The atomic nucleus is the central part of the atom, in which its main mass is concentrated (more than 99.9%). The nucleus is positively charged, the charge of the nucleus determines the chemical element to which the atom is assigned. The dimensions of the nuclei of various atoms are several femtometers, which is more than 10 thousand times smaller than the size of the atom itself.

The atomic nucleus, considered as a class of particles with a certain number of protons and neutrons, is commonly called a nuclide. The number of protons in the nucleus is called its charge number - this number is equal to the ordinal number of the element to which the atom belongs, in the table (Periodic system of elements) of Mendeleev. The number of protons in the nucleus determines the structure of the electron shell of a neutral atom and thus the chemical properties of the corresponding element. The number of neutrons in a nucleus is called its isotopic number. Nuclei with the same number of protons and different numbers of neutrons are called isotopes.

In 1911, Rutherford, in his report "Scattering of α- and β-rays and the structure of the atom" in the Philosophical Society of Manchester, stated:

The scattering of charged particles can be explained by assuming an atom that consists of a central electric charge concentrated at a point and surrounded by a uniform spherical distribution of opposite electricity of equal magnitude. With such a structure of the atom, α- and β-particles, when they pass at a close distance from the center of the atom, experience large deviations, although the probability of such a deviation is small.

Thus, Rutherford discovered the atomic nucleus, from that moment nuclear physics began, studying the structure and properties of atomic nuclei.

After the discovery of stable isotopes of elements, the nucleus of the lightest atom was assigned the role of a structural particle of all nuclei. Since 1920, the nucleus of the hydrogen atom has been officially termed proton. After the intermediate proton-electron theory of the structure of the nucleus, which had many obvious shortcomings, first of all, it contradicted the experimental results of measurements of the spins and magnetic moments of nuclei, in 1932 James Chadwick discovered a new electrically neutral particle, called the neutron. In the same year, Ivanenko and, independently, Heisenberg put forward a hypothesis about the proton-neutron structure of the nucleus. Later, with the development of nuclear physics and its applications, this hypothesis was fully confirmed.

Radioactivity

Radioactive decay (from Latin radius "beam" and āctīvus "effective") is a spontaneous change in the composition (charge Z, mass number A) or the internal structure of unstable atomic nuclei by emitting elementary particles, gamma quanta and / or nuclear fragments. The process of radioactive decay is also called radioactivity, and the corresponding nuclei (nuclides, isotopes and chemical elements) are radioactive. Substances containing radioactive nuclei are also called radioactive.

The law of radioactive decay is a law discovered experimentally by Frederick Soddy and Ernest Rutherford and formulated in 1903. The modern wording of the law:

which means that the number of decays in 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 expression, λ is the decay constant, which characterizes the probability of radioactive decay per unit time and has the dimension c −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 decay of a given nucleus in each subsequent unit of time does not depend on the time that has elapsed since the beginning of the experiment, and on the number of nuclei remaining in the sample.

The solution to this differential equation is:

Or , where T is the half-life equal to the time during which the number of radioactive atoms or the activity of the sample decreases by 2 times.

12. Nuclear reactions.

A nuclear reaction is the process of interaction of an atomic nucleus with another nucleus or elementary particle, accompanied by a change in the composition and structure of the nucleus. The consequence of the interaction may be the fission of the nucleus, the emission of elementary particles or photons. The kinetic energy of the newly formed particles can be much higher than the initial one, and one speaks of the release of energy by a nuclear reaction.

Types of nuclear reactions

Nuclear fission reaction - the process of splitting an atomic nucleus into two (rarely three) nuclei with similar masses, called fission fragments. As a result of fission, other reaction products can also appear: light nuclei (mainly alpha particles), neutrons and gamma quanta. Fission can be spontaneous (spontaneous) and forced (as a result of interaction with other particles, primarily with neutrons). The fission of heavy nuclei is an exoenergetic process, as a result of which a large amount of energy is released in the form of the kinetic energy of the reaction products, as well as radiation.

Nuclear fission serves as a source of energy in nuclear reactors and nuclear weapons.

Nuclear fusion reaction - the process of fusion of two atomic nuclei with the formation of a new, heavier nucleus.

In addition to the new nucleus, in the course of the fusion reaction, as a rule, various elementary particles and (or) quanta of electromagnetic radiation are also formed.

