The binding energy of an atomic nucleus is the energy that must be expended to split the nucleus into individual nucleons. The same energy is released during the formation of a nucleus from free nucleons. It can be calculated using L. Einstein’s formula connecting particle mass and energy:

\(~W = mc^2\)

After the creation of the mass spectrograph, it was possible to measure with great accuracy (up to 0.01%) the masses of all isotopes of the elements of the periodic table, which is what the scientists did.

Analysis of these data shows that for all elements the rest mass of the nucleus is less than the sum of the rest masses of its constituent nucleons, if the latter are in a free state. This difference can be characterized by the magnitude

\(~\Delta m = \sum m_n - n_(ja) = Zm_p + (A-Z)m_n - m_(ja),\)

which is called mass defect. A decrease in mass during the formation of a nucleus from free particles means that the energy of this system of particles decreases by the amount of binding energy

\(~W_(sv) = \Delta mc^2 = (Zm_p+(A - Z)m_n - m_(ja))c^2 .\)

The binding energy is determined by the amount of work that needs to be done to split a nucleus into its constituent nucleons. But where does this energy go?

When a nucleus is formed from nucleons, the latter, due to the action of nuclear forces at short distances, rush towards each other with enormous accelerations. The \(~\gamma\) quanta emitted in this case have a binding energy W sv, i.e. When nuclei are formed from nucleons, this binding energy is released. The binding energy is very high (it is usually expressed in MeV: 1 MeV = 10 6 eV = 1.6 \(\cdot\) 10 -13 J). This value can be judged by the following example: the formation of 4 g of helium is accompanied by the release of the same energy as during the combustion of 5-6 cars of coal.

An important characteristic of the nucleus is the average nuclear binding energy per nucleon (the so-called specific nuclear binding energy),

\(\omega_(sv) = \frac(W_(sv))(A)\)

The larger it is, the stronger the nucleons are connected to each other, the stronger the nucleus. This specific binding energy \(~\omega_(sv)\) can always be calculated. The results show that for most nuclei \(\omega_(sv)\approx 8\) MeV and decreases for very light and very heavy nuclei.

As the number of nucleons in the nucleus increases, the Coulomb repulsive forces between protons increase, weakening the bonds in the nucleus, and the value of \(~\omega_(sv)\) for heavy nuclei decreases. The value \(~\omega_(sv)\) is maximum for nuclei average weight(A = 50...60), therefore, they are distinguished by the greatest strength (Fig. 22.1).

The processes of fission of heavy nuclei and fusion of light nuclei are energetically favorable because they are accompanied by an increase in binding energy, i.e. release of energy. This is the basis, as we will see below, for the production of atomic energy from the fission of heavy nuclei and thermonuclear energy from the fusion of light ones.

Literature

Aksenovich L. A. Physics in high school: Theory. Assignments. Tests: Textbook. allowance for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyhavanne, 2004. - P. 612-613.

Communication energy

the energy of a connected system of any particles (for example, an atom), equal to the work that must be expended in order to decompose this system into its constituent particles that are infinitely distant from each other and do not interact with each other. It is a negative value, because when a bound state is formed, energy is released; its absolute value characterizes the bond strength (for example, the stability of nuclei). According to Einstein's relation, E. s. equivalent to a mass defect (See Mass defect) Δ m: Δ E =Δ mc2(With - speed of light in vacuum). The meaning of E. s. determined by the type of interaction of particles in a given system. So, E. s. nucleus is due to strong interactions (See Strong interactions) of nucleons in the nucleus (for the most stable nuclei of intermediate atoms it is Binding energy8 10 6 eV per 1 nucleon - specific energy. It can be released when light nuclei fuse into heavier ones (see Thermonuclear reactions) , as well as during the fission of heavy nuclei, which is explained by a decrease in specific energy. (see Nuclear reactions) with increasing atomic number.

E. s. electrons in an atom or molecule is determined by electromagnetic interactions (See Electromagnetic interactions) and is proportional for each electron to the ionization potential (See Ionization potential) , for an electron of an atom and in the normal state it is equal to 13.6 ev. These same interactions determine

E. s. atoms in a molecule and crystal (see Chemical bond) . E. With. during gravitational interaction it is usually small, but for some space objects its value can be significant (see, for example, “Black hole” (See Black hole)).

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

Hydrogen isotopes differ from each other in mass by two or three times. Deuterium is non-radioactive and enters as a small mixture into ordinary hydrogen. When deuterium combines with oxygen, heavy water is formed, its physical properties noticeably different from the properties of ordinary water. At normal atmospheric pressure, it boils at 101.2 C and freezes at –3.8 C. Tritium has an atomic mass of 3 and is beta active, with a half-life of 12 years.

