The mass of the nucleus is always the sum of the masses of the nucleons. Atomic nucleus: structure, mass, composition. What does an atom consist of?

In 1932 after the discovery of the proton and neutron by scientists D.D. Ivanenko (USSR) and W. Heisenberg (Germany) put forward a proton-neutron model of the atomic nucleus.

According to this model:
- the nuclei of all chemical elements consist of nucleons: protons and neutrons
- the nuclear charge is due only to protons
- the number of protons in the nucleus is equal to the atomic 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)

Symbol for the nucleus of an atom of a chemical element:

X – chemical element symbol

A is the mass number, which shows:
- mass of the nucleus in whole atomic mass units (amu)
(1 amu = 1/12 the mass of a carbon atom)
- number of nucleons in the nucleus
- (A = N + Z), where N is the number of neutrons in the nucleus of an atom

Z is the charge number, which shows:
- nuclear charge in elementary electric charges (e.e.c.)
(1 e.e.z. = electron charge = 1.6 x 10 -19 C)
- number of protons
- number of electrons in an atom
- serial number in the periodic table

The mass of the nucleus is always less than the sum of the rest masses of the free protons and neutrons that make it up.
This is explained by the fact that protons and neutrons in the nucleus are very strongly attracted to each other. Separating them requires a lot of work. Therefore, the total rest energy of the nucleus is not equal to the rest energy of its constituent particles. It is less by the amount of work required to overcome nuclear gravitational forces.
The difference between the mass of the nucleus and the sum of the masses of protons and neutrons is called the mass defect.

BINDING ENERGY OF ATOMIC NUCLEI

Atomic nuclei are strongly bound systems of a large number of nucleons.
To completely split the nucleus into its component parts and remove them at large distances from each other, it is necessary to expend a certain amount of work A.

Binding energy is the energy equal to the work that must be done to split a nucleus into free nucleons.

E connection = - A

According to the law of conservation, the binding energy is simultaneously equal to the energy that is released during the formation of a nucleus from individual free nucleons.

Specific binding energy

This is the binding energy per nucleon.

Apart from the lightest nuclei, the specific binding energy is approximately constant and equal to 8 MeV/nucleon. The maximum specific binding energy (8.6 MeV/nucleon) is found in elements with mass numbers from 50 to 60. The nuclei of these elements are the most stable.

As the nuclei are overloaded with neutrons, the specific binding energy decreases.
For elements at the end of the periodic table it is equal to 7.6 MeV/nucleon (for example, for uranium).

Release of energy as a result of nuclear fission or fusion

In order to split a nucleus, a certain amount of energy must be expended to overcome nuclear forces.
In order to synthesize a nucleus from individual particles, it is necessary to overcome the Coulomb repulsive forces (for this, energy must be expended to accelerate these particles to high speeds).
That is, in order to carry out nuclear fission or nuclear synthesis, some energy must be expended.

When a nucleus is fused at short distances, nuclear forces begin to act on the nucleons, which cause them to move with acceleration.
Accelerated nucleons emit gamma rays, which have an energy equal to the binding energy.

At the exit of a nuclear fission or fusion reaction, energy is released.

It makes sense to carry out nuclear fission or nuclear synthesis if the resulting, i.e. the energy released as a result of fission or fusion will be greater than the energy expended.
According to the graph, a gain in energy can be obtained either by the fission (splitting) of heavy nuclei, or by the fusion of light nuclei, which is what is done in practice.

MASS DEFECT

Measurements of nuclear masses show that the nuclear mass (Nm) is always less than the sum of the rest masses of the free neutrons and protons composing it.

During nuclear fission: the mass of the nucleus is always less than the sum of the rest masses of the free particles formed.

During nuclear synthesis: the mass of the resulting nucleus is always less than the sum of the rest masses of the free particles that formed it.

The mass defect is a measure of the binding energy of an atomic nucleus.

The mass defect is equal to the difference between the total mass of all nucleons of the nucleus in the free state and the mass of the nucleus:

where Mya is the mass of the nucleus (from the reference book)
Z – number of protons in the nucleus
mp – rest mass of a free proton (from the reference book)
N – number of neutrons in the nucleus
mn – rest mass of a free neutron (from the reference book)

A decrease in mass during the formation of a nucleus means that the energy of the nucleon system decreases.