Without the supply of external energy, the fusion of nuclei is impossible, since positively charged nuclei experience electrostatic repulsion forces - this is the so-called "Coulomb barrier". To synthesize nuclei, it is necessary to bring them closer to a distance of about 10 −15 m, at which the strong interaction will exceed the electrostatic repulsion forces. This is possible if the kinetic energy of the approaching nuclei exceeds the Coulomb barrier.

photonuclear reaction

When a gamma quantum is absorbed, the nucleus receives an excess of energy without changing its nucleon composition, and a nucleus with an excess of energy is a compound nucleus. Like other nuclear reactions, the absorption of a gamma-quantum by the nucleus is possible only if the necessary energy and spin ratios are met. If the energy transferred to the nucleus exceeds the binding energy of the nucleon in the nucleus, then the decay of the resulting compound nucleus occurs most often with the emission of nucleons, mainly neutrons.

Recording nuclear reactions

the method of writing formulas for nuclear reactions is similar to writing formulas for chemical reactions, that is, the sum of the initial particles is written on the left, the sum of the resulting particles (reaction products) is written on the right, and an arrow is placed between them.

Thus, the reaction of radiative capture of a neutron by a cadmium-113 nucleus is written as follows:

We see that the number of protons and neutrons on the right and left remains the same (the baryon number is preserved). The same applies to electric charges, lepton numbers and other quantities (energy, momentum, angular momentum, ...). In some reactions where the weak interaction is involved, protons can turn into neutrons and vice versa, but their total number does not change.

An atom consists of a positively charged nucleus and surrounding electrons. Atomic nuclei have dimensions of approximately 10 -14 ... 10 -15 m (the linear dimensions of an atom are 10 -10 m).

The atomic nucleus is made up of elementary particles protons and neutrons. The proton-neutron model of the nucleus was proposed by the Russian physicist D. D. Ivanenko, and subsequently developed by V. Heisenberg.

Proton ( R) has a positive charge equal to that of an electron and a rest mass t p = 1.6726∙10 -27 kg 1836 m e, where m e is the mass of the electron. Neutron ( n)-neutral particle with rest mass m n= 1.6749∙10 -27 kg 1839t e ,. The mass of protons and neutrons is often expressed in other units - in atomic mass units (a.m.u., a unit of mass equal to 1/12 of the mass of a carbon atom
). The masses of the proton and neutron are approximately equal to one atomic mass unit. Protons and neutrons are called nucleons(from lat. nucleus-kernel). The total number of nucleons in an atomic nucleus is called the mass number BUT).

The radii of the nuclei increase with increasing mass number in accordance with the relation R= 1,4BUT 1/3 10 -13 cm.

Experiments show that nuclei do not have sharp boundaries. There is a certain density of nuclear matter in the center of the nucleus, and it gradually decreases to zero with increasing distance from the center. Due to the lack of a well-defined boundary of the nucleus, its "radius" is defined as the distance from the center at which the density of nuclear matter is halved. The average matter density distribution for most nuclei turns out to be not just spherical. Most of the nuclei are deformed. Often the nuclei are in the form of elongated or flattened ellipsoids.

The atomic nucleus is characterized chargeZe, where Zcharge number nucleus, equal to the number of protons in the nucleus and coinciding with the serial number of the chemical element in the Periodic system of elements of Mendeleev.

The nucleus is denoted by the same symbol as the neutral atom:
, where X- symbol of a chemical element, Z atomic number (number of protons in the nucleus), BUT- mass number (number of nucleons in the nucleus). Mass number BUT approximately equal to the mass of the nucleus in atomic mass units.

Since the atom is neutral, the charge of the nucleus Z determines the number of electrons in an atom. The number of electrons depends on the distribution over states in the atom. The charge of the nucleus determines the specifics of a given chemical element, i.e., determines the number of electrons in an atom, the configuration of their electron shells, the magnitude and nature of the intraatomic electric field.

Nuclei with the same charge numbers Z, but with different mass numbers BUT(i.e. with different numbers of neutrons N=A-Z) are called isotopes, and nuclei with the same BUT, but different Z- isobars. For example, hydrogen ( Z= l) has three isotopes: H - protium ( Z=l, N= 0), H - deuterium ( Z=l, N= 1), H - tritium ( Z=l, N\u003d 2), tin - ten isotopes, etc. In the vast majority of cases, isotopes of the same chemical element have the same chemical and almost the same physical properties.

