TYPES OF RADIOACTIVE DECAY

Radioactivity phenomenon accompanied by transformation of the nucleus one chemical element into the nucleus of another chemical element, as well as release of energy, which is “carried away” with alpha, beta and gamma radiation.

All radioactive elements are subject to radioactive transformations.
In some cases, a radioactive element exhibits alpha and beta radiation simultaneously.
More often, a chemical element exhibits either alpha radiation or beta radiation.
Alpha or beta radiation is often accompanied by gamma radiation.

Emission radioactive particles called radioactive decay.
There are alpha decay (with the emission of alpha particles), beta decay (with the emission of beta particles), the term “gamma decay” does not exist.
Alpha and beta decays are natural radioactive transformations.

Alpha - decay

Alpha particles are emitted only by heavy nuclei, i.e. containing a large number of protons and neutrons. The strength of heavy nuclei is low. In order to leave the nucleus, a nucleon must overcome nuclear forces, and for this it must have sufficient energy.
When two protons and two neutrons combine into an alpha particle, the nuclear forces in such a combination (between the nucleons of the particle) are the strongest, and the bonds with other nucleons are weaker, so the alpha particle is able to “escape” the nucleus. The emitted alpha particle carries away positive charge of 2 units and a mass of 4 units.
As a result of alpha decay, a radioactive element turns into another element, the atomic number of which is 2 units less, and the mass number is 4 units less.

The nucleus that disintegrates is called the mother nucleus, and the one formed is called the daughter nucleus.
The daughter nucleus usually also turns out to be radioactive and decays after some time.
The process of radioactive decay occurs until a stable nucleus appears, most often a lead or bismuth nucleus.

Beta decay

The phenomenon of beta decay is that the nuclei of some elements spontaneously emit electrons and the elementary particle is very low mass- antineutrino.
Since there are no electrons in nuclei, the appearance of beta rays from the nucleus of an atom can be explained by the ability of neutrons in the nucleus to decay into a proton, electron and antineutrino. The emerging proton passes into the newly formed nucleus. The electron emitted from the nucleus is a particle of beta radiation.
This process of neutron decay is typical for nuclei with a large number of neutrons.

As a result of beta decay, a new nucleus is formed with the same mass number, but with a charge greater by one.

Gamma - decay - does not exist

In progress radioactive radiation atomic nuclei can emit gamma rays. Emission of gamma rays not accompanied decay of the atomic nucleus.

Gamma radiation often accompanies alpha or beta decay phenomena.
During alpha and beta decay, the newly formed nucleus is initially in an excited state and, when it goes into normal condition, then emits gamma rays (in the optical or x-ray wavelength range).

Since radioactive radiation consists of alpha particles, beta particles and gamma quanta (i.e. nuclei of a helium atom, electrons and gamma quanta), the phenomenon of radioactivity is accompanied by a loss of mass and energy of the nucleus, atom and matter as a whole.
The proof that radioactive radiation carries energy is the experiment showing that when radioactive radiation is absorbed, a substance heats up.

Remember the topic "Atomic Physics" for 9th grade:

Radioactivity.
Radioactive transformations.
Composition of the atomic nucleus. Nuclear forces.
Energy of communication. Mass defect
Fission of uranium nuclei.
Nuclear chain reaction.
Nuclear reactor.
Thermonuclear reaction.

Other pages on the topic "Atomic Physics" for grades 10-11:

ABOUT FAMOUS SCIENTISTS

While lecturing at the University of Montreal, Professor E. Rutherford always stopped at the blackboard in the same places. Now these places can be determined using Geiger counter!
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Memorial inscription made by Paul Dirac on the wall of his office theoretical physics Moscow state university, reads: " Physical laws must have mathematical beauty".
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E. Rutherford said: “There is three stages of recognition scientific truth: the first is when they say that this is absurd, the second is “there is something in this”..." and the third is “ it's common knowledge».
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In the autumn of 1913, the Solvay Conference at the International physical institute. It was attended by about 30 prominent scientists, including Einstein, Lindemann, Rubens, Langevin, Rutherford and many others. The only woman, present at this congress was Maria Sklodowska - Curie.

The phenomenon of radioactivity is accompanied by the transformation of the nucleus of one chemical element into the nucleus of another chemical element, as well as the release of energy, which is “carried away” with alpha, beta and gamma radiation.

All radioactive elements subject to radioactive transformations.
In some cases, a radioactive element exhibits alpha and beta radiation simultaneously.
More often, a chemical element exhibits either alpha radiation or beta radiation.
Alpha or beta radiation is often accompanied by gamma radiation.

The emission of radioactive particles is called radioactive decay.
There are alpha decay (with the emission of alpha particles), beta decay (with the emission of beta particles), the term “gamma decay” does not exist.
Alpha and beta decays are natural radioactive transformations.

Alpha - decay

Alpha particles are emitted only by heavy nuclei, i.e. containing a large number of protons and neutrons. The strength of heavy nuclei is low. In order to leave the nucleus, a nucleon must overcome nuclear forces, and for this it must have sufficient energy.
When two protons and two neutrons combine into an alpha particle, the nuclear forces in such a combination (between the nucleons of the particle) are the strongest, and the bonds with other nucleons are weaker, so the alpha particle is able to “escape” the nucleus. The emitted alpha particle carries away a positive charge of 2 units and a mass of 4 units.
As a result of alpha decay, a radioactive element turns into another element, the atomic number of which is 2 units less, and the mass number is 4 units less.

The nucleus that disintegrates is called the mother nucleus, and the one formed is called the daughter nucleus.
The daughter nucleus usually also turns out to be radioactive and decays after some time.
The process of radioactive decay occurs until a stable nucleus appears, most often a lead or bismuth nucleus.

Beta decay

The phenomenon of beta decay is that the nuclei of some elements spontaneously emit electrons and an elementary particle of very low mass - an antineutrino.
Since there are no electrons in nuclei, the appearance of beta rays from the nucleus of an atom can be explained by the ability of neutrons in the nucleus to decay into a proton, electron and antineutrino. The emerging proton passes into the newly formed nucleus. The electron emitted from the nucleus is a particle of beta radiation.
This process of neutron decay is typical for nuclei with a large number of neutrons.

As a result of beta decay, a new nucleus is formed with the same mass number, but with a charge greater by one.

Gamma - decay - does not exist

During the process of radioactive radiation, atomic nuclei can emit gamma rays. The emission of gamma rays is not accompanied by the decay of the atomic nucleus.

Gamma radiation often accompanies alpha or beta decay phenomena.
During alpha and beta decay, the newly formed nucleus is initially in an excited state and, when it goes into a normal state, it emits gamma quanta (in the optical or x-ray wavelength range).

Since radioactive radiation consists of alpha particles, beta particles and gamma quanta (i.e. nuclei of a helium atom, electrons and gamma quanta), the phenomenon of radioactivity is accompanied by a loss of mass and energy of the nucleus, atom and matter as a whole.
The proof that radioactive radiation carries energy is the experiment showing that when radioactive radiation is absorbed, a substance heats up.

33. Types of beta decay.

The phenomenon of β-decay is that the nucleus (A,Z) spontaneously emits leptons of the 1st generation - an electron (positron) and an electron neutrino (electron antineutrino), passing into a nucleus with the same mass number A, but with atomic number Z , one more or less. In e-capture, the nucleus absorbs one of the electrons atomic shell(usually from the nearest K-shell), emitting neutrinos. In the literature, the term EC (Electron Capture) is often used for e-capture.
There are three types of β-decay - β - -decay, β + -decay and e-capture.

