuclei.

According to shell model , the nucleons in the nucleus are distributed over discrete energy levels (shells), filled by nucleons according to the Pauli principle, and the stability of nuclei is associated with the filling of these levels. It is believed that kernels with completely filled shells are the most stable, they are called magical - these are kernels containing 2, 8, 20, 28, 50, 82, 126 protons or neutrons. There are also twice magic cores , in which both the number of protons and the number of neutrons are magical - 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.

As experimental data accumulated, the following emerged: generalized kernel model (synthesis of droplet and shell models), optical model of the core (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, emitting particles. This property of nuclei is called radioactivity . Thus, radioactivity is the ability of some atomic nuclei to spontaneously (spontaneously) transform into other nuclei with emission various types radioactive radiation and elementary particles . The phenomenon of radioactivity was discovered in 1896 by French physicist Henri Becquerel, who discovered that uranium salts emit unknown radiation that can penetrate barriers opaque to light and cause blackening of 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 existing in nature) and artificial(observed in isotopes synthesized through nuclear reactions in laboratory conditions). There is no fundamental difference between them.

There are three types of radioactive radiation: α -, β - And γ - radiation. α - And β -rays in a magnetic field experience deflections in opposite directions, and β -the rays are deflected much more. γ -rays in a magnetic field are not deflected at all (Fig. 1).

Figure 1.

Scheme of the experiment to detect α-, β- and γ-radiation. K – lead container, P – radioactive drug, F – photographic plate, IN– magnetic field.

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

β-rays– this is a flow of electrons, they have less ionizing ability, but greater penetrating ability (≈ 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 of 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 a nucleus decaying 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 period dt:

The value λN is called activity (decay rate): A = λN = . The SI unit of activity is the becquerel (Bq). Until now, nuclear physics also uses an extra-systemic unit of activity - the curie (Ci): 1Ci = 3.7 10 10 Bq.

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

Where N 0 – starting number undecayed nuclei (at time t= 0); N – number undecayed nuclei at a point in 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 quantity 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 decreases by half.

Half-life is the main quantity characterizing 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, rather than 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 isotope of carbon arises 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 both isotopes accumulate in them in the same proportion as in the air. After the death of plants, they stop consuming carbon and the unstable isotope gradually turns into nitrogen as a result of β-decay with a half-life of 5730 years. measuring the relative concentration of radioactive carbon in the remains of ancient organisms can determine the time of their death).

Radioactive processes include: 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 a spontaneous transformation atomic nucleus, which is called the mother nucleus into another (daughter) nucleus, and is emitted α -particle – the nucleus of a helium atom.

An example of such a process would be α -decay of radium:

α -nuclear decay is in many cases accompanied by γ - radiation.

Beta decay. If α - decay is characteristic of heavy nuclei, then β - decay is characteristic of 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 is an antiparticle in relation to neutrinos.

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

2) positronic β+-decay in which they escape from the nucleus positron and neutrinos.

+

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

3)Electron capture (K – capture) – the nucleus captures an orbital electron K – shell .

+

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

(Radioactive radiation of all types 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 influence ionizing radiation complex molecules and cellular structures are destroyed, which leads to radiation injury body) .

(Serious danger The inert, colorless, radioactive gas radon may be of concern to human health. Radon is a product α -decay of radium and has a half-life T= 3.82 days. It can accumulate in indoors. Once in the lungs, radon emits α -particles and turns into polonium, which is not a chemically inert substance. Next comes the chain radioactive transformations uranium series. The average person receives 55% of ionizing radiation from radon and only 11% from medical services. The contribution of cosmic rays is approximately 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 we can write : X + a → Y + b or X(a,b)Y, Where X, Y– initial and final kernels; 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 in nuclear reactions, the conservation law of the so-called baryon charge (i.e. the number of nucleons - protons and neutrons). A number of other conservation laws specific to nuclear and particle physics also hold.

Classification of nuclear reactions:

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

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

3) by the type of nuclei involved in them;

4) by the nature of the nuclear transformations occurring - 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

Q = ()c 2 = Δ Mc 2 .

where ∑ M i is the sum of the masses of particles that entered into a nuclear reaction;

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

There are basically two possible different ways liberation of nuclear energy.

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

In 1939, 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%).