E, MeV

Energy levels

and observed transitions for the boron atom nucleus

Quantum theory strictly limits the energy values ​​that the constituent parts of nuclei can have. Sets of protons and neutrons in nuclei can only be in certain discrete energy states characteristic of a given isotope.

When an electron changes from a higher to a lower energy state, the energy difference is emitted in the form of a photon. The energy of these photons is of the order of several electron volts. For nuclei, the level energies lie in the range from approximately 1 to 10 MeV. During transitions between these levels, photons of very high energies (γ-quanta) are emitted. To illustrate such transitions in Fig. 6.1 shows the first five energy levels of the nucleus
.Vertical lines indicate observed transitions. For example, a γ-quantum with an energy of 1.43 MeV is emitted during the transition of the nucleus from a state with an energy of 3.58 MeV to a state with an energy of 2.15 MeV.

atomic nucleus
Atomic nucleus

atomic nucleus - the central and very compact part of the atom, in which almost all of its mass and all positive electric charge are concentrated. The nucleus, holding electrons close to itself by Coulomb forces in an amount that compensates for its positive charge, forms a neutral atom. Most of the nuclei have a shape close to spherical and a diameter of ≈ 10 -12 cm, which is four orders of magnitude smaller than the diameter of an atom (10 -8 cm). The density of matter in the core is about 230 million tons/cm 3 .
The atomic nucleus was discovered in 1911 as a result of a series of experiments on the scattering of alpha particles by thin gold and platinum foils, carried out in Cambridge (England) under the direction of E. Rutherford. In 1932, after the discovery of the neutron by J. Chadwick, it became clear that the nucleus consists of protons and neutrons
(V. Heisenberg, D.D. Ivanenko, E. Majorana).
To designate the atomic nucleus, the symbol of the chemical element of the atom, which includes the nucleus, is used, and the upper left index of this symbol shows the number of nucleons (mass number) in this nucleus, and the lower left index shows the number of protons in it. For example, a nickel nucleus containing 58 nucleons, of which 28 are protons, is denoted. The same nucleus can also be designated 58 Ni, or nickel-58.

The nucleus is a system of densely packed protons and neutrons moving at a speed of 10 9 -10 10 cm/sec and held by powerful and short-range nuclear forces of mutual attraction (their area of ​​action is limited by distances of ≈ 10 -13 cm). Protons and neutrons are about 10 -13 cm in size and are considered as two different states of a single particle called a nucleon. The radius of the nucleus can be approximately estimated by the formula R ≈ (1.0-1.1)·10 -13 A 1/3 cm, where A is the number of nucleons (the total number of protons and neutrons) in the nucleus. On fig. 1 shows how the density of matter changes (in units of 10 14 g/cm3) inside the nickel nucleus, consisting of 28 protons and 30 neutrons, depending on the distance r (in units of 10 -13 cm) to the center of the nucleus.
Nuclear interaction (interaction between nucleons in the nucleus) arises due to the fact that nucleons exchange mesons. This interaction is a manifestation of the more fundamental strong interaction between quarks that make up nucleons and mesons (similarly, chemical bonding forces in molecules are a manifestation of more fundamental electromagnetic forces).
The world of nuclei is very diverse. About 3000 nuclei are known, differing from each other either in the number of protons, or in the number of neutrons, or both. Most of them are obtained artificially.
Only 264 cores are stable, ie. do not experience any spontaneous transformations, called decays, over time. The rest experience various forms of decay - alpha decay (emission of an alpha particle, i.e. the nucleus of a helium atom); beta decay (simultaneous emission of an electron and an antineutrino or a positron and a neutrino, as well as the absorption of an atomic electron with the emission of a neutrino); gamma decay (photon emission) and others.
Different types of nuclei are often referred to as nuclides. Nuclides with the same number of protons and different numbers of neutrons are called isotopes. Nuclides with the same number of nucleons but different ratios of protons and neutrons are called isobars. Light nuclei contain approximately equal numbers of protons and neutrons. In heavy nuclei, the number of neutrons is about 1.5 times the number of protons. The lightest nucleus is the nucleus of the hydrogen atom, which consists of one proton. The heaviest known nuclei (they are obtained artificially) have a number of nucleons of ≈290. Of these, 116-118 are protons.
Different combinations of the number of protons Z and neutrons correspond to different atomic nuclei. Atomic nuclei exist (i.e. their lifetime t > 10 -23 s) in a rather narrow range of changes in the numbers Z and N. In this case, all atomic nuclei are divided into two large groups - stable and radioactive (unstable). Stable nuclei cluster near the line of stability, which is given by the equation

Rice. 2. NZ-diagram of atomic nuclei.