• 1 Theory
• 2 History of discovery
• 3 Law of Radioactive Decay
• 4 Types of particles emitted during radioactive decay
• 5 Alpha decay
• 6 Beta decay
  • 6.1 Beta minus decay
  • 6.2 Positron decay and electron capture
  • 6.3 Double beta decay
  • 6.4 General properties beta decay
• 7 Gamma decay (isomeric transition)
• 8 Special types radioactivity
• 9 See also
• 10 Notes
• 11 Literature

Theory

It has been established that all chemical elements with serial number, greater than 82 (that is, starting with bismuth), and some lighter elements (promethium and technetium do not have stable isotopes, and some elements, such as indium, potassium, rubidium or calcium, have only natural isotopes stable, others are radioactive).

Natural radioactivity is the spontaneous decay of atomic nuclei found in nature.

Artificial radioactivity is the spontaneous decay of atomic nuclei obtained artificially through appropriate nuclear reactions.

The nucleus undergoing radioactive decay and the nucleus resulting from this decay are called the mother and daughter nuclei, respectively. The change in the mass number and charge of the daughter nucleus relative to the parent nucleus is described by Soddy's displacement rule.

Decay accompanied by the emission of alpha particles was called alpha decay; the decay accompanied by the emission of beta particles was called beta decay (it is now known that there are types of beta decay without the emission of beta particles, but beta decay is always accompanied by the emission of neutrinos or antineutrinos). The term "gamma decay" is rarely used; The emission of gamma rays by a nucleus is usually called an isomeric transition. Gamma radiation often accompanies other types of decay, when, as a result of the first stage of decay, a daughter nucleus appears in an excited state, which then experiences a transition to the ground state with the emission of gamma rays.

The energy spectra of α-particles and γ-quanta emitted by radioactive nuclei are intermittent (“discrete”), and the spectrum of β-particles is continuous.

At present, in addition to alpha, beta and gamma decays, decays with the emission of a neutron, proton (as well as two protons), cluster radioactivity, and spontaneous fission have been discovered. Electron capture, positron decay (or β+ decay), and double beta decay (and its species) are generally considered to be different types of beta decay.

Some isotopes can undergo two or more decay modes simultaneously. For example, bismuth-212 decays with a 64% probability to thallium-208 (via alpha decay) and with a 36% probability to polonium-212 (via beta decay).

The daughter nucleus formed as a result of radioactive decay sometimes also turns out to be radioactive and after some time also decays. The process of radioactive decay will continue until a stable, that is, non-radioactive, nucleus appears. The sequence of such decays is called a decay chain, and the sequence of nuclides resulting is called a radioactive series. In particular, for radioactive series starting with uranium-238, uranium-235 and thorium-232, the final (stable) nuclides are lead-206, lead-207 and lead-208, respectively.

Nuclei with the same mass number A (isobars) can transform into each other through beta decay. Each isobar chain contains from 1 to 3 beta-stable nuclides (they cannot undergo beta decay, but are not necessarily stable with respect to other types of radioactive decay). The remaining nuclei of the isobaric chain are beta unstable; through successive beta-minus or beta-plus decays, they transform into the nearest beta-stable nuclide. Nuclei located in an isobaric chain between two beta-stable nuclides can experience both β− and β+ decay (or electron capture). For example, the naturally occurring radionuclide potassium-40 is capable of decaying into adjacent beta-stable nuclei argon-40 and calcium-40:

History of discovery

Radioactivity was discovered in 1896 by the French physicist A. Becquerel. He studied the connection between luminescence and the recently discovered x-rays.

Becquerel came up with an idea: isn’t all luminescence accompanied by X-rays? To test his guess, he took several compounds, including one of the uranium salts, which phosphorescent with yellow-green light. Lighting it up sunlight, he wrapped the salt in black paper and placed it in a dark closet on a photographic plate, also wrapped in black paper. After some time, developing the plate, Becquerel actually saw the image of a piece of salt. But luminescent radiation could not pass through black paper, and only x-rays could expose the record under these conditions. Becquerel repeated the experiment several times and with equal success.

February 24, 1896 at a meeting French Academy Sciences, he made a report “On the radiation produced by phosphorescence.” But after a few days, adjustments had to be made to the interpretation of the results obtained. On February 26 and 27, another experiment with minor changes, but due to cloudy weather it was postponed. Without waiting for good weather, on March 1, Becquerel developed a plate on which lay uranium salt, which had not been irradiated by sunlight. Naturally, it did not phosphorescent, but there was an imprint on the plate. Already on March 2, Becquerel reported on this discovery at a meeting of the Paris Academy of Sciences, entitled his work “On the invisible radiation produced by phosphorescent bodies.”

Subsequently, Becquerel tested other uranium compounds and minerals (including those that did not exhibit phosphorescence), as well as metallic uranium. The record was invariably overexposed. By placing a metal cross between the salt and the plate, Becquerel obtained faint outlines of the cross on the plate. Then it became clear that new rays had been discovered that passed through opaque objects, but were not x-rays.

Becquerel established that the intensity of radiation is determined only by the amount of uranium in the preparation and is completely independent of what compounds it is included in. Thus, this property was inherent not in the compounds, but in the chemical element uranium.

Becquerel shares his discovery with the scientists with whom he collaborated. 1898 Marie Curie and Pierre Curie discovered the radioactivity of thorium, and later they discovered the radioactive elements polonium and radium.

They found that the property natural radioactivity all uranium compounds possess and in the most to a greater extent uranium itself. Becquerel returned to the phosphors that interested him. True, he made another major discovery related to radioactivity. Once, for a public lecture, Becquerel needed radioactive substance, he took it from the Curies and put the test tube in his vest pocket. After giving a lecture, he returned the radioactive drug to the owners, and the next day he discovered redness of the skin in the shape of a test tube on his body under his vest pocket. Becquerel told Pierre Curie about this, and he experimented on himself: he wore a test tube of radium tied to his forearm for ten hours. A few days later he also developed redness, which then turned into a severe ulcer, from which he suffered for two months. This was the first time it was opened biological effect radioactivity.

But even after this, the Curies courageously did their job. Suffice it to say that Marie Curie died of radiation sickness (however, she lived to be 66 years old).

In 1955 they were examined notebooks Marie Curie. They still radiate, thanks radioactive contamination entered when filling them out. One of the sheets bears Pierre Curie's radioactive fingerprint.

Law of Radioactive Decay

Law of Radioactive Decay- a law discovered experimentally by Frederick Soddy and Ernest Rutherford and formulated in 1903. Modern formulation law:

which means that the number of decays over a time interval t in an arbitrary substance is proportional to the number N of radioactive atoms of a given type present in the sample.

In this mathematical expressionλ is the decay constant, which characterizes the probability of radioactive decay per unit time and has a dimension of s−1. The minus sign indicates a decrease in the number of radioactive nuclei over time. The law expresses the independence of the decay of radioactive nuclei from each other and from time: the probability of the decay of a given nucleus in each subsequent unit of time does not depend on the time that has passed since the beginning of the experiment and on the number of nuclei remaining in the sample.

This law is considered the fundamental law of radioactivity, and several have been extracted from it. important consequences, among which are formulations of decay characteristics - the average lifetime of an atom and the half-life.