Nucleons inside the nucleus are held together by nuclear forces. They are held by a certain energy. It is quite difficult to measure this energy directly, but it can be done indirectly. It is logical to assume that the energy required to break the bond of nucleons in the nucleus will be equal to or greater than the energy that holds the nucleons together.

Binding energy and nuclear energy

This applied energy is now easier to measure. It is clear that this value will very accurately reflect the amount of energy that holds nucleons inside the nucleus. Therefore, the minimum energy required to split a nucleus into individual nucleons is called nuclear binding energy.

Relationship between mass and energy

We know that any energy is related to body mass in direct proportion. Therefore, it is natural that the binding energy of a nucleus will depend on the mass of the particles that make up this nucleus. This relationship was established by Albert Einstein in 1905. It is called the law of the relationship between mass and energy. In accordance with this law, the internal energy of a system of particles or rest energy is directly proportional to the mass of the particles that make up this system:

where E is energy, m is mass,
c is the speed of light in vacuum.

Mass defect effect

Now suppose that we split the nucleus of an atom into its constituent nucleons or took a certain number of nucleons from the nucleus. We spent some energy to overcome nuclear forces, since we did work. In the case of the reverse process - the synthesis of a nucleus, or the addition of nucleons to an already existing nucleus, energy, according to the law of conservation, on the contrary, will be released. When the rest energy of a system of particles changes due to some processes, their mass changes accordingly. Formulas in this case will be as follows:

∆m=(∆E_0)/c^2 or ∆E_0=∆mc^2,

where ∆E_0 is the change in the rest energy of the particle system,
∆m – change in particle mass.

For example, in the case of fusion of nucleons and the formation of a nucleus, we experience a release of energy and a decrease in the total mass of nucleons. Mass and energy are carried away by the emitted photons. This is the mass defect effect. The mass of a nucleus is always less than the sum of the masses of the nucleons that make up this nucleus. Numerically, the mass defect is expressed as follows:

∆m=(Zm_p+Nm_n)-M_я,

where M_i is the mass of the nucleus,
Z is the number of protons in the nucleus,
N is the number of neutrons in the nucleus,
m_p – mass of a free proton,
m_n is the mass of a free neutron.

The value ∆m in the two formulas above is the amount by which the total mass of the particles of the nucleus changes when its energy changes due to rupture or fusion. In the case of synthesis, this quantity will be a mass defect.

Atomic nuclei are strongly bound systems of a large number of nucleons. To completely split the nucleus into its component parts and remove them at large distances from each other, it is necessary to expend a certain amount of work A. Binding energy is the energy equal to the work that must be done to split the nucleus into free nucleons. E bonds = - A According to the law of conservation, binding energy simultaneously equal to the energy that is released during the formation of a nucleus from individual free nucleons. Specific binding energy is the binding energy per nucleon.

MASS DEFECT Measurements of nuclear masses show that the nuclear mass (Nm) is always less than the sum of the rest masses of the free neutrons and protons composing it. During nuclear fission: the mass of the nucleus is always less than the sum of the rest masses of the free particles formed. During nuclear synthesis: the mass of the resulting nucleus is always less than the sum of the rest masses of the free particles that formed it.

The mass defect is a measure of the binding energy of an atomic nucleus. The mass defect is equal to the difference between the total mass of all nucleons of the nucleus in the free state and the mass of the nucleus:

where Мa is the mass of the nucleus (from the reference book) Z is the number of protons in the nucleus mp is the rest mass of a free proton (from the reference book) N is the number of neutrons in the nucleus mn is the rest mass of a free neutron (from the reference book) A decrease in mass during the formation of a nucleus means that when this reduces the energy of the nucleon system.

Atomic nucleus- the central part of the atom, in which the bulk of its mass is concentrated (more than 99.9%). The nucleus is positively charged; the charge of the nucleus is determined by the chemical element to which the atom belongs. 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.

Nuclear physics studies atomic nuclei.

The atomic nucleus consists of nucleons - positively charged protons and neutral neutrons, which are connected to each other through strong interaction. The proton and neutron have their own angular momentum (spin) equal to [sn 1] and an associated magnetic moment.

The atomic nucleus, considered as a class of particles with a certain number of protons and neutrons, is usually called nuclide.

