Isobars. Physical foundations of radioecology

Task 26.
The nickel-57 isotope is formed when particles bombard the nuclei of iron-54 atoms. Make up the nuclear reaction equations and write them in abbreviated form.
Solution:
The isotope of element 28, nickel-57, was obtained by bombing -particles of iron-54 atoms. The transformation of atomic nuclei is determined by their interaction with elementary particles or with each other. Nuclear reactions are associated with changes in the composition of the nuclei of atoms of chemical elements. With the help of nuclear reactions, atoms of others can be obtained from atoms of some elements. The transformation of atomic nuclei, both during natural and artificial radioactivity, is written in the form of an equation of nuclear reactions. It should be remembered that the sums of mass numbers (the numbers next to the element symbol at the top left) and algebraic sums the charges (the numbers next to the element symbol at the bottom left) of the particles on the left and right sides of the equation must be equal. This nuclear reaction is expressed by the equation:

Task 28.
What are isotopes? How can we explain that most elements of the periodic table have atomic masses expressed as fractions? Can atoms of different elements have the same mass? What are such atoms called?
Solution:
Atoms that have the same nuclear charge (and, therefore, identical chemical properties), but a different number of neutrons (and therefore a different mass number), are called isotopes (from the Greek words "isos"- identical and "topos"- place). It has been established that, as a rule, each element is a combination of several isotopes. This explains the significant deviations of the atomic masses of many elements from integer values. Thus, natural chlorine consists of 75.53% of the 35Cl isotope and 24.47% of the 37Cl isotope; as a result, the average atomic mass of chlorine is 35.453.

Another phenomenon that occurs in nature is that atoms of different elements have the same atomic mass, but different nuclear charges. Such atoms are called isobars. For example, the potassium isotope and the calcium isotope have the same atomic masses (40), but different nuclear charges, respectively +19 and +20:

Task 29.
The isotope silicon-30 is formed when the nuclei of aluminum-27 atoms are bombarded by -particles. Create an equation for this nuclear reaction and write it in abbreviated form.
Solution:

An abbreviated form of notation for a nuclear reaction is often used. For this reaction it will look like:

The bombarding particle is written in brackets, and the particle formed during a given nuclear process is written separated by a comma. In the abbreviated particle equations

denote respectively p, d, n, e.

Task 31.
The isotope carbon-11 is formed when protons bombard the nuclei of nitrogen atoms-14. Create an equation for this nuclear reaction and write it in abbreviated form.
Solution:
The transformation of atomic nuclei is determined by their interaction with elementary particles or with each other. Nuclear reactions are associated with changes in the composition of the nuclei of atoms of chemical elements. With the help of nuclear reactions, atoms of other elements can be obtained from atoms of some elements. The transformation of atomic nuclei, both during natural and artificial radioactivity, is written in the form of an equation of nuclear reactions. It should be remembered that the sums of mass numbers (the numbers next to the element symbol at the top left) and the algebraic sums of charges (the numbers next to the element symbol at the bottom left) of particles on the left and right sides of the equation must be equal. This nuclear reaction is expressed by the equation:

An abbreviated form of notation for a nuclear reaction is often used. For this reaction it will look like:

The bombarding particle is written in brackets, and the particle formed during a given nuclear process is written separated by a comma. In the abbreviated particle equations

denote respectively p, d, n, e.

Task 328
Name three isotopes of hydrogen. Indicate the composition of their nuclei. What is heavy water? How is it obtained and what are its properties?
Solution:
Three isotopes are known for hydrogen: - protium N , - deuterium D , - tritium T . Protium and deuterium occur naturally; tritium is produced artificially. The protium nucleus consists of one proton, the deuterium nucleus consists of one proton and one neutron, and the tritium nucleus consists of one proton and two neutrons.

Heavy water D 2 O– a combination of deuterium and oxygen. Heavy water is produced by electrolysis natural water. During the electrolysis of water, the discharge of H + ions occurs much faster than D +, therefore, the residue after decomposition by electrolysis large quantity water is concentrated D 2 O.

Heavy water D 2 O By physical and chemical properties different from H 2 O: t pl.= 3.82 0С, t bale. = 101.42 0 C, r raft, equal to 1.1050 g/cm 3 (20 0 C). The enthalpies of dissolution of salts in H 2 O and D 2 O, the dissociation constants of acids and other characteristics of solutions differ markedly.

The nucleus of an atom consists of protons and neutrons.

A chemical element is uniquely characterized by its atomic number Z, coinciding with the number of protons in the nucleus.
A nucleus with a given number of protons Z may have a different number of neutrons N. Protons and neutrons together are called nucleons. Specific core with data Z, N called a nuclide.
The mass number is called full number nucleons in the nucleus: A = Z + N.
Since the masses of protons and neutrons are very close ( mn/mp = 1.0014)

Nuclear forces. The existence of nuclei is possible only if forces of a special nature act between nucleons, counteracting the electrostatic repulsion of protons and compressing all nucleons in a small region of space. Such forces can be neither of an electrostatic nature (on the contrary, these forces must strongly attract protons) nor of a gravitational nature (numerically, the force of gravitational attraction is too small to prevent significant electrostatic repulsion). These new forces are called nuclear forces, and the interaction that generates these forces is called strong.

The following properties of nuclear forces have been experimentally established.

1. These forces are the same in magnitude, regardless of whether they act between two protons, a proton and a neutron, or two neutrons (charge independence of nuclear forces).

2. These forces are short-range in nature, i.e. vanish if the distance between nucleons exceeds the size of the nucleus.

3. In the area of ​​action of nuclear forces, these forces are very large (compared to electromagnetic or, even more so, gravitational forces) and are attractive forces up to distances of the order R0, where they are replaced by repulsive forces. Thus, nucleons in nuclei are held in a region of space with a radius R > R0, however, atomic nuclei cannot be compressed to smaller sizes.

