The composition of the nucleus of an atom

In 1932 after the discovery of the proton and neutron by scientists D.D. Ivanenko (USSR) and W. Heisenberg (Germany) proposed proton-neutronmodel atomic nucleus .
According to this model, the core consists of protons and neutrons. The total number of nucleons (i.e., protons and neutrons) is called mass number A: A = Z + N . Nuclei chemical elements denoted by the symbol:
X is the chemical symbol of the element.

For example, hydrogen

A number of notations are introduced to characterize atomic nuclei. The number of protons that make up the atomic nucleus is denoted by the symbol Z and call charge number (this is the serial number in the periodic table of Mendeleev). The nuclear charge is Ze , where e is the elementary charge. The number of neutrons is denoted by the symbol N .

nuclear forces

In order for atomic nuclei to be stable, protons and neutrons must be kept inside the nuclei. huge forces, many times greater than the forces of the Coulomb repulsion of protons. The forces that hold nucleons in the nucleus are called nuclear . They are a manifestation of the most intense of all types of interaction known in physics - the so-called strong interaction. The nuclear forces are about 100 times greater than the electrostatic forces and are tens of orders of magnitude greater than the forces of the gravitational interaction of nucleons.

Nuclear forces have the following properties:

• have attractive forces
• is the forces short-range(appear at small distances between nucleons);
• nuclear forces do not depend on the presence or absence of an electric charge on the particles.

Mass Defect and Binding Energy of the Nucleus of an Atom

The most important role in nuclear physics is played by the concept nuclear binding energy .

The binding energy of the nucleus is equal to the minimum energy that must be expended for complete splitting nuclei into individual particles. It follows from the law of conservation of energy that the binding energy is equal to the energy that is released during the formation of a nucleus from individual particles.

The binding energy of any nucleus can be determined by accurately measuring its mass. At present, physicists have learned to measure the masses of particles - electrons, protons, neutrons, nuclei, etc. - with very high accuracy. These measurements show that the mass of any nucleus M i is always less than the sum of the masses of its constituent protons and neutrons:

The mass difference is called mass defect. Based on the mass defect using the Einstein formula E = mc 2 it is possible to determine the energy released during the formation of a given nucleus, i.e., the binding energy of the nucleus E St:

This energy is released during the formation of the nucleus in the form of radiation of γ-quanta.

Nuclear energy

In our country, the world's first nuclear power plant was built and launched in 1954 in the USSR, in the city of Obninsk. The construction of powerful nuclear power plants is being developed. There are currently 10 operating nuclear power plants in Russia. After the accident at the Chernobyl nuclear power plant, additional measures were taken to ensure the safety of nuclear reactors.

The atomic nucleus is made up of protons and neutrons. The number of protons determines the charge of the nucleus (serial number in the periodic table).

The mass of the nucleus of an arbitrary element is determined by a value close to the sum of the masses of the protons and neutrons that make up its composition. Therefore, the mass number of the nucleus, denoted by the letter BUT and expressed in atomic mass units, rounded equal to A \u003d N + Z. Z- nuclear charge, determines the number of protons in the nucleus and the number of electrons in the electron shell of a neutral atom. N is the number of neutrons in the nucleus. The proton and neutron have a common name - the nucleon. The symbol is used to designate the nucleus, where X is the symbol of a chemical element. For example, which means Z = 82, N = 126, A = 208.

Different combinations of numbers of protons and neutrons correspond to different nuclei. In this case, the following groups of atoms can be distinguished.

isotopes are atoms whose nuclei have the same number of protons Z and different number neutrons N. Such elements occupy the same place in the periodic system. For example, a group of hydrogen isotopes is common in nature: - light hydrogen, - deuterium and - tritium. Hydrogen isotope nuclei also have own names: proton, deuteron, triton.

isobars are atoms whose nuclei have the same number A ().

Along with the term atom nucleus the term is used nuclide.

Approximate sizes of atoms and their components:

size of nucleus ~ 10–14 m, size of neutron and proton ~10–15 m, size of atom ~ 10–10 m, electron< 10 –18 м.