The decay constant of a radioactive nucleus in most cases is practically independent of environmental conditions (temperature, pressure, chemical composition of the substance, etc.). For example, solid tritium T2 at a few kelvins decays at the same rate as tritium gas at room temperature or thousands of kelvins; tritium in the T2 molecule decomposes at the same rate as in tritiated valine. Weak changes in the decay constant in laboratory conditions were found only for electron capture - the temperatures and pressures available in the laboratory, as well as changes in the chemical composition, can slightly change the density of the electron cloud surrounding the nucleus, which leads to a change in the decay rate by a fraction of a percent. However, under fairly harsh conditions (high ionization of the atom, high electron density, high chemical potential of neutrinos, strong magnetic fields), difficult to achieve in the laboratory, but realized, for example, in the cores of stars, other types of decays can also change their probability.

The constancy of the radioactive decay constant makes it possible to measure the age of various natural and artificial objects by the decay of their constituent radioactive nuclei and the accumulation of decay products. A number of methods have been developed radioisotope dating, allowing one to measure the age of objects in the range from units to billions of years; Among them, the most famous are the radiocarbon method, uranium-lead method, uranium-helium method, potassium-argon method, etc.

Types of particles emitted during radioactive decay

E. Rutherford experimentally established (1899) that uranium salts emit rays three types, which deviate differently in a magnetic field:

• rays of the first type are deflected in the same way as a stream of positively charged particles; they were called α-rays;
• rays of the second type are usually deflected in a magnetic field in the same way as a stream of negatively charged particles, they were called β-rays (there are, however, positron beta rays that are deflected in the opposite direction);
• rays of the third type, which are not deflected by a magnetic field, were called γ-radiation.

Although research has discovered other types of particles emitted during radioactive decay, the names listed have been retained to this day because the corresponding types of decay are the most common.

When a decaying nucleus interacts with an electron shell, particles can be emitted ( x-ray photons, Auger electrons, conversion electrons) from the electron shell. The first two types of radiation arise when a vacancy appears in the electron shell (in particular, during electron capture and during an isomeric transition with emission of a conversion electron) and the subsequent cascade filling of this vacancy. A conversion electron is emitted during an isomeric transition with internal conversion, when the energy released during the transition between nuclear levels is not carried away by a gamma quantum, but is transferred to one of the shell electrons.

During spontaneous fission, a nucleus decays into two (less often three) relatively light nuclei - the so-called fission fragments - and several neutrons. During cluster decay (which is intermediate process between fission and alpha decay), the heavy parent nucleus emits a relatively light nucleus (14C, 16O, etc.).

During proton (two-proton) and neutron decay, the nucleus emits protons and neutrons, respectively.

In all types of beta decay (except for the predicted, but not yet discovered neutrinoless) decay, a neutrino or antineutrino is emitted from the nucleus.

Alpha decay

Alpha decay is a spontaneous decay atomic nucleus into a daughter nucleus and an α particle (the nucleus of the 4He atom).

Alpha decay typically occurs in heavy nuclei with a mass number A ≥ 140 (although there are a few exceptions). Inside heavy nuclei due to the saturation property nuclear forces isolated α-particles are formed, consisting of two protons and two neutrons. The resulting α particle is subject to more action Coulomb repulsive forces from nuclear protons than individual protons. At the same time, the alpha particle experiences less nuclear attraction to the nucleons of the nucleus than other nucleons. The resulting alpha particle at the boundary of the nucleus is reflected from the potential barrier inward, but with some probability it can overcome it (see Tunnel effect) and fly out. As the energy of the alpha particle decreases, the permeability of the potential barrier decreases very quickly (exponentially), so the lifetime of nuclei with less available alpha decay energy, under other conditions, equal conditions more.

Soddy's displacement rule for α decay:

Example (alpha decay of uranium-238 to thorium-234):

As a result of α-decay, the atom shifts by 2 cells to the beginning of the periodic table (that is, the charge of the nucleus Z decreases by 2), the mass number of the daughter nucleus decreases by 4.

Beta decay

Beta minus decay

Becquerel proved that β-rays are a stream of electrons. Beta decay is a manifestation of the weak interaction.

Beta decay (more precisely, beta minus decay, β− decay) is radioactive decay accompanied by the emission of an electron and an electron antineutrino from the nucleus.

Feynman diagram of beta minus decay: a d quark in one of the neutrons in the nucleus becomes a u quark, emitting a virtual W boson, which decays into an electron and an electron antineutrino.

Beta decay is an intranucleon process. Beta-minus decay occurs due to the transformation of one of the d-quarks in one of the neutrons of the nucleus into a u-quark; in this case, a neutron transforms into a proton with the emission of an electron and an antineutrino:

Free neutrons also undergo β− decay, turning into a proton, electron, and antineutrino (see Neutron beta decay).

Soddy displacement rule for β− decay:

Example (beta decay of tritium to helium-3):

After β− decay, the element shifts by 1 cell to the end of the periodic table (the charge of the nucleus increases by one), while the mass number of the nucleus does not change.

Positron decay and electron capture

There are also other types of beta decay. In positron decay (beta-plus decay), the nucleus emits a positron and an electron neutrino. During β+ decay, the charge of the nucleus decreases by one (the nucleus moves one cell to the beginning of the periodic table), that is, one of the protons of the nucleus turns into a neutron, emitting a positron and a neutrino (at the quark level, this process can be described as the transformation of one of the u- quarks in one of the protons of the nucleus into a d-quark; it should be noted that a free proton cannot decay into a neutron, this is prohibited by the law of conservation of energy, since the neutron is heavier than the proton; however, such a process is possible in the nucleus if the mass difference between the parent and daughter is atom is positive). Positron decay is always accompanied by a competing process - electron capture; in this process, the nucleus captures an electron from the atomic shell and emits a neutrino, while the charge of the nucleus also decreases by one. However, the opposite is not true: for many nuclides that experience electron capture (ε-capture), positron decay is prohibited by the law of conservation of energy. depending on which of the electron shells of the atom (K, L, M, ...) the electron is captured during ε-capture, the process is designated as K-capture, L-capture, M-capture, ...; all of them, in the presence of appropriate shells and sufficient decay energy, usually compete, but K-capture is most likely, since the concentration of electrons in the K-shell near the nucleus is higher than in more distant shells. After the capture of an electron, the resulting vacancy in the electron shell is filled by the transition of an electron from a higher shell; this process can be cascade (after the transition, the vacancy does not disappear, but is shifted to a higher shell), and energy is carried away by means of X-ray photons and/or Auger electrons from discrete energy spectrum.

Soddy's displacement rule for β+ decay and electron capture:

Example (ε-capture of beryllium-7 into lithium-7):

After positron decay and ε-capture, the element shifts by 1 cell to the beginning of the periodic table (the charge of the nucleus decreases by one), while the mass number of the nucleus does not change.

Double beta decay

The rarest of all known types Radioactive decay is double beta decay; it has been discovered to date only for eleven nuclides, and the half-life for any of them exceeds 1019 years. Double beta decay, depending on the nuclide, can occur:

• with an increase in the nuclear charge by 2 (in this case, two electrons and two antineutrinos are emitted, 2β− decay)
• with a decrease in the nuclear charge by 2, while two neutrinos are emitted and
  • two positrons (two-positron decay, 2β+ decay)
  • the emission of one positron is accompanied by the capture of an electron from the shell (electron-positron conversion, or εβ+ decay)
  • two electrons are captured (double electron capture, 2ε capture).

Neutrinoless double beta decay has been predicted, but not yet discovered.

General properties of beta decay

All types of beta decay preserve the mass number of the nucleus, since in any beta decay the total number of nucleons in the nucleus does not change, only one or two neutrons turn into protons (or vice versa).