The main interest for nuclear energy is the reaction of nuclear fission. As a result of nuclear fission initiated by a neutron, new neutrons are produced that can trigger fission reactions of other nuclei. When a uranium nucleus fissions, energy of the order of 210 MeV is released per uranium atom. The complete fission of all nuclei contained in 1 g of uranium releases the same energy as the combustion of 3 tons of coal or 2.5 tons of oil.

When a uranium-235 nucleus fissions, 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 appear, capable of causing new decays of uranium nuclei, etc. This avalanche-like process is called chain reaction . Development scheme chain reaction fission of uranium nuclei is presented in Fig. 3.

Figure 2. Chain reaction development diagram

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

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

2. Thermonuclear reactions . The second way to release nuclear energy is associated with fusion reactions. When light nuclei fuse and form a new nucleus, a large amount of energy must be released. Fusion reactions of light nuclei are called thermonuclear reactions, since they can only occur 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 ultra-high temperatures and confining plasma heated to a billion degrees represents the most difficult scientific and technical task on the path to implementing controlled thermal nuclear fusion A. One of the ways to solve this problem 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), etc. To contain the plasma, thermonuclear reactors that are technically complex are created. One of them is Tokamak-10, first created in 1975 at the Institute of Atomic Energy named after. I.V. Kurchatova. IN lately new modifications are being built thermonuclear reactors. Managed thermonuclear fusion- this is the most important problem of modern natural science, the solution of which is expected to open a new promising path for the development of energy.

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

Thermonuclear reactions play 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

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 value for a given radioactive substance, called radioactive decay constant; The minus sign indicates that the total number of 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- time during which original number radioactive nuclei is reduced by half on average. Then, according to (256.2),

Half-lives for natural radioactive elements vary 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) in a 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. Until now, nuclear physics also uses an off-system unit of activity of a nuclide in a radioactive source - 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 series, 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 is a positive integer. 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 ideas, -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 (under normal conditions) is several centimeters; in denser environments 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 tunneling 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 that electrons fly out not from the nucleus, but from the electron shell, is untenable, since then an optical or x-ray radiation, 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 /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 - the recoil nucleus, the electron and the antineutrino - should be equal to zero. This has indeed been confirmed by experience. Direct detection 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 the neutron exceeds the mass of the hydrogen atom, i.e., the proton and 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).

Change in the number of radioactive nuclei over time. Rutherford and Soddy in 1911, summarizing experimental results, showed that the atoms of some elements undergo successive transformations, forming radioactive families, where each member arises from the previous one and, in turn, forms the next.

This can be conveniently illustrated by the formation of radon from radium. If you place it in a sealed ampoule, a gas analysis after a few days will show that helium and radon appear in it. Helium is stable and therefore accumulates, while radon decays on its own. Curve 1 in Fig. 29 characterizes the law of radon decay in the absence of radium. In this case, the ordinate axis shows the ratio of the number of undecayed radon nuclei to their starting number It can be seen that the content decreases according to an exponential law. Curve 2 shows how the number of radioactive radon nuclei changes in the presence of radium.

Experiments carried out with radioactive substances have shown that no external conditions(heating to high temperatures,

magnetic and electric fields, high pressures) cannot affect the nature and rate of decay.

Radioactivity is a property of the atomic nucleus and for a given type of nuclei in a certain energy state, the probability of radioactive decay per unit time is constant.

Rice. 29. Dependence of the number of active radon nuclei on time

Since the decay process is spontaneous (spontaneous), the change in the number of nuclei due to decay over a period of time is determined only by the number of radioactive nuclei at the moment and in proportion to the period of time

where is a constant characterizing the rate of decay. Integrating (37) and assuming that we get

i.e., the number of cores decreases exponentially.

This law refers to statistical average values ​​and is valid only for a sufficiently large number of particles. The value X is called the radioactive decay constant, has a dimension and characterizes the probability of the decay of one atom in one second.

To characterize radioactive elements, the concept of half-life is also introduced. It is understood as the time during which half of the available number of atoms decays. Substituting the condition into equation (38), we obtain

from where, taking logarithms, we find that

and half-life

Under the exponential law of radioactive decay, at any moment in time there is a non-zero probability of finding nuclei that have not yet decayed. The lifetime of these nuclei exceeds

On the contrary, other nuclei that had decayed by this time lived different times, the shorter average lifetime for a given radioactive isotope is defined as

Having denoted we get

Consequently, the average lifetime of a radioactive nucleus is equal to the inverse of the decay constant R. Over time, the initial number of nuclei decreases by a factor.