Isotopes – atoms of the same element that have different mass numbers

Atoms of isotopes of the same element have the same number of protons, but differ from each other in the number of neutrons

for example: hydrogen has three isotopes: protium 1 1 H, deuterium 2 1 H, tritium 3 1 H

Isobars - nuclides of different elements having the same mass number; for example, isobars are 40 Ar, 40 K, 40 Ca.

Ticket 11. Nature and types of intramolecular chemical bonds. Examples of connections with various types chemical bond

There are four types of chemical bonds: ionic, covalent, metallic and hydrogen.

Ionic chemical bond is a bond formed due to the electrostatic attraction of cations to anions.

A covalent chemical bond is a bond that occurs between atoms due to the formation of shared electron pairs.

Donor-acceptor mechanism of formation covalent bond Let's look at the classic example of the formation of ammonium ion NH4+:

Metal connection
Bonding in metals and alloys, which is performed by relatively free electrons between metal ions in a metal crystal lattice, is called metallic. This bond is non-directional, unsaturated, characterized by a small number of valence electrons and a large number of free orbitals, which is typical for metal atoms. Education scheme metal connection(M - metal):

_
M 0 - ne<->M n+

Hydrogen bond

A chemical bond between positively polarized hydrogen atoms of one molecule (or part thereof) and negatively polarized atoms of strongly electronegative elements having lone electron pairs of another molecule (or part thereof) is called hydrogen bonding.

In biopolymers - proteins (secondary structure) there is an intramolecular hydrogen bond between carbonyl oxygen and the hydrogen of the amino group.

Polynucleotide molecules - DNA (deoxyribonucleic acid) are double helices in which two chains of nucleotides are linked to each other by hydrogen bonds. In this case, the principle of complementarity operates, that is, these bonds are formed between certain pairs consisting of purine and pyrimidine bases: the thymine (T) is located opposite the adenine nucleotide (A), and the cytosine (C) is located opposite the guanine (G).

Substances with hydrogen bond have molecular crystal lattices.

Ticket 12. main provisions of the BC method using the example of the formation of the NH 4 cation

Topic 1. PHYSICAL FOUNDATIONS OF RADIOECOLOGY

Lecture 2: Physical characteristics of atoms and radioactive decay of nuclei.

The structure of the atom. Elementary particles. Types of radioactive decay. Law of radioactive decay.

1. The structure of the atom.

Atom – smallest particle chemical element, preserving all its properties. In terms of its structure, an atom (size approximately 10-8 cm) is a complex system consisting of a positively charged nucleus (10-13 cm) located in the center of the atom and negatively charged electrons rotating around the nucleus in different orbits. The radius of an atom is equal to the radius of the orbit of the electron farthest from the nucleus. The negative charge of the electrons is equal to the positive charge of the nucleus, while the atom as a whole is electrically neutral.

In 1911, E. Rutherford proposed a planetary model of the structure of the atom, which was developed by N. Bohr (1913). According to this model, at the center of the atom there is a nucleus that has a positive electric charge. Electrons move around the nucleus in elliptical orbits, forming the electron shell of the atom.

Any atom consists of elementary particles: protons, neutrons and electrons, which are in free state are characterized by such physical quantities, such as mass, electric charge (or lack thereof), stability, speed, etc. The mass of nuclei and elementary particles is usually expressed in atomic mass units (amu), 1\12 of the mass of carbon atoms (12C) is taken as a unit. .

1 a. e.m. = 1.67*10-27 kg

Energy is expressed in electron volts (eV), one electron volt is equal to the kinetic energy that an electron (or any elementary particle of matter with a charge) acquires when passing through electric field with a potential difference of one volt.

1eV = 1.602*10-19 C

In addition, mass is often expressed in energy equivalents (this is the rest energy of a particle whose mass is equal to 1 amu, is 931.5 MeV (106 eV).

Atomic nucleus – the central part of the atom, in which almost all the mass is concentrated (99.9%). The atomic nucleus consists of two types of elementary particles - protons and neutrons. Their common name is nucleon. The proton and electron belong to the so-called stable and stable particles, the neutron is stable only when it is in the nucleus.

The total number of protons and neutrons in the nucleus is called mass number and are designated by the letter A (or M). Since the charge of a neutron is zero, and the proton has an elementary positive charge of +1, the charge of the nucleus is equal to the number of protons in it, which is called charge number(Z) or atomic number. The number of neutrons in the nucleus is equal to the difference between the mass A number and the atomic number Z of the element: N = A-Z (AZX).

The electric charge (q) of the nucleus is equal to the product of the elementary electric charge (e) and the atomic number (Z) of the chemical element of the periodic table:

Nuclear forces.

Protons and neutrons are held within the atomic nucleus nuclear forces . Nuclear forces constitute the potential binding energy of a nucleus. It has been established that the sum of the energies of free protons and neutrons is greater than the energy of the nucleus composed of them, from which it follows that energy must be expended to separate the nucleus into its components. The minimum energy required for this is called nuclear binding energy .

The same picture is observed if we add up the masses of the nucleons that make up the nucleus of an atom. The calculated mass of the nucleus will be greater than the actual mass of the nucleus. The difference between the calculated and actual mass of the nucleus is called mass defect.

Nuclear forces do not depend on the presence or absence of an electric charge on nucleons; they act only at very small distances (10-13 cm) and weaken very quickly as the distance between nuclear particles increases.

Nuclear forces are characterized by the property of saturation, which means that a nucleon is capable of nuclear interaction simultaneously with only a small number of neighboring nucleons, which indicates the possible nature of nuclear forces as exchange-type forces.