Gamma decay (isomeric transition)

Almost all nuclei have, in addition to the ground quantum state, a discrete set of excited states with higher energy (the exceptions are the 1H, 2H, 3H and 3He nuclei). Excited states can be populated during nuclear reactions or the radioactive decay of other nuclei. Most excited states have very short lifetimes (less than a nanosecond). However, there are also fairly long-lived states (whose lifetime is measured in microseconds, days or years), which are called isomeric, although the boundary between them and short-lived states is very arbitrary. Isomeric states of nuclei, as a rule, decay into the ground state (sometimes through several intermediate states). In this case, one or more gamma rays are emitted; the excitation of the nucleus can also be removed through the emission of conversion electrons from the atomic shell. Isomeric states can also decay through ordinary beta and alpha decays.

Special types of radioactivity

• Spontaneous fission
• Cluster radioactivity
• Proton decay
• Two-proton radioactivity
• Neutron radioactivity

See also

• Units of measurement of radioactivity
• Banana equivalent

Notes

1. Physical encyclopedia/ Ch. ed. A. M. Prokhorov. - M.: Soviet Encyclopedia, 1994. - T. 4. Poynting - Robertson - Streamers. - P. 210. - 704 p. - 40,000 copies. - ISBN 5-85270-087-8.
2. Manolov K., Tyutyunnik V. Biography of the atom. Atom - from Cambridge to Hiroshima. - Redesigned lane from Bulgarian.. - M.: Mir, 1984. - P. 20-21. - 246 p.
3. A.N. Klimov. Nuclear physics and nuclear reactors. - Moscow: Energoatomizdat, 1985. - P. 352.
4. Bartolomei G.G., Baibakov V.D., Alkhutov M.S., Bat G.A. Fundamentals of theory and methods of calculation of nuclear power reactors. - Moscow: Energoatomizdat, 1982.
5. I. R. Cameron, University of New Brunswick. Nuclear fission reactors. - Canada, New Brunswick: Plenum Press, 1982.
6. I. Cameron. Nuclear reactors. - Moscow: Energoatomizdat, 1987. - P. 320.

Literature

• Sivukhin D.V. General course physics. - 3rd edition, stereotypical. - M.: Fizmatlit, 2002. - T. V. Atomic and nuclear physics. - 784 p. - ISBN 5-9221-0230-3.

radioactive decay of the Ottoman, radioactive decay of the Roman, radioactive decay of the USSR, radioactive decay of Yugoslavia

A nuclide is stable with respect to radioactive decay if its mass is less than the sum of the masses of all products formed during the expected decay. Therefore, radioactive decay is possible only if the sum of the masses of the resulting products is less than the mass of the original nuclide. Radioactive decay V general view can be represented as follows:

A (mother nuclide) = B (daughter nuclide) + X (emitted particles) + Q (energy)

By energy we mean the kinetic energy of emitted particles and g-quanta. The total energy Q released during radioactive decay is determined by the difference in the masses of the initial nuclide and the products formed after decay in the ground state:

Q=dmc 2 =(mA-mB-mX)c 2.

In all cases of radioactive decay, the laws of conservation of mass and charge are observed.

Based on the type of particles emitted, the following types of radioactive decay are distinguished:

1) a-decay;

2) b-decay, which is divided into b- decay, b+ decay and electron capture (EC);

3) emission of 7-quanta, conversion electrons and Auger electrons;

4) spontaneous division.

Alpha decay. The nuclei of many isotopes of (heavy) elements - uranium, radium, thorium, etc. are subject to alpha decay. The possibility of α decay is due to the fact that the mass (and therefore the rest energy) of the α-radioactive nucleus is greater than the sum of the masses (total rest energy) α-particles and forming a daughter nucleus after α-decay. The excess energy of the original (mother) nucleus is released in the form of kinetic energy of the α particle and the daughter nucleus. The kinetic energy of α-particles for most α-radioactive nuclei is in the small range of 4–9 MeV. Half-lives, on the contrary, vary greatly: from 10-7 seconds to 2∙1017 years.

Beta decay. During the process of β-decay, an electron (electronic β-decay) or a positron (positron β-decay) is spontaneously emitted from a radioactive nucleus, which appears at the very moment of β-decay (they are not in the nucleus). The third type of β-decay is the capture of an electron by a nucleus from the electron shell of its atom (e-capture). In all three casesβ-decay is accompanied by the emission of neutrinos or antineutrinos. As a result of β-decay, the nuclear charge increases, β+-decay and e-capture decreases by one. The mass number of the nucleus remains unchanged.

Electron decay test nuclei with an excess of neutrons. Almost all artificial and some natural radioactive elements (C12, K40, etc.) are susceptible to this type of decay.

During electronic decay, the newly formed daughter nucleus retains the mass number of the original element, and the positive charge of the new nucleus as a result of the transformation of a neutron into a proton turns out to be one unit greater than the charge of the nucleus of the original element.

During electronic decay, the parent and daughter radionuclides are isobars, since the sum of protons and neutrons does not change.

Positron decay test nuclei with an excess of protons. Only some artificial radioactive isotopes are susceptible to this type of decay, for example 6C11, whose nucleus contains 6 protons with 5 neutrons. Positron decay is not observed in natural radioactive isotopes.

Electronic capture. Radioactive isotopes get rid of excess protons through electron capture, which occurs when there is not enough energy in the nucleus for positron decay. Such a nucleus usually captures electrons (e-capture) from the nearest layer (K-layer, sometimes L-layer) and the “extra” proton, combining with this electron, turns into a neutron, emitting a neutrino. Therefore, e-capture is a process directly opposite to electronic decay. IN in this case the daughter element, just as during positron decay, is shifted in the periodic table by one cell to the left of the original one. An electron jumps from the L-layer to the vacant place in the K-layer, to the last place from the M-layer, etc. Each jump is associated with the release of energy, which is emitted with X-ray quanta.

Gamma rays represent a flow of γ-quanta, i.e. short-wave electromagnetic radiation emitted by excited atomic nuclei.

During the process of γ-radiation, the nucleus spontaneously passes from an excited state to a less excited or ground state. In this case, excess energy is released in the form of a short-wave quantum electromagnetic radiation− γ-quanta. γ quanta have no charge and are therefore not deflected by an electric or magnetic field. They spread straightly and evenly in all directions from the source.

In most cases, γ sources emit γ quanta of different energies, i.e. they are monoenergetic. Nuclides in an excited state can decay, emitting neutrons or protons.

Radionuclides undergo spontaneous decay and become sources of radiation of a certain type and energy strictly defined for each atom. There are several main types of radioactive decay and their corresponding types of radiation.

1) Alpha (a) radiation is a stream of nuclei of helium atoms (two protons + two neutrons). It occurs as a result of alpha decay, which is characteristic of radioactive isotopes with a high atomic number. The emission of an a-particle leads to the formation of a new chemical element, in which the nuclear charge is two units less and the mass number is four units less.

2) Beta (b) radiation is a stream of electrons or positrons. It arises as a result of beta decay of the atomic nucleus. If there is an excess of neutrons in the nucleus, then one of them decays to form a proton, which remains in the nucleus, an electron, which is emitted in the form of beta radiation, and an antineutrino, which has neither mass nor charge, but carries away some of the energy from the nucleus. Antineutrinos are very difficult to detect because they practically do not interact with matter.

Positron- the antiparticle of an electron is formed during the decay of a nucleus with an excess of protons. This type of decay is much less common than b-decay.

3) Gamma (g) radiation is a stream of photons or quanta of electromagnetic radiation. If there is excess energy in the nucleus, for example, after a- or b-decay, the transition of the nucleus from an excited state to a stable state can occur through a gamma-isomeric transition, i.e. with the emission of gamma rays. In this case, the atomic number of the element and the mass number of the isotope remain the same, only the energy state kernels.