For processing experimental results It is convenient to present equation (38) in another form:

The quantity is called the activity of a given radioactive drug; it determines the number of decays per second. Activity is a characteristic of the entire decaying substance, and not of an individual nucleus. The practical unit of activity is the curie. 1 curie is equal to the number of decayed nuclei contained in radium in 1 sec of decays/sec). Smaller units are also used - millicuries and microcuries. In the practice of physical experiments, another unit of activity is sometimes used - Rutherford decays/sec.

Statistical nature of radioactive decay. Radioactive decay is a fundamentally statistical phenomenon. We cannot say exactly when a given nucleus will decay, but we can only indicate with what probability it decays over a given period of time.

Radioactive nuclei do not “age” during their existence. The concept of age does not apply to them at all, but we can only talk about the average time of their life.

From the statistical nature of the law of radioactive decay it follows that it is strictly observed when it is large, and when it is small fluctuations should be observed. The number of decaying nuclei per unit time should fluctuate around the average value, characterized by the above law. This is confirmed by experimental measurements of the number of -particles emitted by a radioactive substance per unit time.

Rice. 30. Dependence of the logarithm of activity on time

Fluctuations obey Poisson's law. When making measurements with radioactive drugs, one must always take this into account and determine the statistical accuracy of the experimental results.

Determination of the decay constant X. When determining the decay constant X of a radioactive element, the experiment is reduced to recording the number of particles emitted from the preparation per unit of time, i.e., its activity is determined. Then a graph of changes in activity over time is plotted, usually on a semi-logarithmic scale. The type of dependences obtained when studying a pure isotope, a mixture of isotopes or a radioactive family turns out to be different.

Let's look at a few cases as examples.

1. One radioactive element is studied, the decay of which produces stable nuclei. Taking the logarithm of expression (41), we obtain

Therefore, in this case the logarithm of activity is a linear function of time. The graph of this dependence looks like a straight line, the slope of which (Fig. 30)

2. A radioactive family is studied, in which a whole chain of radioactive transformations occurs. The nuclei resulting from decay, in turn, themselves turn out to be radioactive:

An example of such a chain is the decay:

Let us find the law that describes in this case the change in the number of radioactive atoms over time. For simplicity, we will select only two elements: considering A as the initial one, and B as the intermediate one.

Then the change in the number of nuclei A and nuclei B will be determined from the system of equations

The number of nuclei A decreases due to their decay, and the number of nuclei B decreases due to the decay of nuclei B and increases due to the decay of nuclei A.

If at there are nuclei A, but there are no nuclei B, then the initial conditions will be written in the form

The solution to equations (43) has the form

and the total activity of the source consisting of nuclei A and B:

Let us now consider the dependence of the logarithm of radioactivity on time for different ratios between and

1. The first element is short-lived, the second is long-lived, i.e. . In this case, the curve showing the change in the total activity of the source has the form shown in Fig. 31, a. At the beginning, the course of the curve is determined mainly by a rapid decrease in the number of active nuclei. Nuclei B also decay, but slowly, and therefore their decay does not greatly affect the slope of the curve in the section. Subsequently, there are few nuclei of type A remaining in the mixture of isotopes, and the slope of the curve is determined by the decay constant. If you need to find and then from the slope of the curve at great importance time are found (in expression (45), the first exponential term in this case can be discarded). To determine the value, it is also necessary to take into account the effect of the decay of a long-lived element on the slope of the first part of the curve. To do this, extrapolate the straight line to the region of small times, and at several points subtract the activity determined by element B from the total activity according to the obtained values

construct a straight line for element A and find it using the angle (in this case, you need to move from logarithms to antilogarithms and back).

Rice. 31. Dependence of the logarithm of the activity of a mixture of two radioactive substances on time: a - at at

2. The first element is long-lived, and the second is short-lived: The dependence in this case has the form shown in Fig. 31, b. At the beginning, the activity of the drug increases due to the accumulation of B nuclei. Then radioactive equilibrium occurs, in which the ratio of the number of nuclei A to the number of nuclei B becomes constant. This type of equilibrium is called transitional. After some time, both substances begin to decrease at the rate of decay of the parent element.