The main properties of nuclear forces are explained by the fact that nucleons exchange particles with each other with a mass of slightly more than 200 electron masses (X. Yukawa, 1935), such particles were discovered experimentally (1947) and called π-mesons or pions (there are positive, negative and neutral π-mesons) mesons). Mesons are not components protons and neutrons, but are emitted and absorbed by them (similar to how atoms emit and absorb quanta of electromagnetic radiation), while the proton that emitted a positive pion turns into a neutron, and the neutron after capturing the pion turns into a proton. All these processes ensure strong interaction and thereby the stability of nuclei.

Proton(p) – an elementary particle that is part of any atomic nucleus, having a positive charge equal to a unit elementary charge +1 (1.602 * 10-19 C). The rest mass of a proton is 1.00758 a. e.m. or 938.27 MeV.

Number of protons in the nucleus ( atomic number) for each element is strictly constant and corresponds serial number element (Z) of the table. Since each proton has a positive elementary charge of electricity, the atomic number of an element also shows the number of positive elementary charges in the nucleus of any atom of a chemical element. The element's serial number is also called charge number. The number of protons in the nucleus determines the number of electrons in the shell of the atom (but not vice versa) and, accordingly, the structure of the electron shells and the chemical properties of the elements.

Neutron ( n) – an electrically neutral elementary particle (absent only in the nucleus of light hydrogen), the rest mass of which is 1.00898 a. e.m. or 939.57 MeV. The mass of a neutron is two electron masses greater than the mass of a proton. In the atomic nucleus, neutrons are stable; their number (N) in the nucleus of an atom of the same element can fluctuate, which basically gives only the physical characteristic of the element (1).

Electron – a stable elementary particle with a rest mass equal to 0.000548 a. e.m., and in absolute units of mass - 9.1 * 10-28 kg. Energy equivalent a. e.m. electron is 0.511 MeV and the elementary electric charge is 1.602*10-19 C.

Electrons move around the nucleus in orbitals of a certain shape and radius. The orbits are grouped into electronic layers (there can be a maximum of seven: K, L, M, N, O, P, Q). The smallest number of electrons that can be in the orbitals of one layer is determined by the quantum relationship:

m=2n2,

where n is the main quantum number (in this case it coincides with the layer number. Therefore, the K-layer (n=1) can contain 2 electrons, the L-layer (n=2) can have 8 electrons, and so on.

The main role in the interaction of electrons with the atomic nucleus is played by electromagnetic forces (Coulomb attraction forces of opposite electric charges). The closer an electron is to the nucleus, the more potential energy(binding energy with the nucleus) and less kinetic energy (electron rotation energy). Accordingly, electrons from the outer orbit (binding energy about 1-2 eV) are easier to tear off than from the inner one.

The transition of an individual electron from orbit to orbit is always associated with the absorption or release of energy (a quantum of energy is absorbed or emitted). According to Bohr's postulates, the atomic system is in a stationary state, which is characterized by a certain energy. For an infinitely long time, each atom can only be in a stationary state with minimal energy, which is called main or normal . All other stationary states of the atom with high energies are called excited . The transition of an electron from one energy level to another, more distant from the nucleus (with higher energy) is called process of excitation .

As a result of collisions with other atoms, with any charged particle, or when absorbing a photon of electromagnetic radiation, an atom can move from a stationary state with lower energy to a stationary state with higher energy. The lifetime of an atom in an excited state does not exceed s. From any excited state, the atom spontaneously passes into the ground state, this process is accompanied by emission of photons (quanta). Depending on the difference in the energies of the atom in the two states between which the transition occurs, the emitted quantum of electromagnetic radiation may belong to the range of radio waves, infrared radiation, visible light, ultraviolet or x-ray radiation.

Under strong electrical influences, electrons can escape from the boundaries of the atom. An atom that has lost one or more electrons turns into a positive ion, and an atom that has gained one or more electrons turns into a negative ion. The process of formation of ions from neutral atoms is called ionization . Under ordinary conditions, an atom in the ion state exists very short time. Free space in the orbit of the positive ion is filled with a free electron, and the atom again becomes an electrically neutral system. This process is called ion recombination (deionization) and is accompanied by the release of excess energy in the form of radiation.

Isotopes, isotones, isobars.

Atoms that have nuclei with the same number of protons, but differ in the number of neutrons, are varieties of the same chemical element and are called isotopes. Such elements have the same number in the table, but different mass numbers (3919K, 4019K, 4119K). Since the charges of the nuclei of these atoms are the same, their elementary shells have almost the same structure, and atoms with such nuclei are extremely similar in chemical properties. Most chemical elements in nature are a mixture of isotopes. Typically, in a mixture of isotopes of one particular element, one isotope predominates, and the rest make up only a small percentage (for example, potassium consists of: 39K - 93.08%; 40K - 0.0119%; 41K - 6.91%) (4).

To distinguish isotopes of one chemical element from each other, a mass number is added above the name of the element, equal to the sum all particles of the nucleus of a given isotope, and below - the charge of the nucleus (number of protons), corresponding to the ordinal number of the element in the table. Thus, the most common light hydrogen in nature, 11H (protium), contains 1 proton, which is rarely found among hydrogen atoms 21H (deuterium) - 1 proton and 1 neutron, and 31H (tritium), which is never found in nature, contains 1 proton and 2 neutrons (tritium are obtained artificially by irradiating deuterium with slow neutrons) (4).

Distinguish stable And unstable (radioactive ) isotopes . The first are those isotopes whose nuclei do not undergo any transformations in the absence of external influences, the second are isotopes whose nuclei can spontaneously (without external influence) disintegrate, forming nuclei of atoms of other elements. The nuclei of all isotopes of chemical elements are usually called nuclides, unstable nuclides are called radionuclides . Currently, about 300 stable isotopes and about 1,500 radioactive isotopes are known.