Along with the concept " ionizing radiation"The term "radiation" is used. These concepts have the same meaning and are synonyms.

The radiation energy released during the radioactive decay of the nucleus of an atom is incommensurably greater than the energy of ordinary chemical reactions that occur through interactions between the orbital electrons of atoms. The unit of measurement for nuclear change energy is the electron volt (eV). 1 eV = 1.6×10-19 J.

11) Antioxidants. Program for cleansing the body of radionuclides. Competitive food products that prevent the accumulation of 137 Cs and 90 Sr.

Antioxidants(antioxidants, preservatives) - oxidation inhibitors, natural or synthetic substances that can slow down oxidation.

The most well-known antioxidants are ascorbic acid (vitamin C), tocopherol (vitamin E), ß-carotene (provitamin A) and lycopene (in tomatoes). These also include polyphenols: flavin and flavonoids (often found in vegetables), tannins (in cocoa, coffee, tea), anthocyanins (in red berries).

Lecture 5. Radioactive decay. General patterns

5.1. The essence of the phenomenon of radioactivity. The discovery and study of the phenomenon of radioactive decay was the first step towards understanding the structure of the nucleus and the properties of elementary particles. Research in this area has progressed at an increasing pace since late XIX century, and is currently ongoing.

In 1896, Henri Becquerel discovered the radioactivity of uranium (92 U). A little later it was discovered that thorium compounds (90 Th) are also radioactive. In 1898, Pierre Curie and Marie Skłodowska-Curie isolated uranium ore radium (88 Ra) and polonium (84 Po), the radioactivity of which turned out to be millions of times stronger than the radioactivity of uranium and thorium. However, the nature of radioactivity became clear only after Rutherford and Soddy showed that the radioactivity of elements is accompanied by their transformation into other chemical elements (thus the postulate of the immutability of atoms was refuted).

The phenomenon of radioactivity consists of the spontaneous decay of a nucleus with the emission of one or more particles. As a result of decay, the nucleus may change its charge Z, and mass number A. Nuclei that undergo spontaneous decay are called radioactive, and not experiencing - stable. However, such division is largely arbitrary, and in practice, those nuclei are considered radioactive, the decay of which can be recorded existing on at the moment by physical methods.

The lifetime range of radionuclides covers time intervals from arbitrarily large to noticeably exceeding nuclear time τ I= 10 –22 seconds. It is believed that a change in the composition of the nucleus due to radioactive decay should occur no earlier than 10–12 s after its birth: during this (very large on a nuclear scale) time, all intranuclear processes take place, and the nucleus has time to fully form. If the average lifetime of a nucleus is less than 10–12 s, the decay is no longer considered radioactive. Thus, during nuclear reactions, short-lived aggregates of nucleons are formed, which are highly excited and decay so quickly that they cannot be considered formed atomic nuclei.

Radioactive decay is characterized by the speed of its occurrence, the type of particles emitted and their energy, and when several particles escape from the nucleus, also by the relative angles between the directions of particle emission. The following main types of radioactive decay are distinguished: 1) α- decay; 2) β- decay; 3) γ- decay; 4) spontaneous fission. There are some other types of decay that are observed quite rarely.

During α decay, the nucleus emits an α particle ():

.

A new nucleus is formed, the mass number of which is 4 units less than that of the original one, and the charge is 2 units, i.e. Δ A= –4, Δ Z= –2.

During β-decay, one of three things is possible following processes:

a) emission of electron and antineutrino (β – - decay)

;

b) emission of positron and neutrino (β + - decay)

;

c) capture of an orbital electron and emission of neutrinos ( electronic capture)

.

Thus, in β-decay processes Δ A= 0, and Δ Z= ±1 (the “+” sign corresponds to β – -decay, and the “–” sign to β + -decay and electron capture).

An isomeric transition is the emission of a high energy photon (γ- quantum):

In this case, the charge and mass number of the nucleus do not change, only its energy state changes.

The result spontaneous fission is the formation of two fragments comparable in mass and the emission of several (two or three) neutrons:

A necessary (but not always sufficient) condition for radioactive decay is energy benefit: the mass of the decaying ( maternal) of the nucleus must exceed the sum of the masses of the resulting ( subsidiary) nucleus and emitted particles:

.

It follows that radioactive decay is an exothermic process, i.e. comes with the release of energy

Energy released E– this is the total kinetic energy all decomposition products. As already noted, the positivity condition itself E is not yet sufficient for the core to undergo this type decay. Energetically allowed decay can be prohibited by other conservation laws: angular momentum, electric charge etc. On the other hand, in the absence of a strict prohibition, any energetically beneficial process will necessarily occur with one or another (even if vanishingly small) probability.

5.2. The basic law of radioactive decay. Activity. Radioactive decay is a consequence of the instability of the nucleus, or, more precisely, its state. It is impossible to influence the course of decay without changing the state of the atomic nucleus, therefore radioactive decay is not affected by changes in temperature, pressure or state of aggregation substances, neither electric and magnetic fields, nor chemical reactions, in which a radionuclide is involved.

As observations show, radioactive decay is a statistical process. So, for example, under the same conditions over the same period of time, several decays can be registered, or not a single one can be registered. However average the rate of decay of a radionuclide, calculated from the observation of a very large number of decays of individual nuclei, turns out to be constant in any independent measurements under any conditions. In this case, the decay kinetics will be described as follows. Let at some point in time t there is an ensemble of N identical radioactive nuclei. Let's assume that during the time dt disintegrates dN cores. Magnitude dN will be proportional to the time period dt and number of cores N:

Where λ – proportionality coefficient characterizing the average decay rate of a given radionuclide and called decay constant. The minus sign means that over time the number of undecayed nuclei decreases. Separating the variables and integrating, we get:

, (5.3)

Where N 0 – number of radioactive nuclei at t= 0. Equality (5.3) is called fundamental law of radioactive decay.

Constant decay λ can be associated with average life time radioactive nucleus τ . To do this, let us depict the radioactive decay curve in coordinates N/N 0 – t(Fig. 5.1). According to the mathematical definition of the mean value of a function (ranging from 0 to 1),

.

Considering that the value of the integral is equal to the area S(shaded in Fig. 5.1), and also the fact that the area does not depend on the method of its calculation, we have:

.

Using (5.3), we find the value of the last integral:

.

Thus, the average kernel lifetime

In practice, another quantity is more often used to characterize the decay rate of a radionuclide - Half-life T 1/2. This is the time during which the number of cores is reduced by half. There is also a simple relationship between the half-life and the decay constant: from (5.3) after substitution N = N 0 /2 and taking logarithms we get

Let us emphasize once again that the decay constant λ – a quantity independent of time, since different moments of time are not distinguished from each other in any way from the point of view of the upcoming decay of the nucleus. Because of this, there is no concept of age for radioactive nuclei: they do not “grow old and do not deteriorate.” Radionuclides produced in reactors and accelerators decay at the same rate average speed, as the same radionuclides natural origin, formed many years ago. This is why half-life can be used to identify radionuclides. However, before moving on to measurement methods T 1/2, let's introduce another important definition.