3. The half-life of the first isotope is much longer than the second (it should be noted that the half-life of some isotopes is measured in millions of years). In this case, over time, the so-called secular equilibrium is established, in which the number of nuclei of each isotope is proportional to the half-life of this isotope. Ratio

Laws of radioactive decay of nuclei

The ability of nuclei to spontaneously decay, emitting particles, is called radioactivity. Radioactive decay is a statistical process. Each radioactive nucleus can decay at any moment and the pattern is observed only on average; in the case of decay, it is enough large quantity cores.
Decay constantλ is the probability of nuclear decay per unit time.
If there are N radioactive nuclei in the sample at time t, then the number of nuclei dN that decayed during time dt is proportional to N.

dN = -λNdt. (13.1)

By integrating (1) we obtain the law of radioactive decay

N(t) = N 0 e -λt . (13.2)

N 0 is the number of radioactive nuclei at time t = 0.
Average life time τ –

. (13.3)

Half life T 1/2 - time during which the initial number of radioactive nuclei will decrease by half

T 1/2 = ln2/λ=0.693/λ = τln2. (13.4)

Activity A - average number of nuclei decaying per unit time

A(t) = λN(t). (13.5)

Activity is measured in curies (Ci) and becquerels (Bq)

1 Ki = 3.7*10 10 decays/s, 1 Bq = 1 decay/s.

The decay of the original nucleus 1 into nucleus 2, followed by its decay into nucleus 3, is described by a system of differential equations

(13.6)

where N 1 (t) and N 2 (t) are the number of nuclei, and λ 1 and λ 2 are the decay constants of nuclei 1 and 2, respectively. The solution to system (6) with initial conditions N 1 (0) = N 10 ; N 2 (0) = 0 will be

, (13.7a)

. (13.7b)

Figure 13. 1

The number of cores reaches 2 maximum value at .

If λ 2< λ 1 (), суммарная активностьN 1 (t)λ 1 + N 2 (t)λ 2 будет монотонно уменьшаться.
If λ 2 >λ 1 ()), the total activity initially increases due to the accumulation of nuclei 2.
If λ 2 >> λ 1 , with sufficient big times the contribution of the second exponential in (7b) becomes negligibly small compared to the contribution of the first and the activities of the second A 2 = λ 2 N 2 and the first isotopes A 1 = λ 1 N 1 are almost equal. In the future, the activities of both the first and second isotopes will change over time in the same way.

A 1 (t) = N 10 λ 1 = N 1 (t)λ 1 = A 2 (t) = N 2 (t)λ 2 .(13.8)

That is, the so-called age-old balance, in which the number of isotope nuclei in the decay chain is related to the decay constants (half-lives) by a simple relationship.

. (13.9)

Therefore in natural state all isotopes genetically related in radioactive series are usually found in certain quantitative ratios depending on their half-lives.
In the general case, when there is a chain of decays 1→2→...n, the process is described by a system of differential equations

dN i /dt = -λ i N i +λ i-1 N i-1 .(13.10)

The solution to system (10) for activities with initial conditions N 1 (0) = N 10 ; N i (0) = 0 will be

(13.12)

The prime means that in the product that is in the denominator, the factor with i = m is omitted.

Isotopes

ISOTOPES– varieties of the same chemical element that are similar in their physical and chemical properties, but having different atomic masses. The name “isotopes” was proposed in 1912 by the English radiochemist Frederick Soddy, who formed it from two Greek words: isos - identical and topos - place. Isotopes occupy the same place in a cell of Mendeleev's periodic table of elements.

An atom of any chemical element consists of a positively charged nucleus and a surrounding cloud of negatively charged electrons ( cm.Also ATOM NUCLEUS). The position of a chemical element in the periodic table of Mendeleev (its atomic number) is determined by the charge of the nucleus of its atoms. Isotopes are therefore called varieties of the same chemical element, the atoms of which have the same nuclear charge (and, therefore, practically the same electron shells), but differ in nuclear mass values. According to the figurative expression of F. Soddy, the atoms of isotopes are the same “outside”, but different “inside”.