Condition for the stability of atomic nuclei: Only those atomic nuclei that have minimal energy compared to all the nuclei into which a given nucleus could spontaneously transform are stable.

Atomic nuclei of different elements with equal number neutrons are called isotones . For example, 136C has six protons and seven neutrons, 147N has seven protons and also seven neutrons.

Atomic nuclei of different elements with the same mass number, but with different atomic numbers (i.e., consisting of the same number of nucleons at different ratios protons and neutrons) are called isobars .

For example: 104Be, 105B, 106C, etc.

The difference in the energy of atomic nuclei of isobars is determined by the presence of an electric charge on protons and the existence of differences in the masses of the proton and neutron. Thus, nuclei containing significantly more protons than neutrons turn out to be unstable, since they have an excess of Coulomb interaction energy. Nuclei that have more neutrons than protons are unstable due to the fact that the mass of the neutron is greater than the mass of the proton, and an increase in the mass of the nucleus leads to an increase in its energy. Nuclei can be released from excess energy in two ways:

1. by spontaneous division of nuclei into more stable parts;

2. by spontaneously changing the charge of the nucleus by one (conversion of protons into neutrons or neutrons into protons).

Elementary particles.

Elementary particles are not molecules, atoms or nuclei. They have a radius (R) of 10-14 - 10-15 m and an energy (W) of about 106 - 108 eV. Now total number known elementary particles (together with antiparticles) approaches 400. Some of them are stable or quasi-stable and exist in nature in a free or weakly bound state. This electrons, included in the composition of atoms, their antiparticles - positrons; protons and neutrons, included in the composition of atomic nuclei; photonsγ, which are quanta of the electromagnetic field. This also includes electronic (anti)neutrinoνе, born in the processes of beta transformations and in thermonuclear reactions occurring in stars. All other elementary particles are extremely unstable and are formed in the secondary cosmic radiation or obtained in the laboratory. These include muons (mu-mesons) μ– – a heavy analogue of the electron (mμ ≈ 200mе) registered in cosmic rays; pions (pi-mesons) π+, π0, π– – carriers of nuclear interaction and others.

Every particle has an antiparticle, usually represented by the same symbol but with a "tilde" added above it. The masses, lifetimes and spins of particles and antiparticles are the same. The remaining characteristics, including electric charge and magnetic moment, are equal in magnitude, but opposite in sign.

2. Types of radioactive decay.

Radioactivity- this is the property of the atomic nuclei of certain chemical elements to spontaneously transform into the nuclei of other elements with the emission of a special kind of radiation called radioactive radiation . The phenomenon itself is called radioactive decay.

Radioactive transformations that occur in nature are called natural radioactivity. Similar processes occurring in artificially produced substances (through appropriate nuclear reactions) are artificial radioactivity. Both types of radioactivity obey the same laws.

There are the following types of nuclear transformations, or types of radioactive decay: alpha decay, beta decay (electronic, positronic), electron capture (K-capture), internal conversion, nuclear fission.

Alpha decay is the spontaneous division of an unstable atomic nucleus into an α-particle (the nucleus of a helium atom 42He) and a product nucleus (daughter nucleus). In this case, the charge of the product nucleus decreases by 2 positive units, and the mass number by 4 units. In this case, the resulting product element is shifted to the left relative to the original one by two cells of the periodic system:

Almost all (with rare exceptions) nuclei of atoms of elements with atomic number 82 and higher are alpha radioactive (those in periodic table stand behind lead 82Pb). An alpha particle, escaping from the nucleus, acquires kinetic energy about 4-9 MeV.

Beta decay is a spontaneous transformation of unstable atomic nuclei with the emission of a β-particle, in which their charge changes by one. This process is based on the ability of protons and neutrons to undergo mutual transformations.

If there is an excess of neutrons in the nucleus(“neutron overload” of the nucleus), then what happens is electron β- decay, in which one of the neutrons turns into a proton, and the nucleus emits an electron and an antineutrino (the mass and charge number of which is 0).

10n → 11p + e – + ν – || AZX → AZ+1Y + β – + ν – +Q || 4019K → 4020Ca + β – + ν – + Q.

During this decay, the charge of the nucleus and, accordingly, the atomic number of the element increase by one (the element shifts in the periodic table by one number to the right from the original one), but the mass number remains unchanged. Electronic beta decay is characteristic of many natural and artificially produced radioactive elements.

If the unfavorable ratio of neutrons and protons in the nucleus is due to excess protons, then positronic ( β+ ) decay, in which the nucleus emits a positron (a particle of the same mass as an electron, but with a charge of +1) and a neutrino, and one of the protons turns into a neutron:

11p → 10n + e+ + ν+ || AZX → AZ-1Y + β+ + ν+ +Q || 3015P → 3014Si + β+ + ν+ +Q

The charge of the nucleus and, accordingly, the atomic number of the element decrease by one, and the daughter element will occupy a place in the periodic table one number to the left of the original one, the mass number remains unchanged. Positron decay is observed in some artificially obtained isotopes.

A positron, having flown out of the nucleus, tears off an “extra” electron from the shell of the atom or interacts with a free electron, forming a “positron-electron” pair, which instantly turns into two gamma quanta with an energy equivalent to the mass of the particles (e+ and e-) 0.511 MeV. The process of transforming a positron-electron pair into two γ quanta is called annihilation(destruction), and the resulting electromagnetic radiation - annihilation. Thus, during positron decay, not particles fly outside the parent atom, but two gamma rays with an energy of 0.511 MeV.