The number of protons in a nucleus is called its charge number - this number is equal to the atomic number of the element to which the atom belongs, in the periodic table. 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. Nuclei with the same number of neutrons, but different numbers of protons are called isotones. The terms isotope and isotone are also used to refer to atoms containing these nuclei, as well as to characterize non-chemical varieties of a single chemical element. The total number of nucleons in a nucleus is called its mass number () and is approximately equal to the average mass of an atom shown in the periodic table. Nuclides with the same mass number but different proton-neutron composition are usually 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.

22. Contact of two metals. Thermoelectric phenomena. Thermoelectric phenomena

a set of physical phenomena caused by the relationship between thermal and electrical processes in metals and semiconductors. T. I. are the Seebeck, Peltier and Thomson effects. Seebeck effect consists in the fact that in a closed circuit consisting of dissimilar conductors, an emf (thermoemf) arises if the contact points are maintained at different temperatures. In the simplest case, when an electrical circuit consists of two different conductors, it is called Thermocouple ohm , or thermocouple (See Thermocouple). The magnitude of the thermopower depends only on the temperature of the hot T 1 and cold T 2 contacts and from the material of the conductors. In a small temperature range, thermopower E can be considered proportional to the difference ( T 1 – T 2), that is E= α (T 1 –T 2). Coefficient α is called the thermoelectric ability of the pair (thermopower, thermopower coefficient, or specific thermopower). It is determined by the materials of the conductors, but also depends on the temperature range; in some cases, α changes sign with a change in temperature. The table shows the values ​​of a for some metals and alloys in relation to Pb for the temperature range 0-100 °C (positive sign α assigned to those metals to which current flows through the heated junction). However, the figures given in the table are arbitrary, since the thermopower of the material is sensitive to microscopic amounts of impurities (sometimes beyond the sensitivity of chemical analysis), to the orientation of crystal grains, and thermal or even cold treatment of the material. The method of rejecting materials based on composition is based on this property of thermopower. For the same reason, thermopower can occur in a circuit consisting of the same material in the presence of temperature differences, if different sections of the circuit have been subjected to different technological operations. On the other hand, the emf of a thermocouple does not change when any number of other materials are connected in series in the circuit, if the additional contact points that appear in this case are maintained at the same temperature.

If metals are brought into contact (contact is created between them), then conduction electrons can move from one conductor to another at the point of contact. The work function decreases with increasing Fermi energy. To understand the phenomena in the metal-metal transition, it is necessary to take into account that the Fermi energy depends on the concentration of free electrons in the conduction band - the higher the electron concentration, the higher the Fermi energy. This means that when a transition is formed at the metal-metal interface, the concentration of free electrons on different sides of the boundary is different - it is higher on the metal side (1) with a higher Fermi energy. The change in electron concentration from to occurs in a certain region near the interface between metals, which is called the transition layer (Figure 8.7.3). The change in electric field potential at the transition is shown in Figure 8.7.4. During the formation of the transition, the Fermi energies in the metals at the boundary change. A metal with a higher Fermi energy becomes positively charged and hence the work function of that metal increases

21.Intrinsic and impurity conductivity of semiconductors. P-type and n-type conductivity. P-n contact of two semiconductors. In intrinsic semiconductors, the number of electrons and holes appearing when bonds are broken is the same, i.e. The conductivity of intrinsic semiconductors is provided equally by free electrons and holes. Conductivity of impurity semiconductors. If an impurity with a valence greater than that of the native semiconductor is introduced into a semiconductor, a donor semiconductor is formed. (For example, when pentavalent arsenic is introduced into a silicon crystal. One of the five valence electrons of arsenic remains free). In a donor semiconductor, electrons are the majority charge carriers and holes are the minority charge carriers. Such semiconductors are called n-type semiconductors, and the conductivity is electronic. If an impurity with a valency lower than that of the native semiconductor is introduced into the semiconductor, an acceptor semiconductor is formed. (For example, when introducing trivalent indium into a silicon crystal. Each indium atom lacks one electron to form a pair-electron bond with one of the neighboring silicon atoms. Each of these unfilled bonds is a hole). In acceptor semiconductors, holes are the majority charge carriers and electrons are the minority charge carriers. Such semiconductors are called p-type semiconductors, and the conductivity is hole. Pentavalent impurity atoms are called donors: they increase the number of free electrons. Each atom of such an impurity adds one extra electron. In this case, no extra holes are formed. An impurity atom in the structure of a semiconductor turns into a stationary positively charged ion. The conductivity of the semiconductor will now be determined mainly by the number of free impurity electrons. In general, this type of conductivity is called conductivity n– type, and the semiconductor itself is a semiconductor n-type. When a trivalent impurity is introduced, one of the valence bonds of the semiconductor turns out to be unfilled, which is equivalent to the formation of a hole and a stationary negatively charged impurity ion. Thus, in this case, the hole concentration increases. Impurities of this type are called acceptors and, and conductivity due to the introduction of an acceptor impurity is called conductivity R-type. This type of semiconductor is called a semiconductor R-type.