The neutron was discovered in 1932 – a particle that has no charge, with a mass close to the mass of the nucleus of a hydrogen atom - a proton , and a proton-neutron model of the nucleus was created. As a result, science established the final modern definition of the concept of isotopes: isotopes are substances whose atomic nuclei consist of the same number protons and differ only in the number of neutrons in the nucleus . Each isotope is usually denoted by a set of symbols, where X is the symbol of the chemical element, Z is the charge of the atomic nucleus (the number of protons), A is the mass number of the isotope (the total number of nucleons - protons and neutrons in the nucleus, A = Z + N). Since the charge of the nucleus appears to be uniquely associated with the symbol of the chemical element, simply the notation A X is often used for abbreviation.

Of all the isotopes known to us, only hydrogen isotopes have proper names. Thus, the isotopes 2 H and 3 H are called deuterium and tritium and are designated D and T, respectively (the isotope 1 H is sometimes called protium).

Occurs in nature as stable isotopes , and unstable - radioactive, the nuclei of atoms of which are subject to spontaneous transformation into other nuclei with the emission of various particles (or processes of so-called radioactive decay). About 270 stable isotopes are now known, and stable isotopes are found only in elements with atomic number Z Ј 83. The number of unstable isotopes exceeds 2000, the vast majority of them were obtained artificially as a result of various nuclear reactions. The number of radioactive isotopes of many elements is very large and can exceed two dozen. The number of stable isotopes is significantly smaller. Some chemical elements consist of only one stable isotope (beryllium, fluorine, sodium, aluminum, phosphorus, manganese, gold and a number of other elements). Largest number stable isotopes - 10 were found in tin, in iron, for example, there are 4 of them, in mercury - 7.

Discovery of isotopes, historical background. In 1808, the English scientist naturalist John Dalton first introduced the definition of a chemical element as a substance consisting of atoms of the same type. In 1869, chemist D.I. was discovered by Mendeleev periodic law chemical elements. One of the difficulties in substantiating the concept of an element as a substance occupying a certain place in a cell of the periodic table was the experimentally observed non-integer atomic weights of elements. In 1866, the English physicist and chemist Sir William Crookes put forward the hypothesis that each natural chemical element is a certain mixture of substances that are identical in their properties, but have different atomic masses, but at that time such an assumption did not yet have experimental confirmation and therefore did not last long noticed.

An important step towards the discovery of isotopes was the discovery of the phenomenon of radioactivity and the hypothesis of radioactive decay formulated by Ernst Rutherford and Frederick Soddy: radioactivity is nothing more than the decay of an atom into a charged particle and an atom of another element, different in its chemical properties from the original one. As a result, the idea of ​​radioactive series or radioactive families arose , at the beginning of which there is the first parent element, which is radioactive, and at the end - the last stable element. Analysis of the chains of transformations showed that during their course, the same radioactive elements, differing only in atomic masses, can appear in one cell of the periodic table. In fact, this meant the introduction of the concept of isotopes.

Independent confirmation of the existence of stable isotopes of chemical elements was then obtained in the experiments of J. J. Thomson and Aston in 1912–1920 with beams of positively charged particles (or so-called channel beams ) emanating from the discharge tube.

In 1919, Aston designed an instrument called a mass spectrograph (or mass spectrometer). . A discharge tube was still used as an ion source, but Aston found a method in which the sequential deflection of a beam of particles in electrical and magnetic fields led to the focusing of particles with the same value the ratio of charge to mass (regardless of their speed) at the same point on the screen. Along with Aston, a mass spectrometer of a slightly different design was created in the same years by the American Dempster. As a result of the subsequent use and improvement of mass spectrometers through the efforts of many researchers, by 1935 almost full table isotopic compositions of all chemical elements known at that time.

Methods for isotope separation. To study the properties of isotopes and especially for their use for scientific and applied purposes, it is necessary to obtain them in more or less noticeable quantities. In conventional mass spectrometers, almost complete separation of isotopes is achieved, but their quantity is negligible. Therefore, the efforts of scientists and engineers were aimed at searching for other possible methods isotope separation. First of all, physicochemical methods of separation were mastered, based on differences in such properties of isotopes of the same element as evaporation rates, equilibrium constants, chemical reactions etc. The most effective among them were the methods of rectification and isotope exchange, which found wide application in the industrial production of isotopes of light elements: hydrogen, lithium, boron, carbon, oxygen and nitrogen.