The energy spectrum of β-particles of any beta source is continuous (from hundredths of MeV - soft radiation, to 2-3 MeV - hard radiation).

Electronic capture– spontaneous transformation of an atomic nucleus, in which its charge decreases by one due to the capture of one of the orbital electrons and the transformation of a proton into a neutron.

This occurs if there is an excess of protons in the nucleus, but not enough energy for positron decay. One of the protons of the nucleus captures an electron from one of the shells of the atom, most often from the K-layer closest to it (K-capture) or, less commonly, the L-layer (L-capture) and turns into a neutron with the emission of neutrinos. In this case, the daughter element, as in positron decay, is shifted in the periodic table by one cell to the left of the original one.

11p + 0-1е → 10n + ν+ || AZX + 0-1е → AZ-1Y + ν+ + hν || 12352Te + 0-1е → 12351Sb + ν+ + hν

An electron jumps to the vacant place in the K-layer from the L-layer, to the place of the latter from the next layer, etc. Each transition of an electron from layer to layer is accompanied by the release of energy in the form of quanta of electromagnetic radiation (X-ray range).

Positron decay and electron capture, as a rule, are observed only in artificially radioactive isotopes (4).

Nuclear fission- this is the spontaneous fission of the nucleus, in which it, without any external influence, breaks up into two, usually unequal parts. Thus, a uranium nucleus can be divided into barium (56Ba) and krypton (36Kr) nuclei. This type of decay is typical for isotopes of elements beyond uranium in the periodic table. Under the influence of electrostatic repulsion forces of like charges, the fragment nuclei acquire a kinetic energy of the order of 165 MeV and scatter into different sides at enormous speeds.

Internal conversion. The excited nucleus transfers the excitation energy to one of the electrons of the inner layers (K-, L-, or M-layer), which as a result escapes outside the atom. Then one of the electrons from more distant layers (from higher energy levels) makes a quantum transition to the “vacant” place with the emission of characteristic X-ray radiation.

3. The law of radioactive decay.

The amount of any radioactive isotope decreases over time due to radioactive decay (transformation of nuclei). Radioactive decay occurs continuously, the rate of this process and its nature are determined by the structure of the nucleus. Therefore, this process cannot be influenced by any ordinary physical or chemical means without changing the state of the atomic nucleus. In addition, decay is probabilistic in nature, that is, it is impossible to determine exactly when and which atom will decay, but in each period of time, on average, some kind of atom will decay. certain part atoms.

For each radioactive isotope average speed the decay of its atoms is constant, unchanging and characteristic only of a given isotope. The radioactive decay constant λ for a particular isotope shows what proportion of nuclei will decay per unit time. The decay constant is expressed in reciprocal time units s-1, min-1, h-1, etc., to show that the number of radioactive nuclei decreases over time, rather than increasing.

The spontaneous transformation of the nuclei of any radioactive isotope is subject to the law of radioactive decay, which establishes that the same fraction of available nuclei decays per unit time.

The mathematical expression of this law, which describes the process of decreasing the number of radioactive nuclei over time, is displayed by the following formula:

Nt = N0e-λt, (Nt = N0e-0.693t/T) (1),

where, Nt is the number of radioactive nuclei remaining after time;

N0 – initial number of radioactive nuclei at time t=0;

λ – radioactive decay constant (=0.693/T);

T is the half-life of a given radioisotope.

In practice, half-life is used to characterize the rate of decay of radioactive elements.

Half life is the time during which half of the original number of radioactive nuclei decays. It is denoted by the letter T and is expressed in units of time.

For various radioactive isotopes, half-lives range from fractions of a second to millions of years. Moreover, the same element can have isotopes with different half-lives. Accordingly, radioactive elements are divided into short-lived (hours, days) - 13153I (8.05 days), 21484Po (1.64 * 10-4 sec.) and long-lived (years) - 23892U (T = 4.47 billion years), 13755Cs ( 30 years), 9038Sr (29 years).

There is an inverse relationship between the half-life and the decay constant, i.e., the larger λ, the smaller T, and vice versa.

Graphically, the law of radioactive decay is expressed by an exponential curve (Fig. 2.1.). As can be seen from the figure, with an increase in the number of half-lives, the number of undecayed atoms decreases, gradually approaching zero [et al., 1999].

Rice. 2.1. Graphic representation of the law of radioactive decay.

Radioactive element activity equal to the number of decays per unit time. The more radioactive transformations experience the atoms of a given substance, the higher its activity. As follows from the law of radioactive decay, the activity of a radionuclide is proportional to the number of radioactive atoms, that is, it increases with increasing amount of a given substance. Since the decay rate of radioactive isotopes is different, equal amounts of different radionuclides by mass have different activities.

The SI unit of activity is the becquerel (Bq) - disintegration per second (dec/s). Along with Bq, a non-systemic unit is used - the curie (Ci). 1Ki is the activity of anyone radioactive substance(isotope) in which 3.7 * 1010 decay events occur per second. A unit of curie corresponds to the radioactivity of 1 g of radium.

1Ci = 3.7*1010 Bq; 1 mCi = 37 MBq 1 μCi = 37 kBq

The activity of any radioactive drug after time t is determined by the formula corresponding to the basic law of radioactive decay:

At =A0e-0.693t/T (2),

where At is the activity of the drug after time t;

A0 – initial activity of the drug;

e – base natural logarithms(e=2.72);

t is the time during which the radioisotope decayed;

T – half-life; the T and t values ​​must have the same dimensions (min., sec., hours, days, etc.).

(Example: The A0 activity of the radioactive element 32P on a certain day is 5 mCi. Determine the activity of this element after a week. The half-life T of the element 32P is 14.3 days. The activity of 32P after 7 days. At = 5 * 2,720,693*7/14.3 = 5 * 2.720.34 = 3.55 mCi).