20. Band theory of solids. Metals, dielectrics and semiconductors.

Band theory of solids- quantum mechanical theory of electron motion in a solid.

According to quantum mechanics, free electrons can have any energy - their energy spectrum is continuous. Electrons belonging to isolated atoms have certain discrete energy values. In a solid, the energy spectrum of electrons is significantly different; it consists of separate allowed energy zones, separated by zones of forbidden energies.

Dielectric(insulator) - a substance that practically does not conduct electric current. The concentration of free charge carriers in the dielectric does not exceed 10 8 cm −3 . The main property of a dielectric is its ability to polarize in an external electric field. From the point of view of the band theory of solids, a dielectric is a substance with a band gap greater than 3 eV. Semiconductors - a semiconductor differs from a dielectric only in that the width Δ of the band gap separating the valence band from the conduction band is much smaller (tens of times). At T= 0, the valence band in a semiconductor, as in a dielectric, is completely filled, and current cannot flow through the sample. But due to the fact that the energy Δ is small, even with a slight increase in temperature, some electrons can move into the conduction band (Fig. 3). Then electric current in the substance will become possible, and through two “channels” at once.

Firstly, in the conduction band, electrons, acquiring energy in the electric field, move to higher energy levels. Secondly, the contribution to the electric current comes from... empty levels left in the valence band by electrons that have gone to the conduction band. Indeed, the Pauli principle allows any electron to occupy a vacant level in the valence band. But, having occupied this level, it leaves its own level free, etc. If you follow not the movement of electrons through the levels in the valence band, but the movement of the empty levels themselves, then it turns out that these levels, which have the scientific name holes, also become current carriers. The number of holes is obviously equal to the number of electrons that have gone into the conduction band (the so-called conduction electrons), but holes have a positive charge because a hole is a missing electron.

Metals - Electrons in metals finally “forget” their atomic origin, their levels form one very wide zone. It is always filled only partially (the number of electrons is less than the number of levels) and therefore can be called the conduction band (Fig. 6). It's clear that in metals, current can flow even at zero temperature. Moreover, using quantum mechanics it can be proven that in ideal metal(the lattice of which has no defects) at T= 0 current must flow without resistance [2]!

Unfortunately, there are no ideal crystals, and zero temperature cannot be achieved. In reality, electrons lose energy by interacting with vibrating lattice atoms, so The resistance of real metal increases with temperature(as opposed to semiconductor resistance). But the most important thing is that at any temperature the electrical conductivity of a metal is significantly higher than the electrical conductivity of a semiconductor because the metal contains many more electrons capable of conducting electric current.

19. Molecule. Chemical bonds. Molecular spectra. Absorption of light. Spontaneous and stimulated emission. Optical quantum generators.

Molecule- an electrically neutral particle formed from two or more atoms linked by covalent bonds, the smallest particle of a chemical substance.

Chemical bond is the interaction of two atoms carried out by exchanging electrons. When a chemical bond is formed, atoms tend to acquire a stable eight-electron (or two-electron) outer shell, corresponding to the structure of the atom of the nearest inert gas. The following types of chemical bonds are distinguished: covalent(polar and nonpolar; exchange and donor-acceptor), ionic, hydrogen And metal.