Another group of methods consists of the so-called molecular kinetic methods: gas diffusion, thermal diffusion, mass diffusion (diffusion in a vapor flow), centrifugation. Gas diffusion methods, based on different rates of diffusion of isotopic components in highly dispersed porous media, were used during the Second World War to organize industrial production separation of uranium isotopes in the USA as part of the so-called Manhattan Project to create atomic bomb. To obtain the required quantities of uranium, enriched up to 90% with the light isotope 235 U - the main “combustible” component of the atomic bomb, plants were built, occupying an area of ​​​​about four thousand hectares. More than 2 billion dollars were allocated for the creation of an atomic center with plants for the production of enriched uranium. After the war, plants for the production of enriched uranium for military purposes, also based on the diffusion method of separation, were developed and built in the USSR. IN recent years this method gave way to the more efficient and less expensive method of centrifugation. In this method, the effect of isotope mixture separation is achieved due to the different effects of centrifugal forces on the components of the isotope mixture filling the centrifuge rotor, which is a thin-walled cylinder limited at the top and bottom, rotating at a very high speed in a vacuum chamber. Hundreds of thousands of centrifuges connected in cascades, the rotor of each of which makes more than a thousand revolutions per second, are currently used in modern separation plants both in Russia and in other developed countries of the world. Centrifuges are used not only to obtain enriched uranium, which is necessary to ensure the operation of nuclear reactors nuclear power plants, but also for the production of isotopes of approximately thirty chemical elements in the middle part of the periodic table. Electromagnetic separation units with powerful ion sources are also used to separate various isotopes; in recent years, laser separation methods have also become widespread.

Application of isotopes. Various isotopes of chemical elements are widely used in scientific research, in various fields of industry and agriculture, in nuclear energy, modern biology and medicine, in environmental research and other fields. In scientific research (for example, in chemical analysis), as a rule, small quantities rare isotopes of various elements, calculated in grams and even milligrams per year. At the same time, for a number of isotopes widely used in nuclear energy, medicine and other industries, the need for their production can amount to many kilograms and even tons. Thus, due to the use of heavy water D 2 O in nuclear reactors, its global production by the early 1990s of the last century was about 5000 tons per year. The hydrogen isotope deuterium, which is part of heavy water, the concentration of which in the natural mixture of hydrogen is only 0.015%, along with tritium, will become in the future, according to scientists, the main component of the fuel of thermonuclear power reactors operating on the basis of nuclear fusion reactions. In this case, the need for the production of hydrogen isotopes will be enormous.

In scientific research, stable and radioactive isotopes are widely used as isotopic indicators (tags) in the study of a wide variety of processes occurring in nature.

IN agriculture isotopes (“labeled” atoms) are used, for example, to study the processes of photosynthesis, the digestibility of fertilizers, and to determine the efficiency of plants’ use of nitrogen, phosphorus, potassium, trace elements, and other substances.

Isotope technologies are widely used in medicine. So in the USA, according to statistics, more than 36 thousand medical procedures are performed per day and about 100 million. laboratory tests using isotopes. The most common procedures associated with computed tomography. The carbon isotope C13, enriched to 99% (natural content about 1%), is actively used in the so-called “diagnostic breathing control”. The essence of the test is very simple. The enriched isotope is introduced into the patient's food and, after participating in the metabolic process in various organs of the body, is released as exhaled by the patient carbon dioxide CO 2 which is collected and analyzed using a spectrometer. The differences in the rates of processes associated with the release of different amounts of carbon dioxide, labeled with the C 13 isotope, make it possible to judge the condition of the patient’s various organs. In the US, the number of patients who will undergo this test is estimated at 5 million per year. Now laser separation methods are used to produce highly enriched C13 isotope on an industrial scale.

Related information.

Lecture 2. The basic law of radioactive decay and the activity of radionuclides

The rate of decay of radionuclides is different - some decay faster, others slower. An indicator of the rate of radioactive decay is radioactive decay constant, λ [sec-1], which characterizes the probability of the decay of one atom in one second. For each radionuclide, the decay constant has its own value; the larger it is, the faster the nuclei of the substance decay.