On fig. 2 shows an NZ diagram of atomic nuclei. Black dots show stable nuclei. The area where stable nuclei are located is usually called the stability valley. On the left side of the stable nuclei are nuclei overloaded with protons (proton-rich nuclei), on the right - nuclei overloaded with neutrons (neutron-rich nuclei). Atomic nuclei currently discovered are highlighted in color. There are about 3.5 thousand of them. It is believed that there should be 7 - 7.5 thousand of them in total. Proton-rich nuclei (crimson color) are radioactive and turn into stable ones mainly as a result of β + decays, the proton that is part of the nucleus turns into a neutron. Neutron-rich nuclei (blue color) are also radioactive and become stable as a result of - -decays, with the transformation of a nucleus neutron into a proton.
The heaviest stable isotopes are those of lead (Z = 82) and bismuth (Z = 83). Heavy nuclei, along with the processes of β + and β - decay, are also subject to α-decay (yellow color) and spontaneous fission, which become their main decay channels. The dotted line in fig. 2 outlines the region of possible existence of atomic nuclei. The line B p = 0 (B p is the proton separation energy) limits the region of existence of atomic nuclei on the left (proton drip-line). The line B n = 0 (B n is the neutron separation energy) is on the right (neutron drip-line). Outside these boundaries, atomic nuclei cannot exist, since they decay in a characteristic nuclear time (~10 -23 – 10 -22 s) with the emission of nucleons.
When connecting (synthesis) of two light nuclei and fission of a heavy nucleus into two lighter fragments, a lot of energy is released. These two methods of obtaining energy are the most efficient of all known. So 1 gram of nuclear fuel is equivalent to 10 tons of chemical fuel. The fusion of nuclei (thermonuclear reactions) is the source of energy for stars. Uncontrolled (explosive) fusion is carried out when a thermonuclear (or so-called “hydrogen”) bomb is detonated. Controlled (slow) synthesis underlies a promising energy source being developed - a thermonuclear reactor.
Uncontrolled (explosive) fission occurs during the explosion of an atomic bomb. Controlled fission is carried out in nuclear reactors, which are sources of energy in nuclear power plants.
For the theoretical description of atomic nuclei, quantum mechanics and various models are used.
The nucleus can behave both as a gas (quantum gas) and as a liquid (quantum liquid). Cold nuclear liquid has the properties of superfluidity. In a strongly heated nucleus, nucleons decay into their constituent quarks. These quarks interact by exchanging gluons. As a result of such a decay, the set of nucleons inside the nucleus turns into a new state of matter - quark-gluon plasma

The questions “What is matter made of?”, “What is the nature of matter?” has always occupied mankind. Since ancient times, philosophers and scientists have been looking for answers to these questions, creating both realistic and completely amazing and fantastic theories and hypotheses. However, literally a century ago, humanity came as close as possible to unraveling this mystery by discovering the atomic structure of matter. But what is the composition of the nucleus of an atom? What does everything consist of?

From theory to reality

By the beginning of the twentieth century, atomic structure had ceased to be just a hypothesis, but had become an absolute fact. It turned out that the composition of the nucleus of an atom is a very complex concept. It consists of But the question arose: the composition of the atom and include a different number of these charges or not?

planetary model

Initially, they imagined that the atom was built very similar to our solar system. However, it quickly turned out that this view was not entirely correct. The problem of a purely mechanical transfer of the astronomical scale of the picture to an area that occupies millionths of a millimeter has led to a significant and dramatic change in the properties and qualities of phenomena. The main difference was in the much more stringent laws and rules by which the atom is built.

Disadvantages of the planetary model

First, since atoms of the same kind and element must be exactly the same in terms of parameters and properties, then the orbits of the electrons of these atoms must also be the same. However, the laws of motion of astronomical bodies could not provide answers to these questions. The second contradiction lies in the fact that the movement of an electron along the orbit, if well-studied physical laws are applied to it, must necessarily be accompanied by a permanent release of energy. As a result, this process would lead to the depletion of the electron, which would eventually die out and even fall into the nucleus.