MOLECULAR SPECTRA- absorption, emission or scattering spectra arising during quantum transitions of molecules from the same energy. states to another. M. s. determined by the composition of the molecule, its structure, the nature of the chemical. communication and interaction with external fields (and, therefore, with the atoms and molecules surrounding it). Naib. characteristic are M. s. rarefied molecular gases, when there is no broadening of spectral lines by pressure: such a spectrum consists of narrow lines with a Doppler width. ABSORPTION SVETA- decrease in optical intensity. radiation when passing through a cell. environment due to interaction with it, as a result of which light energy is converted into other types of energy or into optical energy. radiation of other spectral composition. Basic P.'s law relating intensity I beam of light passing through a layer of absorbing medium thick l with intensity of the incident beam I 0, is Bouguer's law Coefficient independent of light intensity. called absorption index, and, as a rule, is different for different wavelengths. This law was experimentally established by P. Bouguer (P. Bouguer, 1729) and subsequently theoretically derived by I. Lambert (J. N. Lambert, 1760) under very simple assumptions that when When passing through any layer of matter, the intensity of the light flux decreases by a certain fraction, depending only on the thickness of the layer l, i.e. dI/l =

The process of emission of an electromagnetic wave by an atom can be of two types: spontaneous and forced. In spontaneous emission, an atom moves from a higher energy level to a lower one spontaneously, without external influences on the atom. Spontaneous emission of an atom is due only to the instability of its upper (excited) state, as a result of which the atom is sooner or later freed from excitation energy by emitting a photon. Various atoms emit spontaneously, i.e. independently of each other, and generate photons that propagate in different directions, have different phases and polarization directions. Therefore, spontaneous emission is incoherent. Radiation can also arise if an electromagnetic wave with a frequency ν acts on an excited atom, satisfying the relation hν=Em-En, where Em, and En are the energies of the quantum states of the atom (the frequency ν is called resonant). The resulting radiation is stimulated. Each act of stimulated emission involves two photons. One of them, propagating from an external source (an external source for the atom in question can also be a neighboring atom), affects the atom, as a result of which a photon is emitted. Both photons have the same direction of propagation and polarization, as well as the same frequencies and phases. That is, stimulated emission is always coherent with the forcing one. Optical quantum generators (OQGs) or lasers are the only

sources of powerful monochromatic light. The principle of light amplification with

using atomic systems was first proposed in 1940 by V.A. Manufacturer.

However, justification for the possibility of creating an optical quantum

generator was given only in 1958 by C. Townes and A. Shavlov based on

achievements in the development of quantum devices in the radio range. First

optical quantum generator was realized in I960. It was a laser with

ruby crystal as a working substance. Creating an Inversion

population in it was carried out by the method of three-level pumping,

commonly used in paramagnetic quantum amplifiers.

18. Quantum theory of electrical conductivity.

Quantum theory of electrical conductivity of metals - theory of electrical conductivity, based on quantum mechanics and quantum statistics of Fermi - Dirac, - reconsidered the question of the electrical conductivity of metals, considered in classical physics. Calculation of the electrical conductivity of metals, performed on the basis of this theory, leads to an expression for the specific electrical conductivity of the metal, which in appearance resembles the classical formula (103.2) for g, but has a completely different physical content. Here P - concentration of conduction electrons in the metal, b l Fс is the mean free path of an electron having Fermi energy, b u F ñ - the average speed of thermal motion of such an electron.

The conclusions obtained on the basis of formula (238.1) are fully consistent with experimental data. The quantum theory of electrical conductivity of metals, in particular, explains the dependence of specific conductivity on temperature: g ~ 1/T(classical theory gives that g ~1/), as well as anomalously large values ​​(of the order of hundreds of lattice periods) of the mean free path of electrons in the metal.

17. Heat capacity of solids. As a model of a solid body, let us consider a correctly constructed crystal lattice, at the nodes of which particles (atoms, ions, molecules), taken as material points, oscillate around their equilibrium positions - lattice nodes - in three mutually perpendicular directions. Thus, each particle composing the crystal lattice is assigned three vibrational degrees of freedom, each of which, according to the law of equidistribution of energy among degrees of freedom, has the energy kT.