The size of the nucleus is characterized by the radius of the nucleus, which has a conditional meaning, since the boundaries of the nucleus are blurred, like in any quantum system. It has been experimentally established that each nucleus has an inner region where the density of matter is constant. This area is surrounded by surface layer, where the density of matter drops to zero. Empirical formula for core radius

1 fm (femtometer) = 10 -15 m (1)

This expression can be interpreted as the proportionality of the volume of the nucleus to the number of nucleons in it V ~ A. (1) means that the average density of the nucleus is independent of the mass number.

The mass of the nucleus is expressed in atomic mass units or in MeV / With 2 .

1a.u.m. \u003d 1/12 the mass of a carbon atom with atomic mass 12,000. 1a.u.m. \u003d 1.66 × 10 -27 kg "931.5 MeV / With 2 .

When a nucleus is formed from nucleons, its mass decreases by D m, which is called the mass defect.

Dm is expressed in atomic mass units or in MeV/ With 2 .

An important characteristic of the nucleus is the binding energy of the nucleus W(A,Z) is the energy that must be expended to divide the nucleus into its individual protons and neutrons without imparting kinetic energy to them.

W(A,Z) = Δ ts 2 = [Zm p +(A-Z)m n – M i(A,Z)]· With 2 , (3)

The specific binding energy is the average energy per 1 nucleon: . (four)

For most nuclei, the specific binding energy is almost the same and ~ 8 MeV. Therefore, the total binding energy is approximately proportional to the mass number, i.e. the number of nucleons in the nucleus. This speaks of a property of nuclear forces called saturation. It lies in the fact that each nucleon interacts only with a limited number of neighboring nucleons.

Nucleons in the nucleus are held by specific nuclear forces, which are a manifestation of the strong interaction. Nuclear forces have the following properties:

– are short-range, their radius of action is 10–14 m;

- the most intense, they are 2-3 orders of magnitude more powerful than electromagnetic forces. Nuclear forces ensure the existence of nuclei with a specific binding energy of about 8 MeV.

- They have the property of saturation. This is manifested in the fact that in the nucleus a proton can form a bound state with no more than two neutrons. For this reason, the hydrogen isotope tritium is already unstable.

– They have charge independence, i.e. the forces acting between a proton and a neutron, a proton and a proton, a neutron and a neutron are the same. This property does not mean the complete identity of the systems p - p, p - p, p - p, since protons and neutrons are fermions and systems r - r, n - n consist of identical particles, and the system r - p - from different.

- They are exchangeable. When interacting, nucleons can exchange their coordinates, charges, projections of spins.

– Depend on the spin of nucleons. This dependence is indicated by the fact that there is no deuteron state with spin 0. That is, the spins of the proton and neutron in this state are only parallel.

– They are non-central, i.e., they depend on the orientation of the nucleon spins relative to the straight line connecting the nucleons.

In 1935, the Japanese physicist H. Yukawa hypothesized that the nuclear interaction is the result of the exchange of nucleons by a virtual particle. These particles must have a mass greater than the mass of an electron, but less than the mass of a proton, so they were called mesons. (From the Greek . mesos- intermediate, average). Mesons began to be searched experimentally. In 1947 they were discovered in cosmic radiation. These particles are called pi mesons. primary- primary). Now these particles are called more briefly - pions. The pion exists in the form p 0 , p – , p + .

Pi mesons play an important role in nucleon-nucleon interaction at distances of 1.5–2 fm. The essence of the meson theory of nuclear forces is as follows. Two nucleons, being at distances r£ h/2 m p c, exchange pions, which is the reason for the nuclear interaction. 4 types of exchange are possible:

p « p+ p 0 , (5)

n « n+ p 0 , (6)

p « n+ p + , n « p+ p – , (7)

at which the nucleons are surrounded by a cloud of virtual pions, which form the field of nuclear forces. Absorption of mesons by another nucleon leads to a strong interaction between nucleons.

At distances less than 1.5 fm, nucleons exchange heavier mesons: h (549 MeV), r (770 MeV), w (782 MeV), which determine the repulsion of nucleons.

Lecture 18 Elements of nuclear physics

Lecture plan

Atomic nucleus. Mass defect, nuclear binding energy.

Radioactive radiation and its types. Law of radioactive decay.