Wave structure of the mother and

In 1924, a young aristocrat, Louis de Broglie, came up with an idea that turned the scientific community around such questions as the composition of atomic nuclei. The idea was that an electron is not just a moving ball that revolves around the nucleus. This is a blurry substance that moves according to laws resembling the propagation of waves in space. Quite quickly, this idea was extended to the movement of any body as a whole, explaining that we notice only one side of this very movement, but the second is not actually manifested. We can see the propagation of waves and not notice the movement of the particle, or vice versa. In fact, both of these sides of motion always exist, and the rotation of an electron in orbit is not only the movement of the charge itself, but also the propagation of waves. This approach is fundamentally different from the previously accepted planetary model.

Elementary basis

The nucleus of an atom is the center. Electrons revolve around it. Everything else is determined by the properties of the core. It is necessary to talk about such a concept as the composition of the nucleus of an atom from the most important point - from the charge. In the composition of the atom, there is a certain one that carries a negative charge. The nucleus itself has a positive charge. From this we can draw certain conclusions:

1. The nucleus is a positively charged particle.
2. Around the nucleus is a pulsating atmosphere created by charges.
3. It is the nucleus and its characteristics that determine the number of electrons in an atom.

Kernel Properties

Copper, glass, iron, wood have the same electrons. An atom can lose a couple of electrons or even all. If the nucleus remains positively charged, then it is able to attract the right amount of negatively charged particles from other bodies, which will allow it to survive. If an atom loses a certain number of electrons, then the positive charge on the nucleus will be greater than the remainder of the negative charges. In this case, the entire atom will acquire an excess charge, and it can be called a positive ion. In some cases, an atom can attract more electrons, and then it will become negatively charged. Therefore, it can be called a negative ion.

How much does an atom weigh ?

The mass of an atom is mainly determined by the nucleus. The electrons that make up the atom and the atomic nucleus weigh less than one thousandth of the total mass. Since mass is considered a measure of the energy reserve that a substance possesses, this fact is considered incredibly important when studying such a question as the composition of the nucleus of an atom.

Radioactivity

The most difficult questions arose after the discovery that radioactive elements emit alpha, beta, and gamma waves. But such radiation must have a source. Rutherford in 1902 showed that such a source is the atom itself, or rather, the nucleus. On the other hand, radioactivity is not only the emission of rays, but also the conversion of one element into another, with completely new chemical and physical properties. That is, radioactivity is a change in the nucleus.

What do we know about nuclear structure?

Almost a hundred years ago, the physicist Prout put forward the idea that the elements in the periodic system are not incoherent forms, but are combinations. Therefore, one could expect that both the charges and the masses of the nuclei would be expressed in terms of integer and multiple charges of hydrogen itself. However, this is not quite true. Studying the properties of atomic nuclei using electromagnetic fields, the physicist Aston found that elements whose atomic weights were not integers and multiples were in fact a combination of different atoms, and not one substance. In all cases where the atomic weight is not an integer, we observe a mixture of different isotopes. What it is? If we talk about the composition of the nucleus of an atom, isotopes are atoms with the same charges, but with different masses.

Einstein and the nucleus of the atom

The theory of relativity says that mass is not a measure by which the amount of matter is determined, but a measure of the energy that matter possesses. Accordingly, matter can be measured not by mass, but by the charge that makes up this matter, and the energy of the charge. When the same charge approaches another of the same, the energy will increase, otherwise it will decrease. This, of course, does not mean a change in matter. Accordingly, from this position, the nucleus of an atom is not a source of energy, but rather, a residue after its release. So there is some contradiction.

Neutrons

The Curies, when bombarded with alpha particles of beryllium, discovered some incomprehensible rays, which, colliding with the nucleus of an atom, repel it with great force. However, they are able to pass through a large thickness of matter. This contradiction was resolved by the fact that the given particle turned out to have a neutral electric charge. Accordingly, it was called the neutron. Thanks to further research, it turned out that it is almost the same as that of the proton. Generally speaking, the neutron and the proton are incredibly similar. Taking into account this discovery, it was definitely possible to establish that both protons and neutrons are included in the composition of the nucleus of an atom, and in equal quantities. Everything gradually fell into place. The number of protons is the atomic number. Atomic weight is the sum of the masses of neutrons and protons. An isotope can also be called an element in which the number of neutrons and protons will not be equal to each other. As mentioned above, in such a case, although the element remains essentially the same, its properties may change significantly.