In practice, one often has to deal with such small quantities of radionuclides that the usual units of measurement of mass or quantity of a substance (gram, mole, etc.) turn out to be more than redundant. On the other hand, to determine the amount of a radionuclide, registration of the radiation emitted by it (α-, β-, γ-, neutrons, etc.) is most often used. Therefore, it is more appropriate to characterize this quantity in units activity, i.e. number of cores n, decaying per unit time. The activity of a radionuclide is related to the number of its nuclei as follows:

. (5.6)

The SI unit of activity is one decay per second, or one becquerel(Bk). A non-systemic unit is also often used - curie(Ki). 1 Ci is the activity of a radioactive sample in which 3.7 10 10 decays occur in 1 second (1 Ci = 3.7 10 10 Bq). Historically, the latter unit owes its appearance to the discovery of radium: one curie approximately corresponds to the activity of one gram of the isotope 226 Ra.

Experimental determination The half-life (decay constant) of a radionuclide is determined using nuclear radiation detectors. Knowing the number of cores N and measuring the activity using a detector A, we can determine the decay constant from equality (5.6). This method absolute account suitable for long-lived radionuclides whose activity during the experiment (including, by definition, N) remains virtually unchanged. Otherwise the method is used direct definition . Number of particles (α-, β-, γ - quanta, neutrons) recorded by the detector over short periods of time, proportional to the activity at the time of measurement. In turn,

. (5.7)

Thus, the graph of the particle counting rate of the detector in semi-logarithmic coordinates is a straight line, the slope of which is the decay constant λ .

The direct determination method is used when the half-life ranges from a few minutes to several days or weeks. For shorter-lived radionuclides, the difficulties associated with determining the time elapsed since the start of the experiment are now being overcome. electronic circuits, turning the detector on and off at short and strictly fixed intervals.

5.3. Statistical nature of radioactive decay. As noted above, the law of decreasing the number of radioactive nuclei is satisfied statistically, i.e. the more accurate the number of them. Some decays occur completely randomly: it is impossible to predict at what point in time this or that nucleus will decay. Thus, the number of decays per unit time is a random variable. IN this section we will find the type of distribution of this random variable and determine how large the deviations of the decay rate from the average value can be.

Let us consider the decay in an ensemble of N 0 radioactive nuclei over time t. The ensemble cores can be divided into two groups. The first will include those nuclei that decay within the time t, in the second - those that will not disintegrate during this time. Probability of decay of one nucleus p = 1 – q. Then the probability of this complex event when after time t will fall apart n kernels from N 0 will be equal

, (5.8)

where is the probability of decay n nuclei of the first group, is the probability that the nuclei of the second group will not decay,

(5.9)

– number of ways to choose n kernels from total number N 0 . Addiction W(n) probability of a random event from a quantitative characteristic n in the form we received it is called binomial distribution discrete random variable, since it can be represented as one of the terms of the expansion of Newton’s binomial:

(from the last equality it is clear that the sum of the probabilities of all possible events is equal to one). It can be shown (see APPENDIX D) that for a binomial distribution the mean value

. (5.10)

The actual number of decays, being a random variable, always differs more or less from the average. To estimate the spread of values ​​of a random variable, variance is used D, defined as the mean square deviation from the mean value:

.

For binomial distribution

The binomial distribution law can be simplified if the following conditions are met: n << N 0 and r<< 1, т.е. если начальное количество ядер велико, а распадаются они не слишком часто. В этом случае биномиальное распределение переходит в распределение Пуассона

. (5.12)

In contrast to the binomial distribution (5.8), characterized by two parameters ( N 0 and r), it contains only one parameter. Experiments to determine the true number of decays per unit time give results that are in good agreement with such a distribution. The variance of a random variable distributed according to Poisson's law is

This result follows directly from (5.11) if r<< 1.

Poisson distribution defined for integer values n. In this case, a smooth curve can be drawn through the corresponding points. For small values, an asymmetrical curve is obtained. As , and hence the number of points, increases, the curve becomes more and more symmetrical, with its maximum occurring at (Fig. 5.2). Thus, for >> 1, the number of decays can be considered as a continuous random variable, distributed normally, or according to Gauss’s law:

. (5.14)

The variance of the normal distribution (5.14) is related to the mean in the same way as in the Poisson distribution: .

The derivation of the mean and variance of the binomial distribution, as well as the relationship between the three distributions, is given in APPENDIX D.

To determine the confidence interval of a normally distributed value n use the following expression:

Where kP– quantile of the normal distribution corresponding to the selected confidence probability R. In practice, when processing experimental data, they often use standard deviation Δ n, for which kP= 1, a R≈ 0.683 (i.e., the average number of decays with a probability of 68.3% differs from the experimentally obtained one by no more than ). Magnitude

represents the relative measurement error. If a sufficiently large number of decays are recorded in the experiment, then the value itself can be used to determine the error instead of the unknown average n. Since , relative error

It follows that to achieve a given level of measurement accuracy it is necessary to register 1/ r 2 decays (for example, for a measurement with a 1% error n should be equal to 10 4).

Lecture 6. Radioactive decay. General patterns (end)

6.1. Complex disintegration. Consecutive and parallel transformations. Let us now turn again to the experiment to determine the half-life of a radionuclide. The statistical nature of radioactive decay leads to the fact that in real measurements of activity with arbitrarily sophisticated equipment, experimental points plotted in ln coordinates A – t, will always have a scatter on both sides of a straight line drawn using the least squares method. In this case, you should make sure that the standard deviation does not exceed , i.e. the straight line lies within the confidence interval defined for each of the points. If it is not possible to draw a straight line (Fig. 6.1), then the equipment registers a more complex phenomenon than the simple decay of nuclei of the same type. Let's consider different types of complex decay.

Firstly, complex decay may be due to the fact that the substance under study contains not one, but several different radionuclides. Then the dependence of activity on time will look like this:

where is activity i th radionuclide at the initial time. In the case of a mixture of two radionuclides

If the half-lives of radionuclides differ sufficiently ( λ 1 >> λ 2), then for small t exponent at A 02 is close to zero. Then

At large t we can neglect the first term under the logarithm in (6.1):

Thus, constant λ 1 and λ 2 are determined by angle coefficients tangent to the graph at a point t= 0 and asymptotes at (Fig. 6.1).

Secondly, as a result of the disintegration of the mother nucleus E 1 daughter nucleus formed E 2 may also be radioactive. In this case we are dealing with a sequence of radioactive transformations, for example

E 1 (l 1) → E 2 (l 2) → E 3 (l 3) → …

The number of daughter nuclei of each type as a function of time is determined, on the one hand, by the rate of their decay and, on the other hand, by the rate of their formation, equal speed decay of the corresponding mother nuclei. Then, in accordance with (5.2), we obtain the following system differential equations:

, (6.2)

etc. Its solution for the simplest case of two successive decays at initial conditions and has the form:

,

. (6.3)

Note that the first term in (6.3) describes the change over time in the number of daughter nuclei that already existed at the time the initial moment time. If (there is no daughter radionuclide yet), then the total activity will be determined by the following expression:

A. Let the parent radionuclide be short-lived compared to the long-lived daughter, i.e. λ 1 >> λ 2. Then from (6.4) we obtain

This expression is similar in form to (6.1). Consequently, the dependence of activity on time will in this case look the same as shown in Fig. 6.1: The parent radionuclide decays very quickly, and long-lived activity is determined by the decay rate of the daughter radionuclide.

B. Of greatest interest is the opposite case, when the daughter radionuclide is short-lived compared to the long-lived parent, i.e. When λ 2 > λ 1. From (6.3) we find that

The logarithm of the total activity will be expressed as

The value of the exponent in the second term quickly approaches zero, so in the initial period of time the activity quickly increases and then slowly decreases in accordance with the change A 1 (Fig. 6.2).

If the time that has passed since t= 0, is several times greater than the half-life of daughter nuclei, then

, (6.6)

Those. The activities of the parent and daughter radionuclides at any time are equal up to a constant factor λ 2 /(λ 2 – λ 1).