Curie units (Ci) are not suitable for characterizing the gamma activity of sources. For these purposes, another unit was introduced - the equivalent of 1 mg of radium (mg-eq. radium). Milligram equivalent of radium - this is the activity of any radioactive drug, the gamma radiation of which, under identical measurement conditions, creates the same exposure dose rate as the gamma radiation of 1 mg of radium of the State Standard of Radium of the Russian Federation when using a platinum filter 0.5 mm thick. The milligram equivalent unit of radium is not established by existing standards, but is widely used in practice.

A point source of 1 mg (1 mCi) of radium, in equilibrium with the decay products, after initial filtration through a 0.5 mm thick platinum plate creates a dose rate of 8.4 R/h in the air at a distance of 1 cm. This quantity is called ionization gamma constant of radium and denoted by the letter Kγ . The gamma constant of radium is taken as the standard for radiation dose rate. The Kγ of all other gamma emitters is compared with it. There are tables of gamma constants for most radioactive isotopes.

Thus, the gamma constant of 60Co is 13.5 R/h. A comparison of the gamma constants of radium and 60Co shows that 1 mCi of the radionuclide 60Co creates a radiation dose 1.6 times greater than 1 mCi of radium (13.5/8.4 = 1.6). In other words, in terms of the radiation dose created in the air, 1 mCi of radionuclide 60Co is equivalent to 1.6 mCi of radium, i.e., gamma radiation emitted by the drug 60Co with an activity of 0.625 mCi creates the same radiation dose as 1 mCi of radium.

The gamma equivalent of the M isotope is related to its activity A (mCi) through the ionization gamma constant Kγ by the relations:

M = AKγ/8.4 or A = 8.4M/Kγ (3),

which allow us to move from the activity of a radioactive substance, expressed in mEq. radium to activity expressed in mCi and vice versa.

A variety of atoms whose nuclei have a certain number of nucleons (protons and neutrons) is called nuclide.

The symbolic notation for nuclides includes the chemical symbol for the nucleus X and indexes at the bottom left “ Z"(number of protons in the nucleus) and “ A" at the top left is the total number of nucleons. For example,

Depending on the nucleon content, nuclides can be combined into various groups: isotopes, isobars, isotones.

Isotopic nuclides (isotopes) are nuclides that have the same number of protons. They differ only in the number of neutrons. Therefore, all isotopes belong to the same chemical element. For example, isotopes

are isotopes of the same element uranium (Z= const).

Since isotopes have the same number of protons and the same structure of electron shells, they are twin atoms; their chemical properties are almost the same. The exception is the isotopes of hydrogen - protium H, deuterium D, tritium T, which, due to too large a relative difference in atomic masses, differ significantly in physical and chemical properties (Table 2.1).

Table 2.1 Comparison of the properties of ordinary and heavy water

	Properties
	Boiling point, 0 C
	Critical temperature, 0 C
	Liquid density at 298.15 K, kg/dm 3
	Dielectric constant at 298.15 K
	Temperature of maximum density, 0 C
	Melting point, 0 C
	Ice density at melting point, kg/dm 3

Chemical transformations with heavy hydrogen occur more slowly than with its light isotope.

Isotonic nuclides (isotones) are nuclides with the same number of neutrons and different numbers of protons. Examples of isotones: Ca and Ti, which belong to different nuclides. This term is used extremely rarely.

Isobars are called a variety of nuclides whose nuclei have different numbers of protons and neutrons, but have the same number of nucleons. Example of isobars: Ti and Ca.

Therefore, we can say that nuclides with the same number of protons are different isotopes of the same element; nuclides with the same number of nucleons are isobars; nuclides with the same number of neutrons are isotones.

2.4 Core energy

Energy is one of the most important characteristics of any physical process. IN nuclear physics its role is especially great, since the inviolability of the law of conservation of energy makes it possible to make accurate calculations even in cases where many details of the phenomena remain unknown. In relation to the nucleus, let's look at several different forms of energy.

2.4.1 Rest energy

According to the theory of relativity, the mass of an atom m you can compare the total rest energy

If in this formula With express in meters per second, and m- in kilograms, then E 0 will be in joules. Let us denote by m 0 unit atomic mass, expressed in kilograms: m 0 = 1.66∙10 -27 kg . Then m= m 0 A r and E 0 = A r m 0 c 2 . Size m 0 c 2 easy to calculate in joules and then in electron volts: m 0 c 2 = 931.5 MeV. From here

E 0 = 931.5A r . (2.6)

Here A r- relative atomic mass, E 0 - total rest energy of the atom, MeV.

Back in the 5th century BC, the Greek thinkers Leucippus and Democritus formulated the results of their reflections on the structure of matter in the form of an atomic hypothesis: matter cannot be endlessly divided into smaller and smaller parts, there are “final”, indivisible particles of matter. All material objects are made up of a variety of atoms

(from Greek atomos-- “indivisible”, “uncut”). Connecting various types atoms form new substances.

According to legend, Democritus, sitting on a rock by the sea, held an apple in his hand and thought: “If I cut this apple with a knife into smaller and smaller pieces, will I always have a part in my hands that still has the properties of an apple?” Having considered this hypothesis, Democritus came to the following conclusions: “The beginning of the Universe is atoms and emptiness, everything else exists only in opinion. There are countless worlds, and they have a beginning and an end in time. And nothing arises from non-existence, nothing is resolved into non-existence. And the atoms are countless in size and multitude, but they rush around the universe, whirling in a whirlwind, and thus everything complex is born: fire, water, air, earth... Atoms are not susceptible to any influence and are unchangeable due to their hardness.”