The number of decays recorded in a radioactive sample per unit time is called activity (a ), or the radioactivity of the sample. The activity value is directly proportional to the number of atoms N radioactive substance:

a =λ· N , (3.2.1)

Where λ – radioactive decay constant, [sec-1].

Currently, according to the current International System of Units SI, the unit of measurement of radioactivity is becquerel [Bk]. This unit received its name in honor of the French scientist Henri Becquerel, who discovered the phenomenon of natural radioactivity of uranium in 1856. One becquerel equals one decay per second 1 Bk = 1 .

However, the non-system unit of activity is still often used – curie [Ki], introduced by the Curies as a measure of the decay rate of one gram of radium (in which ~3.7 1010 decays occur per second), therefore

1 Ki= 3.7·1010 Bk.

This unit is convenient for assessing activity large quantities radionuclides.

The decrease in radionuclide concentration over time as a result of decay obeys an exponential relationship:

, (3.2.2)

Where N t– the number of atoms of a radioactive element remaining after time t after the start of observation; N 0 – number of atoms at the initial moment of time ( t =0 ); λ – radioactive decay constant.

The described dependence is called basic law of radioactive decay .

The time it takes for half of the total number radionuclides is called half-life T½ . After one half-life, out of 100 radionuclide atoms, only 50 remain (Fig. 2.1). Over the next similar period, of these 50 atoms, only 25 remain, and so on.

The relationship between half-life and decay constant is derived from the equation of the fundamental law of radioactive decay:

at t=T½ And

we get https://pandia.ru/text/80/150/images/image006_47.gif" width="67" height="41 src="> Þ ;

https://pandia.ru/text/80/150/images/image009_37.gif" width="76" height="21">;

i.e..gif" width="81" height="41 src=">.

Therefore, the law of radioactive decay can be written as follows:

https://pandia.ru/text/80/150/images/image013_21.gif" width="89" height="39 src=">, (3.2.4)

Where at – drug activity over time t ; a0 – activity of the drug at the initial moment of observation.

It is often necessary to determine the activity of a given amount of any radioactive substance.

Remember that the unit of quantity of a substance is the mole. A mole is the amount of a substance containing the same number of atoms as are contained in 0.012 kg = 12 g of the carbon isotope 12C.

One mole of any substance contains Avogadro's number N.A. atoms:

N.A. = 6.02·1023 atoms.

For simple substances(elements) the mass of one mole corresponds numerically to atomic mass A element

1mol = A G.

For example: For magnesium: 1 mol 24Mg = 24 g.

For 226Ra: 1 mol 226Ra = 226 g, etc.

Taking into account what has been said in m grams of the substance will be N atoms:

https://pandia.ru/text/80/150/images/image015_20.gif" width="156" height="43 src="> (3.2.6)

Example: Let's calculate the activity of 1 gram of 226Ra, which λ = 1.38·10-11 sec-1.

a= 1.38·10-11·1/226·6.02·1023 = 3.66·1010 Bq.

If a radioactive element is included in the composition chemical compound, then when determining the activity of a drug, it is necessary to take into account its formula. Taking into account the composition of the substance, the mass fraction is determined χ radionuclide in a substance, which is determined by the ratio:

https://pandia.ru/text/80/150/images/image017_17.gif" width="118" height="41 src=">

Example of problem solution

Condition:

Activity A0 radioactive element 32P per day of observation is 1000 Bk. Determine the activity and number of atoms of this element after a week. Half life T½ 32P = 14.3 days.

Solution:

a) Let’s find the activity of phosphorus-32 after 7 days:

https://pandia.ru/text/80/150/images/image019_16.gif" width="57" height="41 src=">

Answer: after a week, the activity of the drug 32P will be 712 Bk, and the number of atoms of the radioactive isotope 32P is 127.14·106 atoms.

Security questions

1) What is the activity of a radionuclide?

2) Name the units of radioactivity and the relationship between them.

3) What is the radioactive decay constant?

4) Define the basic law of radioactive decay.

5) What is half-life?

6) What is the relationship between activity and mass of a radionuclide? Write the formula.