In which other particles serve as the nucleus instead of the nucleon.

The number of protons in a nucleus is called its charge number. Z (\displaystyle Z)- this number is equal to the ordinal number of the element to which the atom belongs, in the table (Periodic system of elements) of Mendeleev. The number of protons in the nucleus determines the structure of the electron shell of a neutral atom and thus the chemical properties of the corresponding element. The number of neutrons in a nucleus is called its isotopic number N (\displaystyle N). Nuclei with the same number of protons and different numbers of neutrons are called isotopes. Nuclei with the same number of neutrons but different numbers of protons are called isotones. The terms isotope and isotone are also used in relation to atoms containing the indicated nuclei, as well as to characterize non-chemical varieties of one chemical element. The total number of nucleons in a nucleus is called its mass number. A (\displaystyle A) (A = N + Z (\displaystyle A=N+Z)) and is approximately equal to the average mass of an atom, indicated in the periodic table. Nuclides with the same mass number but different proton-neutron composition are called isobars.

Like any quantum system, nuclei can be in a metastable excited state, and in some cases the lifetime of such a state is calculated in years. Such excited states of nuclei are called nuclear isomers.

Story

The scattering of charged particles can be explained by assuming an atom that consists of a central electric charge concentrated at a point and surrounded by a uniform spherical distribution of opposite electricity of equal magnitude. With such a structure of the atom, α- and β-particles, when they pass at a close distance from the center of the atom, experience large deviations, although the probability of such a deviation is small.

Thus, Rutherford discovered the atomic nucleus, from that moment nuclear physics began, studying the structure and properties of atomic nuclei.

After the discovery of stable isotopes of elements, the nucleus of the lightest atom was assigned the role of a structural particle of all nuclei. Since 1920, the nucleus of the hydrogen atom has had an official term - proton. In 1921, Lise Meitner proposed the first, proton-electron, model of the structure of the atomic nucleus, according to which it consists of protons, electrons and alpha particles: 96 . However, in 1929 there was a "nitrogen catastrophe" - W. Heitler and G. Herzberg found that the nucleus of the nitrogen atom obeys Bose-Einstein statistics, and not Fermi-Dirac statistics, as predicted by the proton-electron model: 374. Thus, this model came into conflict with the experimental results of measurements of spins and magnetic moments of nuclei. In 1932, James Chadwick discovered a new electrically neutral particle called the neutron. In the same year, Ivanenko and, independently, Heisenberg put forward a hypothesis about the proton-neutron structure of the nucleus. Later, with the development of nuclear physics and its applications, this hypothesis was fully confirmed.

Theories of the structure of the atomic nucleus

In the process of development of physics, various hypotheses were put forward for the structure of the atomic nucleus; however, each of them is capable of describing only a limited set of nuclear properties. Some models may be mutually exclusive.

The most famous are the following:

• Drop model of the nucleus - proposed in 1936 by Niels Bohr.
• Shell model of the nucleus - proposed in the 30s of the XX century.

Nuclear physics

For the first time, the charges of atomic nuclei were determined by Henry Moseley in 1913. The scientist interpreted his experimental observations by the dependence of the X-ray wavelength on a certain constant Z (\displaystyle Z), changing by one from element to element and equal to one for hydrogen:

1 / λ = a Z − b (\displaystyle (\sqrt (1/\lambda ))=aZ-b), where

A (\displaystyle a) and b (\displaystyle b)- permanent.

From which Moseley concluded that the atomic constant found in his experiments, which determines the wavelength of the characteristic X-ray radiation and coincides with the serial number of the element, can only be the charge of the atomic nucleus, which became known as Moseley's law .

Weight

Due to the difference in the number of neutrons A − Z (\displaystyle A-Z) isotopes of an element have different masses M (A , Z) (\displaystyle M(A,Z)), which is an important characteristic of the kernel. In nuclear physics, the mass of nuclei is usually measured in atomic mass units ( a. eat.), for one a. e. m. take 1/12 of the mass of the 12 C nuclide. It should be noted that the standard mass that is usually given for a nuclide is the mass of a neutral atom. To determine the mass of the nucleus, it is necessary to subtract the sum of the masses of all electrons from the mass of the atom (a more accurate value will be obtained if we also take into account the binding energy of electrons with the nucleus).