The beginning of the 19th century saw the emergence of the theory of the atomic-molecular structure of the world. It was possible to prove experimentally that each chemical element consists of identical atoms only in 1808.

This was done by the English chemist and physicist John Dalton, who went down in history as the creator of chemical atomism. Dalton imagined atoms in the form of elastic balls and believed in them so much real existence that he even drew oxygen and nitrogen atoms on paper.

In 1811, the Italian physicist and chemist Amedeo Avogadro put forward a hypothesis according to which the molecules of simple gases consist of one or more atoms. Based on this hypothesis, Avogadro formulated one of the fundamental laws ideal gases and a method for determining atomic and molecular masses.

He discovered one of the gas laws, named after him. On its basis, a method for determining molecular and atomic weights was developed. So, all substances in nature consist of atoms. They are usually divided into simple ones, consisting of atoms of the same elements (O2, N2, H2, etc.), and complex ones, which include atoms various elements(H2O, NaCl, H2SO4, etc.).

An atom is the smallest structural unit of any of the simplest chemicals, called elements.

Although the concept of an atom, like the term itself, is of ancient Greek origin, it was only in the twentieth century that the truth of the atomic hypothesis of the structure of substances was firmly established.

The size and mass of atoms are extremely small. Thus, the diameter of the lightest atom (hydrogen) is only 0.53. 10-8 cm, and its mass is 1.67. 10-24 years

Research Development radioactive radiation, on the one hand, and quantum theory, on the other, led to the creation Rutherford's quantum model of the atom-Bora. After the discovery of the electron in 1897 by Joseph John Thomson, he discovered that charged particles are detached from atoms when exposed to a strong electric field. According to his estimates, the mass of the “electricity atom” is about a thousand times less than the mass of a hydrogen atom, and the charge exactly matches the charge of the hydrogen ion.

Later, already in 1910 and 1913, Robert Millikan greatly improved the accuracy of measurements of the charge and mass of the electron. So, despite individual opinions, by the end of the 19th century it became clear that particles even smaller than atoms actually exist, and that, most likely, they are part of atoms and are carriers of some small amount of electricity.

Joseph Thomson, developing W. Thomson's model, in 1903 proposed his own model of the atom (“pudding with raisins”): electrons are interspersed in the positive sphere. They are held inside a positively charged sphere by elastic forces. Those of them that are on the surface can be “knocked out” quite easily, leaving an ionized atom in Fig. 1.

Rice. 1.

In multielectron atoms, electrons are arranged in stable configurations calculated by Thomson. He considered each such configuration to determine the chemical properties of atoms. J. Thomson attempted to theoretically explain periodic table elements D.I. Mendeleev.

Niels Bohr later pointed out that since this attempt the idea of ​​dividing the electrons in an atom into groups became the starting point. In 1911, Joseph Thomson developed the so-called parabola method for measuring the ratio of a particle's charge to its mass, which played a major role in the study of isotopes.

In 1903, with the idea of planetary model of atomic structure The Japanese theorist Hantaro Nagaoka spoke at the Tokyo Physics and Mathematics Society, calling this model “Saturn-like.”

H. Nagaoka presented the structure of the atom as similar to the structure of the solar system: the role of the Sun is played by the positively charged central part of the atom, around which “planets” - electrons - move in established ring-shaped orbits. At slight displacements, electrons excite electromagnetic waves. But his work, which E. Rutherford did not know about, was not further developed.

But it soon turned out that new experimental facts refute Joseph Thomson’s model and, on the contrary, testify in favor of the planetary model. These facts were discovered by the outstanding English physicist E. Rutherford. First of all, it should be noted that he discovered the nuclear structure of the atom.

Joseph Thomson's student Ernest Rutherford, as a result of his famous experiments on the scattering of b-particles by gold foil, “divided” the atom into a small positively charged nucleus and electrons surrounding it (Fig. 2).

In 1908-1909 Hans Geiger, who worked at the University of Victoria (Manchester, England) with Rutherford, who had recently designed an alpha particle counter together with him, and Ernest Marsden established that when alpha particles pass through thin plates of gold foil, the vast majority of them fly right through, but single particles are deflected at angles greater than 90°, i.e. are completely reflected.

Rice. 2.

Most of the alpha particles flew through the foil, only a small part of them were reflected, and E. Rutherford realized that alpha particles were reflected when they hit small, massive objects, and that these objects were located far from each other. This is how atomic nuclei were discovered. The volume of the nucleus turned out to be millions of billions of times less than the volume of the atom, and this negligibly small volume contained almost all the substance of the atom.

By this time they already knew that electric current is a stream of particles, these particles are called electrons. And here Rutherford turned to the planetary model of the structure of the atom.

According to her, he resembled a miniature solar system, in which “planets” - electrons rotate around the “Sun” - core (Fig. 3).

Rice. 3.

Thanks to Rutherford's work, it became clear how atoms are structured: in the middle of the atom there is a tiny massive nucleus, and electrons “swarm” around the nucleus and form a light shell of the atom. In this case, the electrons, located and rotating in different planes, create a negative total charge, and the nucleus creates a positive one. In general, the atom remains electrically neutral, since the positive charge of the nucleus is completely compensated by the negative charge of the electrons.

However, according to the laws of classical mechanics and electrodynamics, the rotation of an electron around a nucleus must be accompanied by electromagnetic radiation with a continuous spectrum.

But this contradicted the line spectra of gases and vapors of chemical elements, known since 1880.

The contradiction was resolved in 1913 by Rutherford's student, the Danish physicist Niels Bohr, who developed a quantum model of the structure of the atom based on the quantum theory of radiation and absorption of light created by Max Planck and Albert Einstein.