Internal energy of a mole of a solid

Where N A - Avogadro's constant; N A k= R (R - molar gas constant). Molar heat capacity of a solid

i.e. molar (atomic) heat capacity chemically simple bodies in crystalline

Heat capacity, the amount of heat consumed to change the temperature by 1°C. According to a more strict definition, heat capacity- thermodynamic quantity determined by the expression:

where Δ Q- the amount of heat imparted to the system and causing its temperature to change by Delta; T. Finite difference ratio Δ Q/ΔТ is called average heat capacity, the ratio of infinitesimal quantities d Q/dT- true heat capacity. Since d Q is not a complete differential of the state function, then heat capacity depends on the transition path between two states of the system. Distinguish heat capacity system as a whole (J/K), specific heat capacity[J/(g K)], molar heat capacity[J/(mol K)]. All formulas below use molar quantities heat capacity.

16. Degeneration of a system of particles.

Degeneracy in quantum mechanics lies in the fact that a certain quantity f, describing a physical system (atom, molecule, etc.) has the same meaning for different states of the system. The number of such different states that correspond to the same value f, is called the multiplicity of V. of a given quantity. DEGENERATION in quantum theory - the existence of various. states of a quantum system, in which there are certain physical states. magnitude A takes the same values. The operator corresponding to such a value has a set of linearly independent eigenfunctions corresponding to one eigenfunction. meaning A. Number TO called multiplicity of degeneracy of proper. values A, it can be finite or infinite; k can take on a discrete or continuous series of values. With infinite multiplicity (continuum powers) are degenerate, for example, proper. values ​​of the free particle energy operator in all possible directions of momentum (T and -mass and energy of the particle).

15. The principle of particle identity. Fermions and bosons. Distribution functions for bosons and fermions.

Fermions and bosons. Distribution functions for bosons and fermions. Boson(from the surname of the physicist Bose) - a particle with an integer spin value. The term was coined by physicist Paul Dirac. Bosons, unlike fermions, obey Bose-Einstein statistics, which allows an unlimited number of identical particles to exist in one quantum state. Systems of many bosons are described by wave functions that are symmetric with respect to particle permutations. There are elementary and composite bosons.

Elementary bosons are quanta of gauge fields, with the help of which the interaction of elementary fermions (leptons and quarks) in the Standard Model is carried out. These gauge bosons include:

photon (electromagnetic interaction),

gluon (strong interaction)

W ± and Z bosons (weak interaction).

Fermion- a particle (or quasiparticle) with a half-integer spin value. They got their name in honor of the physicist Enrico Fermi.

Examples of fermions: quarks (they form protons and neutrons, which are also fermions), leptons (electrons, muons, tau leptons, neutrinos), holes (quasiparticles in a semiconductor).

Fermions obey Fermi-Dirac statistics: no more than one particle can exist in one quantum state (Pauli principle). The Pauli exclusion principle is responsible for the stability of the electron shells of atoms, making the existence of complex chemical elements possible. It also allows the existence of degenerate matter under high pressures (neutron stars). The wave function of a system of identical fermions is antisymmetric with respect to the permutation of any two fermions. A quantum system consisting of an odd number of fermions is itself a fermion (for example, a nucleus with an odd mass number A; atom or ion with odd sum A and number of electrons).

Distribution functions for fermions and bosons can be easily obtained within the framework of a large canonical ensemble, choosing as a subsystem the set of all particles located in a given quantum state L. The energy of the system in this state is = The expression for the thermodynamic potential has the form

pl = -APpE exp[(ts-el)^A/(AG)]

For fermions = 0, 1; That's why

PL = -kT In ] . (3.1)

For bosons N^ = 0, 1, 2, ... Finding the sum of an infinite geometric progression, we obtain

fy = W In ] . (3.2)

and c< 0 Средние числа заполнения (или функции распре­деления) получаются с помощью термодинамического равенства

<"А>- f(ex) = Therefore, using (3.1) and (3.2) we have

KeA> = exp[(eA-fi)/(H")riT- (3-3>

The plus sign refers to fermions, the minus sign to bosons. Chemical potential /1 is determined from the condition of normalization of distribution functions:

$expL(eA-»i)V)J + 1 = N" (3"4)

where N is the total number of particles in the system. By introducing the density of states p(e), we can rewrite equality (3.4) in the form

N = Jde р(е) f(e). (3.5)

In order to break a nucleus into separate (free) nucleons that do not interact with each other, it is necessary to do work to overcome nuclear forces, that is, to impart a certain energy to the nucleus. On the contrary, when free nucleons combine into a nucleus, the same energy is released (according to the law of conservation of energy).