In addition, the energy equivalent of mass is often used in nuclear physics. According to the Einstein relation, each mass value M (\displaystyle M) corresponds to the total energy:

E = M c 2 (\displaystyle E=Mc^(2)), where c (\displaystyle c) is the speed of light in vacuum.

The ratio between a. e.m. and its energy equivalent in joules:

E 1 = 1.660 539 ⋅ 10 − 27 ⋅ (2.997 925 ⋅ 10 8) 2 = 1.492 418 ⋅ 10 − 10 (\displaystyle E_(1)=1(,)660539\cdot 10^(-27)\cdot (2 (,)997925\cdot 10^(8))^(2)=1(,)492418\cdot 10^(-10)), E 1 = 931.494 (\displaystyle E_(1)=931(,)494).

Radius

Analysis of the decay of heavy nuclei refined Rutherford's estimate and related the radius of the nucleus to the mass number by a simple relationship:

R = r 0 A 1 / 3 (\displaystyle R=r_(0)A^(1/3)),

where is a constant.

Since the radius of the nucleus is not a purely geometric characteristic and is associated primarily with the radius of action of nuclear forces, then the value r 0 (\displaystyle r_(0)) depends on the process in the analysis of which the value is obtained R (\displaystyle R), average value r 0 = 1 , 23 ⋅ 10 − 15 (\displaystyle r_(0)=1(,)23\cdot 10^(-15)) m, thus the core radius in meters:

R = 1 , 23 ⋅ 10 − 15 A 1 / 3 (\displaystyle R=1(,)23\cdot 10^(-15)A^(1/3)).

Kernel moments

Like the nucleons that make it up, the nucleus has its own moments.

Spin

Since nucleons have their own mechanical moment, or spin, equal to 1 / 2 (\displaystyle 1/2), then the nuclei must also have mechanical moments. In addition, nucleons participate in the nucleus in orbital motion, which is also characterized by a certain angular momentum of each nucleon. Orbital moments take only integer values ℏ (\displaystyle \hbar )(Dirac constant). All mechanical moments of nucleons, both spins and orbital, are summed algebraically and constitute the spin of the nucleus.

Despite the fact that the number of nucleons in a nucleus can be very large, the spins of nuclei are usually small and amount to no more than a few ℏ (\displaystyle \hbar ), which is explained by the peculiarity of the interaction of nucleons of the same name. All paired protons and neutrons interact only in such a way that their spins cancel each other out, that is, pairs always interact with antiparallel spins. The total orbital momentum of a pair is also always zero. As a result, nuclei consisting of an even number of protons and an even number of neutrons do not have a mechanical momentum. Non-zero spins exist only for nuclei that have unpaired nucleons in their composition, the spin of such a nucleon is added to its own orbital momentum and has some half-integer value: 1/2, 3/2, 5/2. Nuclei of odd-odd composition have integer spins: 1, 2, 3, etc. .

Magnetic moment

Spin measurements have been made possible by the presence of directly related magnetic moments. They are measured in magnetons and for different nuclei they are from -2 to +5 nuclear magnetons. Due to the relatively large mass of nucleons, the magnetic moments of nuclei are very small compared to those of electrons, so measuring them is much more difficult. Like spins, magnetic moments are measured by spectroscopic methods, the most accurate being the nuclear magnetic resonance method.

The magnetic moment of even-even pairs, like the spin, is equal to zero. The magnetic moments of nuclei with unpaired nucleons are formed by the intrinsic moments of these nucleons and the moment associated with the orbital motion of the unpaired proton.

Electric quadrupole moment

Atomic nuclei with a spin greater than or equal to unity have non-zero quadrupole moments, indicating that they are not exactly spherical. The quadrupole moment has a plus sign if the nucleus is extended along the spin axis (fusiform body), and a minus sign if the nucleus is stretched in a plane perpendicular to the spin axis (lenticular body). Nuclei with positive and negative quadrupole moments are known. The absence of spherical symmetry in the electric field created by a nucleus with a non-zero quadrupole moment leads to the formation of additional energy levels of atomic electrons and the appearance of hyperfine structure lines in the spectra of atoms, the distances between which depend on the quadrupole moment.