Conservation laws in radioactive decays and nuclear reactions.

1. Atomic nucleus. Mass defect, nuclear binding energy.

The composition of the atomic nucleus

Nuclear physics- the science of the structure, properties and transformations of atomic nuclei. In 1911, E. Rutherford established in experiments on the scattering of α-particles as they pass through matter that a neutral atom consists of a compact positively charged nucleus and a negative electron cloud. W. Heisenberg and D.D. Ivanenko (independently) hypothesized that the nucleus is made up of protons and neutrons.

atomic nucleus- the central massive part of the atom, consisting of protons and neutrons, which received the general name nucleons. Almost the entire mass of an atom is concentrated in the nucleus (more than 99.95%). The sizes of the nuclei are on the order of 10 -13 - 10 -12 cm and depend on the number of nucleons in the nucleus. The density of nuclear matter for both light and heavy nuclei is almost the same and is about 10 17 kg/m 3 , i.e. 1 cm 3 of nuclear matter would weigh 100 million tons. Nuclei have a positive electric charge equal to the absolute value of the total charge of electrons in the atom.

Proton (symbol p) - an elementary particle, the nucleus of a hydrogen atom. The proton has a positive charge equal in magnitude to the charge of the electron. Proton mass m p = 1.6726 10 -27 kg = 1836 m e , where m e is the electron mass.

In nuclear physics, it is customary to express masses in atomic mass units:

1 amu = 1.65976 10 -27 kg.

Therefore, the mass of the proton, expressed in a.m.u., is

m p = 1.0075957 amu

The number of protons in a nucleus is called charge number Z. It is equal to the atomic number of a given element and, therefore, determines the place of the element in the periodic system of elements of Mendeleev.

Neutron (symbol n) - an elementary particle that does not have an electric charge, the mass of which is slightly greater than the mass of a proton.

Neutron mass m n \u003d 1.675 10 -27 kg \u003d 1.008982 a.m.u. The number of neutrons in a nucleus is denoted N.

The total number of protons and neutrons in the nucleus (number of nucleons) is called mass number and is denoted by the letter A,

The symbol is used to designate nuclei, where X is the chemical symbol of the element.

isotopes- varieties of atoms of the same chemical element, the atomic nuclei of which have the same number of protons (Z) and a different number of neutrons (N). The nuclei of such atoms are also called isotopes. Isotopes occupy the same place in the periodic table of elements. As an example, we give hydrogen isotopes:

The concept of nuclear forces.

The nuclei of atoms are extremely strong formations, despite the fact that similarly charged protons, being at very small distances in the atomic nucleus, must repel each other with great force. Consequently, extremely strong attractive forces between nucleons act inside the nucleus, many times greater than the electrical repulsive forces between protons. Nuclear forces are a special kind of forces, they are the strongest of all known interactions in nature.

Studies have shown that nuclear forces have the following properties:

nuclear attractive forces act between any nucleons, regardless of their charge state;

nuclear forces of attraction are short-range: they act between any two nucleons at a distance between the centers of particles of about 2 10 -15 m and drop sharply with increasing distance (at distances of more than 3 10 -15 m they are already practically equal to zero);

nuclear forces are characterized by saturation, i.e. each nucleon can only interact with the nucleus nucleons closest to it;

nuclear forces are not central, i.e. they do not act along the line connecting the centers of interacting nucleons.

At present, the nature of nuclear forces is not fully understood. It is established that they are the so-called exchange forces. Exchange forces are of a quantum nature and have no analogue in classical physics. Nucleons are bound together by a third particle, which they constantly exchange. In 1935, the Japanese physicist H. Yukawa showed that nucleons exchange particles whose mass is about 250 times the mass of an electron. The predicted particles were discovered in 1947 by the English scientist S. Powell while studying cosmic rays and subsequently named  mesons or pions.

Mutual transformations of the neutron and proton are confirmed by various experiments.

Mass defect of atomic nuclei. The binding energy of the atomic nucleus.

The nucleons in an atomic nucleus are interconnected by nuclear forces, therefore, in order to divide the nucleus into its individual protons and neutrons, it is necessary to spend a lot of energy.