• The minimum energy required to split a nucleus into individual nucleons is called the nuclear binding energy

How can one determine the value of the binding energy of a nucleus?

The simplest way to find this energy is based on the application of the law on the relationship between mass and energy, discovered by the German scientist Albert Einstein in 1905.

Albert Einstein (1879-1955)
German theoretical physicist, one of the founders of modern physics. Discovered the law of the relationship between mass and energy, created the special and general theories of relativity

According to this law, there is a direct proportional relationship between the mass m of a particle system and the rest energy, i.e., the internal energy E 0 of this system:

where c is the speed of light in vacuum.

If the rest energy of a system of particles as a result of any processes changes by the value ΔE 0 1, then this will entail a corresponding change in the mass of this system by the value Δm, and the relationship between these quantities will be expressed by the equality:

ΔE 0 = Δmс 2.

Thus, when free nucleons merge into a nucleus, as a result of the release of energy (which is carried away by the photons emitted during this process), the mass of the nucleons should also decrease. In other words, the mass of a nucleus is always less than the sum of the masses of the nucleons of which it consists.

The lack of nuclear mass Δm compared to the total mass of its constituent nucleons can be written as follows:

Δm = (Zm p + Nm n) - M i,

where M i is the mass of the nucleus, Z and N are the number of protons and neutrons in the nucleus, and m p and m n are the masses of the free proton and neutron.

The quantity Δm is called the mass defect. The presence of a mass defect is confirmed by numerous experiments.

Let us calculate, for example, the binding energy ΔE 0 of the nucleus of a deuterium (heavy hydrogen) atom, consisting of one proton and one neutron. In other words, let's calculate the energy required to split a nucleus into a proton and a neutron.

To do this, we first determine the mass defect Δm of this nucleus, taking the approximate values ​​of the masses of nucleons and the mass of the nucleus of the deuterium atom from the corresponding tables. According to the tabular data, the proton mass is approximately 1.0073 a. e.m., neutron mass - 1.0087 a. e.m., the mass of the deuterium nucleus is 2.0141 a.m. a.m. So, Δm = (1.0073 a.u.m. + 1.0087 a.u.m.) - 2.0141 a.u. e.m. = 0.0019 a. eat.

To obtain the binding energy in joules, the mass defect must be expressed in kilograms.

Considering that 1 a. e.m. = 1.6605 10 -27 kg, we get:

Δm = 1.6605 10 -27 kg 0.0019 = 0.0032 10 -27 kg.

Substituting this value of the mass defect into the binding energy formula, we obtain:

The energy released or absorbed during any nuclear reactions can be calculated if the masses of interacting nuclei and particles formed as a result of this interaction are known.

Questions

1. What is the binding energy of a nucleus?
2. Write down the formula for determining the mass defect of any nucleus.
3. Write down the formula for calculating the binding energy of a nucleus.

1 The Greek letter Δ (“delta”) usually denotes a change in the physical quantity whose symbol is preceded by this letter.

By studying the composition of matter, scientists came to the conclusion that all matter consists of molecules and atoms. For a long time, the atom (translated from Greek as “indivisible”) was considered the smallest structural unit of matter. However, further research showed that the atom has a complex structure and, in turn, includes smaller particles.

What does an atom consist of?

In 1911, the scientist Rutherford suggested that the atom has a central part with a positive charge. This is how the concept of the atomic nucleus first appeared.

According to Rutherford's scheme, called the planetary model, the atom consists of a nucleus and elementary particles with a negative charge - electrons, moving around the nucleus, just as the planets orbit the Sun.

In 1932, another scientist, Chadwick, discovered the neutron, a particle that has no electrical charge.

According to modern ideas, the nucleus corresponds to the planetary model proposed by Rutherford. The nucleus carries most of the atomic mass. It also has a positive charge. The atomic nucleus contains protons - positively charged particles and neutrons - particles that do not carry a charge. Protons and neutrons are called nucleons. Negatively charged particles - electrons - move in orbit around the nucleus.

The number of protons in the nucleus is equal to those moving in orbit. Therefore, the atom itself is a particle that does not carry a charge. If an atom gains electrons from others or loses its own, it becomes positive or negative and is called an ion.

Electrons, protons and neutrons are collectively called subatomic particles.