Tasks

1. Calculate activity 1 G 226Ra. T½ = 1602 years.

2. Calculate activity 1 G 60Co. T½ = 5.3 years.

3. One M-47 tank shell contains 4.3 kg 238U. Т½ = 2.5·109 years. Determine the activity of the projectile.

4. Calculate the activity of 137Cs after 10 years, if at the initial moment of observation it is equal to 1000 Bk. T½ = 30 years.

5. Calculate the activity of 90Sr a year ago if it is currently equal to 500 Bk. T½ = 29 years.

6. What kind of activity will 1 create? kg radioisotope 131I, T½ = 8.1 days?

7. Using reference data, determine activity 1 G 238U. Т½ = 2.5·109 years.

Using reference data, determine activity 1 G 232Th, Т½ = 1.4·1010 years.

8. Calculate the activity of the compound: 239Pu316O8.

9. Calculate the mass of a radionuclide with an activity of 1 Ki:

9.1. 131I, T1/2=8.1 days;

9.2. 90Sr, T1/2=29 years;

9.3. 137Cs, Т1/2=30 years;

9.4. 239Pu, Т1/2=2.4·104 years.

10. Determine mass 1 mCi radioactive carbon isotope 14C, T½ = 5560 years.

11. It is necessary to prepare a radioactive preparation of phosphorus 32P. After what period of time will 3% of the drug remain? Т½ = 14.29 days.

12. The natural potassium mixture contains 0.012% of the 40K radioactive isotope.

1) Determine the mass of natural potassium, which contains 1 Ki 40K. Т½ = 1.39·109 years = 4.4·1018 sec.

2) Calculate the radioactivity of the soil using 40K, if it is known that the potassium content in the soil sample is 14 kg/t.

13. How many half-lives are required for the initial activity of a radioisotope to decrease to 0.001%?

14. To determine the effect of 238U on plants, seeds were soaked in 100 ml solution UO2(NO3)2 6H2O, in which the mass of radioactive salt was 6 G. Determine the activity and specific activity of 238U in solution. Т½ = 4.5·109 years.

15. Identify activity 1 grams 232Th, Т½ = 1.4·1010 years.

16. Determine mass 1 Ki 137Cs, Т1/2=30 years.

17. The ratio between the content of stable and radioactive isotopes of potassium in nature is a constant value. The 40K content is 0.01%. Calculate the radioactivity of the soil using 40K, if it is known that the potassium content in the soil sample is 14 kg/t.

18. Lithogenic radioactivity of the environment is formed mainly due to three main natural radionuclides: 40K, 238U, 232Th. The proportion of radioactive isotopes in the natural sum of isotopes is 0.01, 99.3, ~100, respectively. Calculate radioactivity 1 T soil, if it is known that the relative content of potassium in the soil sample is 13600 g/t, uranium – 1·10-4 g/t, thorium – 6·10-4 g/t.

19. In shells bivalves discovered 23200 Bq/kg 90Sr. Determine the activity of samples after 10, 30, 50, 100 years.

20. The main pollution of closed reservoirs in the Chernobyl zone took place in the first year after the accident at the nuclear power plant. In the bottom sediments of the lake. Azbuchin in 1999 discovered 137Cs with a specific activity of 1.1·10 Bq/m2. Determine the concentration (activity) of fallen 137Cs per m2 of bottom sediments as of 1986-1987. (12 years ago).

21. 241Am (T½ = 4.32·102 years) is formed from 241Pu (T½ = 14.4 years) and is an active geochemical migrant. Taking advantage reference materials, calculate with an accuracy of 1% the decrease in the activity of plutonium-241 in time, in which year after the Chernobyl disaster the formation of 241Am in environment will be maximum.

22. Calculate the activity of 241Am in the emissions of the Chernobyl reactor as of April
2015, provided that in April 1986 the activity of 241Am was 3.82 1012 Bk,Т½ = 4.32·102 years.

23. 390 were found in soil samples nCi/kg 137Cs. Calculate the activity of samples after 10, 30, 50, 100 years.

24. Average concentration of lake bed pollution. Glubokoye, located in the Chernobyl exclusion zone, is 6.3 104 Bk 241Am and 7.4·104 238+239+240Pu per 1 m2. Calculate in what year these data were obtained.