The minimum energy required to split a nucleus into its constituent nucleons is called nuclear binding energy. The same amount of energy is released when free neutrons and protons combine to form a nucleus.

Accurate mass-spectroscopic measurements of the masses of nuclei have shown that the rest mass of an atomic nucleus is less than the sum of the rest masses of free neutrons and protons from which the nucleus was formed. The difference between the sum of the rest masses of free nucleons from which the nucleus is formed and the mass of the nucleus is called mass defect:

This mass difference m corresponds to the binding energy of the nucleus E St., determined by the Einstein relation:

or, substituting the expression for  m, we get:

The binding energy is usually expressed in megaelectronvolts (MeV). Let us determine the binding energy corresponding to one atomic mass unit (, the speed of light in vacuum
):

Let's translate the obtained value into electronvolts:

In this regard, in practice it is more convenient to use the following expression for the binding energy:

where the factor m is expressed in atomic mass units.

An important characteristic of the nucleus is the specific binding energy of the nucleus, i.e. binding energy per nucleon:

.

The more , the more strongly the nucleons are bound to each other.

The dependence of the value of  on the mass number of the nucleus is shown in Figure 1. As can be seen from the graph, nucleons in nuclei with mass numbers of the order of 50-60 (Cr-Zn) are most strongly bound. The binding energy for these nuclei reaches

Proton-electron theory

By the beginning of $1932$, only three elementary particles: electron, proton and neutron. For this reason, it was assumed that the nucleus of an atom consists of protons and electrons (proton-electron hypothesis). It was believed that the composition of the nucleus with number $Z$ in Mendeleev's periodic system of elements and mass number $A$ includes $A$ protons and $Z-A$ neutrons. In accordance with this hypothesis, the electrons that were part of the nucleus acted as a “cementing” agent, with the help of which positively charged protons were retained in the nucleus. Supporters of the proton-electron hypothesis of the composition of the atomic nucleus believed that $\beta ^-$ - radioactivity - is a confirmation of the correctness of the hypothesis. But this hypothesis was not able to explain the results of the experiment and was discarded. One of these difficulties was the impossibility to explain the fact that the spin of the nitrogen nucleus $^(14)_7N$ is equal to the unit $(\hbar)$. According to the proton-electron hypothesis, the $^(14)_7N$ nitrogen nucleus should consist of $14$ protons and $7$ electrons. The spin of protons and electrons is equal to $1/2$. For this reason, the nucleus of the nitrogen atom, which according to this hypothesis consists of $21$ particles, must have spin $1/2,\ 3/2,\ 5/2,\dots 21/2$. This discrepancy between the proton-electron theory is called the "nitrogen catastrophe". It was also incomprehensible that in the presence of electrons in the nucleus, its magnetic moment has a small magnetic moment compared to the magnetic moment of the electron.

In $1932$, J. Chadwick discovered the neutron. After this discovery, D. D. Ivanenko and E. G. Gapon put forward a hypothesis about the proton-neutron structure of the atomic nucleus, which was developed in detail by V. Heisenberg.

Remark 1

The proton-neutron composition of the nucleus is confirmed not only by theoretical conclusions, but also directly by experiments on the splitting of the nucleus into protons and neutrons. It is now generally accepted that the atomic nucleus consists of protons and neutrons, which are also called nucleons(from Latin nucleus kernel, grain).

The structure of the atomic nucleus

Nucleus is the central part of the atom, in which the positive electric charge and the main part of the mass of the atom are concentrated. The dimensions of the nucleus, in comparison with the orbits of electrons, are extremely small: $10^(-15)-10^(-14)\ m$. Nuclei are made up of protons and neutrons, which are almost identical in mass, but only the proton carries an electric charge. The total number of protons is called the atomic number $Z$ of the atom, which is the same as the number of electrons in the neutral atom. Nucleons are held in the nucleus by large forces, by their nature these forces are neither electrical nor gravitational, and in magnitude they are much greater than the forces that bind electrons to the nucleus.