Bond energy

Core Stability

From the fact that the average binding energy decreases for nuclides with mass numbers greater than or less than 50–60, it follows that for nuclei with small A (\displaystyle A) the fusion process is energetically favorable - thermonuclear fusion, leading to an increase in the mass number, and for nuclei with large A (\displaystyle A)- division process. At present, both of these processes leading to the release of energy have been carried out, with the latter being the basis of modern nuclear energy, and the former being under development.

Detailed studies have shown that the stability of nuclei also depends significantly on the parameter N/Z (\displaystyle N/Z)- the ratio of the numbers of neutrons and protons. Average for the most stable nuclei N / Z ≈ 1 + 0.015A 2 / 3 (\displaystyle N/Z\approx 1+0.015A^(2/3)), therefore the nuclei of light nuclides are most stable at N ≈ Z (\displaystyle N\approx Z), and as the mass number increases, the electrostatic repulsion between protons becomes more and more noticeable, and the stability region shifts towards N > Z (\displaystyle N>Z)(see explanatory figure).

If we consider the table of stable nuclides found in nature, we can pay attention to their distribution by even and odd values. Z (\displaystyle Z) and N (\displaystyle N). All nuclei with odd values ​​of these quantities are nuclei of light nuclides 1 2 H (\displaystyle ()_(1)^(2)(\textrm (H))), 3 6 Li (\displaystyle ()_(3)^(6)(\textrm (Li))), 5 10 B (\displaystyle ()_(5)^(10)(\textrm (B))), 7 14 N (\displaystyle ()_(7)^(14)(\textrm (N))). Among the isobars with odd A, as a rule, only one is stable. In the case of even A (\displaystyle A) often there are two, three or more stable isobars, therefore, the most stable are even-even, the least - odd-odd. This phenomenon indicates that both neutrons and protons tend to cluster in pairs with antiparallel spins, which leads to a violation of the smoothness of the above dependence of the binding energy on A (\displaystyle A) .

Thus, the parity of the number of protons or neutrons creates a certain margin of stability, which leads to the possibility of the existence of several stable nuclides, which differ respectively in the number of neutrons for isotopes and in the number of protons for isotones. Also, the parity of the number of neutrons in the composition of heavy nuclei determines their ability to fission under the influence of neutrons.

nuclear forces

Nuclear forces are forces that hold nucleons in the nucleus, which are large attractive forces that act only at small distances. They have saturation properties, in connection with which the nuclear forces are assigned an exchange character (with the help of pi-mesons). Nuclear forces are spin dependent, independent of electric charge, and are not central forces.

Kernel levels

Unlike free particles, for which the energy can take on any value (the so-called continuous spectrum), bound particles (that is, particles whose kinetic energy is less than the absolute value of the potential), according to quantum mechanics, can only be in states with certain discrete energy values , the so-called discrete spectrum. Since the nucleus is a system of bound nucleons, it has a discrete energy spectrum. It is usually in its lowest energy state, called main. If energy is transferred to the nucleus, it will turn into excited state.

The location of the energy levels of the nucleus in the first approximation:

D = a e − b E ∗ (\displaystyle D=ae^(-b(\sqrt (E^(*))))), where:

D (\displaystyle D)- average distance between levels,

E ∗ (\displaystyle E^(*)) is the excitation energy of the nucleus,

A (\displaystyle a) and b (\displaystyle b)- coefficients constant for a given kernel:

A (\displaystyle a)- average distance between the first excited levels (about 1 MeV for light nuclei, 0.1 MeV for heavy nuclei)

B (\displaystyle b) is a constant that determines the rate of concentration of levels with increasing excitation energy (for light nuclei, approximately 2 MeV −1/2 , for heavy nuclei, 4 MeV −1/2).

With an increase in the excitation energy, the levels converge faster in heavy nuclei, and the level density also depends on the parity of the number of neutrons in the nucleus. For nuclei with even (especially magic) numbers of neutrons, the level density is lower than for nuclei with odd ones; at equal excitation energies, the first excited level in a nucleus with an even number of neutrons is located higher than in a nucleus with an odd one.

In all excited states, the nucleus can stay only for a finite time, until the excitation is removed in one way or another. States whose excitation energy is less than the binding energy of a particle or a group of particles in a given nucleus are called related; in this case, the excitation can only be removed by gamma radiation. States with an excitation energy greater than the binding energy of the particles are called quasi-stationary. In this case, the nucleus can emit a particle or a gamma ray.