Charge of the atomic nucleus

The nucleus has a charge number Z. It is determined by the number of protons that make up the atomic nucleus. Finding out this quantity is easy: just turn to Mendeleev’s periodic table. The atomic number of the element to which the atom belongs is equal to the number of protons in the nucleus. Thus, if the chemical element oxygen has an atomic number of 8, then the number of protons will also be eight. Since the number of protons and electrons in an atom is the same, there will also be eight electrons.

The number of neutrons is called the isotopic number and is designated by the letter N. Their number can vary in an atom of the same chemical element.

The sum of protons and electrons in the nucleus is called the mass number of the atom and is denoted by the letter A. Thus, the formula for calculating the mass number looks like this: A = Z + N.

Isotopes

When elements have equal numbers of protons and electrons, but different numbers of neutrons, they are called isotopes of a chemical element. There can be one or more isotopes. They are placed in the same cell of the periodic table.

Isotopes are of great importance in chemistry and physics. For example, an isotope of hydrogen - deuterium - in combination with oxygen gives a completely new substance called heavy water. It has a different boiling and freezing point than normal. And the combination of deuterium with another isotope of hydrogen, tritium, leads to a thermonuclear fusion reaction and can be used to generate huge amounts of energy.

Mass of the nucleus and subatomic particles

The size and mass of atoms are negligible in human perception. The size of the nuclei is approximately 10 -12 cm. The mass of an atomic nucleus is measured in physics in the so-called atomic mass units - amu.

For one amu take one twelfth of the mass of a carbon atom. Using the usual units of measurement (kilograms and grams), mass can be expressed by the following equation: 1 amu. = 1.660540·10 -24 g. Expressed in this way, it is called the absolute atomic mass.

Despite the fact that the atomic nucleus is the most massive component of an atom, its size relative to the electron cloud surrounding it is extremely small.

Nuclear forces

Atomic nuclei are extremely stable. This means that protons and neutrons are held in the nucleus by some force. These cannot be electromagnetic forces, since protons are similarly charged particles, and it is known that particles with the same charge repel each other. Gravitational forces are too weak to hold nucleons together. Consequently, particles are held in the nucleus by another interaction - nuclear forces.

Nuclear force is considered the strongest of all existing in nature. Therefore, this type of interaction between the elements of the atomic nucleus is called strong. It is present in many elementary particles, just like electromagnetic forces.

Features of nuclear forces

1. Short action. Nuclear forces, unlike electromagnetic ones, appear only at very small distances, comparable to the size of the nucleus.
2. Charge independence. This feature is manifested in the fact that nuclear forces act equally on protons and neutrons.
3. Saturation. The nucleons of the nucleus interact only with a certain number of other nucleons.

Nuclear binding energy

Another thing closely related to the concept of strong interaction is the binding energy of nuclei. Nuclear bond energy refers to the amount of energy required to split an atomic nucleus into its constituent nucleons. It equals the energy required to form a nucleus from individual particles.

To calculate the binding energy of a nucleus, it is necessary to know the mass of subatomic particles. Calculations show that the mass of a nucleus is always less than the sum of its constituent nucleons. A mass defect is the difference between the mass of a nucleus and the sum of its protons and electrons. Using the relationship between mass and energy (E=mc 2), one can calculate the energy generated during the formation of a nucleus.

The strength of the binding energy of a nucleus can be judged by the following example: the formation of several grams of helium produces the same amount of energy as the combustion of several tons of coal.

Nuclear reactions

The nuclei of atoms can interact with the nuclei of other atoms. Such interactions are called nuclear reactions. There are two types of reactions.

1. Fission reactions. They occur when heavier nuclei, as a result of interaction, decay into lighter ones.
2. Synthesis reactions. The reverse process of fission: nuclei collide, thereby forming heavier elements.

All nuclear reactions are accompanied by the release of energy, which is subsequently used in industry, the military, the energy sector, and so on.

Having familiarized ourselves with the composition of the atomic nucleus, we can draw the following conclusions.

1. An atom consists of a nucleus containing protons and neutrons, and electrons around it.
2. The mass number of an atom is equal to the sum of the nucleons in its nucleus.
3. Nucleons are held together by strong interactions.
4. The enormous forces that give stability to the atomic nucleus are called nuclear binding energies.