According to the proton-neutron model of the structure of the nucleus:

• the nuclei of all chemical elements consist of nucleons;
• the charge of the nucleus is due only to protons;
• the number of protons in the nucleus is equal to the ordinal number of the element;
• the number of neutrons is equal to the difference between the mass number and the number of protons ($N=A-Z$)

A proton ($^2_1H\ or\ p$) is a positively charged particle: its charge is equal to the charge of an electron $e=1.6\cdot 10^(-19)\ Cl$, and its rest mass is $m_p=1.627\cdot 10^( -27)\kg$. The proton is the nucleus of the nucleon of the hydrogen atom.

To simplify records and calculations, the mass of the nucleus is often determined in atomic mass units (a.m.u.) or in units of energy (recording instead of mass the corresponding energy $E=mc^2$ in electron volts). The atomic mass unit is $1/12$ of the mass of the carbon nuclide $^(12)_6C$. In these units we get:

A proton, like an electron, has its own angular momentum - spin, which is equal to $1/2$ (in units of $\hbar $). The latter, in an external magnetic field, can orient only in such a way that its projection and field directions are equal to $+1/2$ or $-1/2$. The proton, like the electron, is subject to Fermi-Dirac quantum statistics, i.e. belongs to fermions.

The proton is characterized by its own magnetic moment, which for a particle with spin $1/2$, charge $e$ and mass $m$ is equal to

For an electron, its own magnetic moment is equal to

To describe the magnetism of nucleons and nuclei, the nuclear magneton is used ($1836$ times smaller than the Bohr magneton):

At first, it was believed that the magnetic moment of the proton is equal to the nuclear magneton, because. its mass is $1836$ times the mass of an electron. But the measurements showed that in fact the intrinsic magnetic moment of the proton is $2.79$ times greater than that of the nuclear magnetron, has a positive sign, i.e. direction coincides with the spin.

Modern physics explains these disagreements by the fact that protons and neutrons are mutually transformed and for some time are in a state of dissociation into $\pi ^\pm $ - a meson and another nucleon of the corresponding sign:

The rest mass of the $\pi ^\pm $ - meson is $193.63$ MeV, so its own magnetic moment is $6.6$ times greater than the nuclear magneton. Some effective value of the magnetic moment of the proton and $\pi ^+$ -- of the meson environment appears in the measurements.

Neutron ($n$) -- electrically neutral particle; its rest mass

Although the neutron is devoid of charge, it has a magnetic moment $\mu _n=-1.91\mu _Я$. The "$-$" sign shows that behind the direction the magnetic moment is opposite to the spin of the proton. The magnetism of the neutron is determined by the effective value of the magnetic moment of the particles into which it is able to dissociate.

In the free state, the neutron is an unstable particle and randomly decays (half-life $12$ min): emitting a $\beta $ -- particle and an antineutrino, it turns into a proton. The neutron decay scheme is written in the following form:

In contrast to the intranuclear decay of the $\beta $ neutron -- decay belongs to both internal decay and elementary particle physics.

The mutual transformation of the neutron and proton, the equality of spins, the approximation of masses and properties give grounds to assume that we are talking about two varieties of the same nuclear particle - the nucleon. The proton-neutron theory agrees well with experimental data.

As constituents of the nucleus, protons and neutrons are found in numerous fission and fusion reactions.

In arbitrary and piece fission of nuclei, flows of electrons, positrons, mesons, neutrinos and antineutrinos are also observed. The mass $\beta $ of a particle (electron or positron) is $1836$ times less than the mass of a nucleon. Mesons - positive, negative and zero particles - occupy an intermediate place in mass between $\beta $ - particles and nucleons; the lifetime of such particles is very short and amounts to millionths of a second. Neutrinos and antineutrinos are elementary particles whose rest mass is zero. However, electrons, positrons and mesons cannot be constituents of the nucleus. These light particles cannot be localized in a small volume, which is a nucleus with radius $\sim 10^(-15)\ m$.

To prove this, we define the energy of the electrical interaction (for example, an electron with a positron or proton in the nucleus)

and compare it with the self-energy of the electron

Since the energy of the external interaction exceeds the electron's own energy, it cannot exist and retain its own individuality; under the conditions of the nucleus, it will be destroyed. Another situation with nucleons, their own energy is more than $900$ MeV, so they can retain their features in the nucleus.

Light particles are emitted from nuclei in the process of their transition from one state to another.