Finally, let us consider the case when the same nuclei undergo several types of radioactive transformations (examples include the competition of α- and β – decay in heavy nuclei, β – and β + decay in odd-odd nuclei, the formation of various nuclear isomers etc.). The important thing is that each transformation is characterized by its own decay constant, which determines its probability.

Let the core E 1 is capable of turning into one of the nuclei E i. The equation for the decay rate would then look like

,

those. decay constant λ 1 is the sum of constants λ 1i in all possible ways, or decay channels. If, in turn, E i is a radioactive nucleus, then

.

Size

called output i th transformation product. It is obvious that the total output over all channels (as the total probability of transformation)

6.2. Radioactive chains. Parallel and sequential transformations of radioactive nuclei often lead to quite complex radioactive chains, For example

E 1 (l 1) → E 2 (l 2) → E 3 (l 3) → E 5 (l 5) →…→E n(l n) →….

E 4 (l 4) → E 6 (l 6)

As was shown by G. Bateman (1910), for an unbranched chain consisting of two or more links, when t= 0 only radionuclide available E 1, number of cores n-th radionuclide

. (6.9)

In the case where a general solution is required N 02 ,N 03 ,… ≠ 0, it can be obtained by adding to (6.9) similar solutions for shorter chains starting with E 2 , E 3, etc.

If in a chain of successive transformations for any i th child kernel λ i >> λ 1, then over time, equilibrium is established for all daughter radionuclides, i.e. at t >> T 1/2 of the longest-lived decay product

The secular equilibrium law, written in the form (6.10), can be used to determine the half-life of long-lived parent nuclei if the relative abundance of any daughter nuclei in a radioactive sample is first determined. For example, in uranium-containing minerals, for every 2.8 10 6 nuclei of 238 U, there is one nucleus of 226 Ra, a product of its decay with a half-life of 1620 years. Using (6.10), we find that the half-life of 238 U is about 4.5·10 9 years.

If the chain contains branches caused by different decay channels, solution (6.9) is also applicable to it, but the constants λ i, standing before the sum sign, at branch points i should be multiplied by the output values y i+ 1. Each branch of the chain must be calculated independently. If, following branching after a series of decays, the branches of the chain are connected again, the number of nuclei behind the connection point is obtained by summing the solutions over all branches.

6.3. Radioactive families. Radionuclides in nature. As noted in Lecture 2, the nuclear binding energy per nucleon decreases with increasing mass number A due to the increasing role of the Coulomb repulsion of protons. As a result, heavy nuclei become unstable with respect to the emission of α particles and become stable through one or more successive α decays. However, as a result of α-decay, the nucleus loses the same number of protons and neutrons, which leads to a violation of the optimal ratio Z/A: The resulting daughter nucleus contains an excess number of neutrons and is stabilized by β− decay. Therefore, on the path of transformation of heavy radioactive nuclei (uranium, thorium, etc.) into stable ones, an alternation of α- and β−-decay processes is observed.

During α-decay, the mass number of the nucleus decreases by four, and during β-decay it does not change. Therefore, all heavy radioactive nuclei can be distributed into four groups, or radioactive families(Table 6.1), in accordance with their mass number, where n− some integer, and m− remainder of division A by four, i.e. 0, 1, 2 or 3. The transformation of a radionuclide of one family into a radionuclide belonging to another is practically impossible, because this would require changing the mass number to a number other than 4. Although such types of radioactive transformations are known, the yield of the corresponding products is negligible.

Table 6.1

Radioactive families

Radionuclides of three families—thorium, uranium-radium and uranium-actinium—are found in nature. Contents in earth's crust uranium is 3·10−4, and thorium 1·10−3% wt. The content of daughter radionuclides can be determined from relation (6.10), which expresses the secular equilibrium, since all daughter radionuclides have much shorter half-lives than their long-lived parents. The neptunium family is not found in nature, and therefore was studied later than the others, only after the technology for producing artificial radionuclides had reached a sufficiently high level.

The end products of decay in natural radioactive families are isotopes of lead. This is due to the increased stability of nuclei containing the magic number of protons ( Z= 82). As for 209 Bi (neptunium family), this nucleus contains the magic number of neutrons ( N= 126). That is why 209 Bi is the heaviest stable nucleus. The noticeable content of 209 Bi in the earth's crust may indicate that many millions of years ago radionuclides of the neptunium-237 family were also present in it, but due to the short half-life of its parent, they ceased to exist.

In addition to representatives of three radioactive families, the earth’s crust contains about twenty more long-lived radionuclides, which, as a rule, give stable nuclei during decay. The most important of them are 40 K ( T 1/2 = 1.28 10 9 years) and 87 Rb ( T 1/2 = 4.75 10 10 years).

Under the influence cosmic rays Nuclear reactions occur in the Earth’s atmosphere, leading to the formation of many radionuclides with relatively short half-lives: 3 H (12.3 years), 10 Be (1.6 10 6 years), 14 C, etc. These radionuclides are called cosmogenic. Thanks to continuing education, compensating for their decay, cosmogenic radionuclides are present on Earth in quantities sufficient for their detection.

6.4. Nuclear geochronology. Nuclear geochronology uses the phenomenon of radioactive decay to determine the age of geological features. The rate of radioactive decay remained constant in all geological epochs, being independent of external conditions. Therefore, the readings of “nuclear clocks” made by nature itself can be considered very reliable.

Currently, a number of methods are used to date geological objects. Nuclear geochronology has become an independent branch of Earth science. Generalization and systematization of the results of nuclear geochronological research led to the creation of a scale of absolute chronology of the Earth. Improvement analytical technique(mainly mass spectrometry) made it possible to use several methods when analyzing the same sample. Only if the results obtained different methods, are consistent with each other, a certain absolute age is assigned to this sample.

To solve nuclear geochronological problems, the following notation of the basic law of radioactive decay (5.3) is more convenient:

Accumulated over time t the number of nuclei of the daughter nuclide is determined by the difference D= N 0 – N, from which the formula for the age of the sample follows:

. (6.11)

When deriving (6.11), it was assumed that at the time of formation of the object (mineral, rock), no daughter nuclide atoms were found in its composition. If the newly formed object already contained D 0 such atoms, then D=D 0 + N 0 – N, And

. (6.12)

Therefore, to date a sample, it is necessary to measure the content of its parent (radioactive) and daughter (stable) nuclides. For this purpose, mass spectrometric analysis is most often used. Timing accuracy t, which is taken as the absolute geological age of a mineral or rock, depends on the accuracy of the determination D And N, as well as on the accuracy with which the decay constant is known λ .

An important prerequisite for the successful use of nuclear geochronology methods is the closure of the studied sample for the parent and daughter nuclides. This means that during the entire period of the “life” of the object, neither one nor the other was removed or added from the outside. The possibility of partial “opening” at one time or another should always be taken into account. Yes, when high temperature diffusion, and hence the removal of some elements from minerals, becomes possible. Reliable confirmation of the closedness of the system is the coincidence of ages obtained by different methods, i.e. when using various mother and daughter nuclides.

IN total More than a dozen nuclear geochronological methods have been developed. Suitability of a particular method for assessment absolute age depends on the lifetime of the research object. When determining the age of young formations, radionuclides with a relatively short half-life should be used. On the contrary, when studying ancient minerals or rocks, radionuclides with a half-life of 1 billion years or more are required. The most widely used methods include those related to the decay of uranium isotopes, 40 K and 14 C.