(December 14, 1900) Planck demonstrated the derivation of this formula, based on the assumption that the energy of the oscillator is an integer multiple of hv, where v is the frequency of radiation, and h is a new universal constant, called by Max Planck the elementary quantum of action (now it is a constant Planck). The introduction of this quantity was the beginning of the era of new, quantum physics.

Niels Bohr put forward the assumption that the hydrogen atom (proton-electron system) can only be in certain stationary energy states (electrons in certain orbits), and one of them corresponds to the minimum energy and is ground (unexcited). The emission or absorption of energy by an atom can occur, according to Bohr's theory, only during electron transitions from one energy state to another (from one orbit to another).

Based on this, Bohr formulated his postulates:

• 1. An electron in an atom is in a “stationary” state (moving in a stationary orbit) and does not emit any energy.
• 2. Being removed from the stationary state (transferred to another orbit), the electron, returning, emits a quantum of light hn = E2 - E1.
• 3. An electron in an atom can only be in those “allowed” orbits for which the angular momentum (mvr) takes on certain discrete values, namely mvr = nh/2p, where n is an integer 1, 2, 3...

The nuclear charge turned out to be the most important characteristic atom. In 1913 it was shown that the charge of the nucleus coincides with the number of the element in the periodic table.

Bohr's theory made it possible to very accurately calculate the position of lines in the emission spectrum of atomic hydrogen. However, she could not predict the ratio of line intensities even in this simplest system.

For systems containing more than one electron, for example a helium atom, Bohr's theory no longer gave exact values spectral lines.

Therefore, in 1923-26 Louis de Broglie (France), Werner Heisenberg (Germany) and Erwin Schrödinger (Austria) developed a new theory of quantum (wave) mechanics.

The brilliant idea expressed by Heisenberg was to treat quantum events as phenomena on a completely different level than in classical physics. He approached them as phenomena that did not allow for precise visual representation, for example, using a picture of electrons rotating in orbits.

A few months later, E. Schrödinger proposed a different formulation of quantum mechanics, describing these phenomena in the language of wave concepts.

Schrödinger's approach originated in the work of Louis de Broglie, who hypothesized the so-called waves of matter: just as light, traditionally considered waves, can have corpuscular properties (photons or quanta of radiation), particles can have wave properties. It was later proven that matrix and wave mechanics are essentially equivalent. Taken together, they form what is now called quantum mechanics. Soon, this mechanics was expanded by the English theoretical physicist of the 20th century, Paul Dirac (Nobel Prize in Physics, 1933), who included elements of Einstein’s theory of relativity in the wave equation, taking into account the electron spin.

At the core modern theory The structure of the atom is based on the following basic principles:

1). the electron has a dual (particle-wave) nature. It can behave both as a particle and as a wave. Like a particle, an electron has a certain mass and charge. At the same time, a moving electron exhibits wave properties, i.e. for example, it is characterized by diffraction ability. The electron wavelength l and its speed v are related by the de Broglie relation:

where m is the electron mass;

• 2). It is impossible for an electron to simultaneously accurately measure its position and velocity. The more accurately we measure the speed, the greater the uncertainty in the coordinate, and vice versa. The mathematical expression of the uncertainty principle is the relation: ?x m ?v > ћ/2, where?x is the uncertainty of the coordinate position; ?v - speed measurement error;
• 3). electron in an atom does not move along certain trajectories, but can

be in any part of the perinuclear space, but the probability of its being in different parts this space is not the same. The space around the nucleus in which the probability of finding an electron is quite high is called an orbital;

4). atomic nuclei are made up of protons and neutrons ( common name- nucleons). The number of protons in the nucleus is equal to the atomic number of the element, and the sum of the numbers of protons and neutrons corresponds to its mass number.

In 1932, our domestic physicist Dmitry Dmitrievich Ivanenko and the German scientist Werner Heisenberg (Heisenberg) independently suggested that the neutron, along with the proton, is a structural element of the nucleus.

However, the proton-neutron model of the nucleus was met with skepticism by most physicists. Even E. Rutherford believed that a neutron is just a complex formation of a proton and an electron.

In 1933, Dmitry Ivanenko gave a report on the nuclear model, in which he defended the proton-neutron model, formulating the main thesis: there are only heavy particles in the nucleus. Ivanenko rejected the idea of ​​a complex structure of the neutron and proton. In his opinion, both particles should have the same degree of elementarity, i.e. both a neutron and a proton are capable of transforming into each other.

Subsequently, the proton and neutron began to be considered as two states of one particle - the nucleon, and Ivanenko’s idea became generally accepted, and in 1932 another elementary particle was discovered in cosmic rays - the positron.

Currently, there is a hypothesis about the divisibility of a number of elementary particles into quark subparticles.

Quarks are hypothetical particles from which it is assumed that all known elementary particles participating in strong interactions (hadrons) may consist.

The hypothesis about the existence of quarks was put forward in 1964 independently by the American physicist Marie Gell-Mann and the Austrian (and subsequently American) scientist Georg(George) Zweig in order to explain the laws established for hadrons.

By the way, the term “quark” does not have an exact translation. It has a purely literary origin: it was borrowed by Gell-Mann from J. Joyce’s novel “Finnegans Wake”, where it meant “something vague”, “mystical”. This name for the particles was obviously chosen because quarks exhibited a number of unusual properties that set them apart from all known elementary particles (for example, fractional electric charge).

Figure 4 shows modern model structure of the atom.

Rice. 4.

So, atoms consist of three types of elementary particles. At the center of the atom there is a nucleus formed by protons and neutrons. Electrons rotate rapidly around it, forming so-called electron clouds. The number of protons in the nucleus is equal to the number of electrons moving around it. The mass of a proton is approximately equal to the mass of a neutron. The mass of an electron is much less than their masses (1836 times).