Obviously, the maximum age established for the Earth's rocks indicates a lower limit on the age of the Earth as a planet. To determine the upper limit of the age of the Earth, the patterns of distribution of lead isotopes in lead minerals are studied. By modern estimates, obtained by this method, the age of the Earth is 4.53 - 4.55 billion years.

Uranium-lead dating. Uranium-lead dating is the earliest nuclear geochronological method used to determine absolute ages. In 1907, B. Boltwood measured the age of the uranium mineral using this method and concluded that geological times should be calculated in hundreds of millions and billions of years.

The average isotopic composition of lead on Earth is characterized by the following data: 204 Pb – 1.5%; 206 Pb – 23.6%; 207 Pb – 22.6%; 208 Pb – 52.3%. The nuclei of the last three isotopes (or part of them) are radiogenic, representing the end products of the decay of natural radioactive families.

When analyzing a sample for the content of U, Th and Pb isotopes, three isotope ratios can be obtained: 206 Pb/ 238 U, 207 Pb/ 235 U, 208 Pb/ 232 Th. Substituting them into (6.11) gives three independent estimates of the absolute geological age. Because of the very long period The half-life of Th ratio 208 Pb/ 232 Th is characterized by low sensitivity, so it is not always used. Thus, the essence of uranium-lead dating consists, first of all, in determining the ratios 206 Pb/ 238 U and 207 Pb/ 235 U; hence the name of the method: “uranium-lead”. Convenient objects for its use are uranium-containing minerals such as uraninite, zircon, monazite, etc.

If the system's integrity is broken, lead loss due to diffusion is possible. However, if all lead isotopes are lost in the same proportion, then the equality remains valid

. (6.13)

The ratio 238 U/235 U for the modern geological epoch is constant and equal to 137.8 for almost all objects. Therefore, the ratio 207 Pb/ 206 Pb can serve as an additional factor, allowing one to calculate the age using equation (6.13) t. If the resulting relationship is consistent with the values ​​following from (6.11), this indicates that the system is closed.

The presence of primary lead of non-radiogenic origin leads, according to (6.11), to an overestimation of the age of uranium minerals. One can correct for this overestimation by measuring the content of the non-radiogenic isotope 204 Pb. The ratios 206 Pb/ 204 Pb and 207 Pb/ 204 Pb (as well as 208 Pb/ 204 Pb, if the age is additionally determined by 208 Pb/ 232 Th) in radioactive minerals are compared with the same ratios in accompanying minerals, where the content of U and Th is negligible is small, and all lead isotopes can be considered non-radiogenic.

In the presence of uranium losses, the ages calculated from various ratios should be as follows: t(206 Pb/ 238 U) > t(207 Pb/ 235 U) > t(207 Pb/ 206 Pb). In the case of lead losses, the sequence of values t reverse.

Potassium-argon dating. The potassium-argon method for determining geological age was developed by E.K. Gerling (1949). Natural potassium has a radioactive isotope of 40 K, the average content of which in the natural mixture is 0.012%. The decay of 40 K occurs by β – - decay or electron capture. The first channel with the formation of 40 Ca is of no practical importance, since potassium-containing minerals usually contain non-radiogenic 40 Ca, the contribution of which cannot be accurately accounted for. The second channel leads to the formation of 40 Ar and is used for dating. The fraction of 40 K converted into 40 Ar can be calculated from the relationship between the yield of β-decay y β(88%) and electron capture output y e(12%):

. (6.14)

The total amount of radiogenic isotopes 40 Ar and 40 Ca formed over time t, equals

(λ – decay constant 40 K). On the other hand, from (6.14) it follows that

. (6.16)

Comparing (6.15) and (6.16), we obtain a formula for determining age:

. (6.17)

The potassium-argon method is more universal compared to the uranium-lead method, since potassium-containing minerals are more widespread.

Argon produced by 40 K decay tends to diffuse out of minerals. For most minerals, diffusion becomes significant at temperatures > 300 o C. The rate of argon diffusion from a mineral depends on the size of its grains: a fine-grained mineral loses argon faster due to larger size area to volume ratio. The loss of argon due to diffusion results in inconsistent dating results for the same type of mineral in a given rock. Values ​​of this age are usually underestimated compared to the true ones, moreover, than more loss argon, the more the apparent age is underestimated. IN in some cases it is possible to identify the specific reason for the inconsistency of age determination results.

Radiocarbon dating. IN upper layers atmosphere, the composition of cosmic rays changes. Primary particles cosmic radiation(mainly protons) having high energy, can split the nuclei of atoms encountered in their path. As a result of fission, neutrons are produced, which in turn can cause nuclear reactions. The most important reaction caused by neutrons is the conversion of 14 N to 14 C. Cosmogenic 14 C, called radiocarbon, has a half-life of 5730 years. Emitting β-particles, it turns into stable 14 N. Formed in the Earth's atmosphere, radiocarbon quickly oxidizes, turning into radioactive carbon dioxide 14 CO 2, which in 10-15 years is completely mixed with the entire mass of carbon dioxide in the atmosphere. Through carbon dioxide, 14 C enters plants, and from there into other living organisms. The equilibrium concentration of 14 C in the exchangeable carbon of the biosphere is 1.2∙10 -10%.

As soon as the body's metabolism stops, the concentration of radiocarbon in the tissues begins to decrease. Thus, by the amount of 14 C present in the remains of organisms, it is possible to determine the moment of cessation of carbon exchange with the atmosphere, i.e. moment of death. The time that has passed since this moment is determined by the formula:

, (6.18)

Where WITH arr and WITH atm – concentration of 14 C in the sample and atmospheric carbon; λ – decay constant 14 C.

The radiocarbon dating method was proposed in 1951 by W. Libby and was first used to determine the age of archaeological objects of organic origin. The radiocarbon method is of great importance for absolute Quaternary chronology. The range of objects for 14C dating is very wide. Usually organic residues found in rocks are used - wood, peat, humus, etc. The relatively short half-life of radiocarbon limits the upper limit of applicability of the method, which, when modern level measuring technology is 50 thousand years old. The lower limit of applicability of the method is estimated at 1 thousand years; It is not advisable to date objects younger than 1000 years using 14 C, because error in measuring the difference between WITH atm and WITH arr becomes large.

At the core radiocarbon method lies the assumption that the content of 14 C in the external environment (air, water) at the moment recording the cessation of metabolism in the object was the same as at the present time. This assumption is not entirely strict. Over the past 200 years, as a result of the combustion of fossil fuels, the atmosphere has been diluted with technical CO 2, which practically does not contain the 14 C isotope (in coal and oil the concentration of radiocarbon is negligible). Thermonuclear explosions, at which it is formed large number neutrons, on the contrary, in individual periods significantly increased the content of 14 C in the atmosphere.

In addition, the equilibrium concentration of 14 C in the atmosphere depends on the intensity of cosmic radiation. Protons from cosmic radiation are deflected by the Earth's magnetic field, which acts like a screen. Judging by paleomagnetic data, the tension magnetic field The Earth has been continuously changing over the past 10 thousand years. Accordingly, the intensity of the flow of cosmic protons reaching the upper layers of the atmosphere, and therefore the number of secondary neutrons responsible for the formation of 14 C, also changed. This circumstance can introduce an error (about 10%) into the results of age determination using the radiocarbon method.

The widespread use of the radiocarbon dating method made it possible to create a climatochronological scheme of the newest stage geological history. At the same time the most important result Research has provided evidence of synchronous climate changes in different regions of the Earth. For example, a pronounced cooling between 33 and 30 thousand years ago and warming between 16.5 and 15 thousand years ago can be traced in all parts of the globe.