A mixture of three isotopes is natural uranium, which consists of U-238 (99.28%), U-235 (0.714%), U-234 (0.006%), the nucleus of these isotopes

In total, about 2000 natural and artificially produced radioactive isotopes are known. Some isotopes found in nature, and almost all isotopes produced artificially, cannot survive indefinitely. Such unstable isotopes are usually called radionuclides.

The term "isotopes" should be used only in cases where we are talking about atoms of the same chemical element. If we mean atoms of different chemical elements, it is recommended to use the term “nuclides”.

For example, a mixture of radionuclides Sr-90, I-131, Cs-137, but carbon isotopes C-12, C-14. Natural potassium is represented by three isotopes: K-39, K-40, K-41; respectively, 93.08%, 0.0119% and 6.91%.

Atomic nuclei with the same mass number A and different Z are called isobars, and atomic nuclei with the same number of neutrons N (at N = A – Z) are called isotones.

For example: nuclei 40 18 Ar, 40 19 K, 40 20 Ca are isobars (for them A = 40);

nuclei 136 54 Xe, 138 56 Ba, 139 57 La are isotones (for them N = 82).

The existence of isotopes proves that the charge of the nucleus does not determine all the properties of the atom, but only its chemical properties and those physical properties that depend on the electron shell, such as dimensions. The mass of an atom and its radioactive properties are not determined serial number in the periodic table.

3.2. Communication energy atomic nuclei

Nucleons in nuclei are in states that differ significantly from their free states. With the exception of the ordinary hydrogen nucleus, all nuclei have at least two nucleons, between which

In these cases, there is a nuclear strong interaction - an attraction that ensures the stability of nuclei, despite the repulsion of like-charged protons, i.e., between the nucleons that make up the nucleus of an atom, there are a special kind of force called nuclear. The peculiarity of these forces is that they act only at very small distances only between neighboring nucleons.

The strength of nuclei is characterized by binding energy. In its magnitude, the binding energy is equal to the work that must be expended to break a nucleus into its constituent nucleons without imparting kinetic energy to them. The same amount of energy is released when a nucleus is formed from nucleons. The binding energy of a nucleus is the difference between the energy of all the free nucleons that make up the nucleus and their energy in the nucleus.

The binding energy of nucleons in a nucleus is millions of times higher than the binding energy of atoms in a molecule. Therefore, during chemical transformations of substances, atomic nuclei do not change.

When a nucleus is formed, its mass decreases: the mass of the nucleus is less than the sum of the masses of its constituent nucleons. The decrease in the mass of the nucleus during its formation is explained by the release of binding energy. The amount of energy contained in a substance is directly related to its mass by Einstein’s relation

The most accurate measurements of nuclear masses show that the rest mass of a nucleus is always less than the sum of the rest masses of its constituent protons and neutrons:

A decrease in mass during the formation of a nucleus from nucleons means that the energy of this system of nucleons decreases by the amount of binding energy Eb:

		m c2 Z m			m c2 .

When a nucleus is formed from particles, the latter, due to the action of nuclear forces at short distances, rush towards each other with enormous acceleration. The gamma rays emitted in this case have energy Eb and mass m.

The binding energy per nucleon (i.e., the total binding energy divided by the number of nucleons in the nucleus) is called specific binding energy:

			E St.

The greater the absolute value of the specific binding energy, the stronger the interaction between nucleons and the stronger the nucleus. Highest energy the bond per nucleon, about 8.75 MeV, is inherent in the elements in the middle part of the periodic table.

3.3. Radioactivity. Law of Radioactive Decay

The phenomenon of spontaneous (spontaneous) change in the structure of the nucleus of an atom of one element and its transformation into a more stable nucleus of an atom of another element is called radioactivity, and the unstable core itself is radioactive.

Each such individual act of spontaneous transformation of nuclei with emission elementary particles or their groups are called radioactive decay. If radioactive decay is accompanied by the emission of alpha particles, then it is alpha decay; beta particles - beta decay. Alpha and beta decays are usually accompanied by gamma radiation.

Flows of elementary particles or their groups arising during independent transformations of atomic nuclei are ionizing radiation. There are three types of radioactive radiation: alpha, beta and gamma radiation.

From total number(about 2 thousand) of currently known radioactive nuclides, only about 300 are natural, the rest are obtained artificially as a result of nuclear reactions.

Spontaneous transformations of radioactive nuclei lead to a continuous decrease in the number of atomic nuclei of the original radionuclide and the formation of daughter products.

For a given radioactive substance, the probability of each nucleus decaying is the same at any time, since the nuclei decay independently of each other.

Law radioactive decay for any nuclear transformations, it establishes that the same fraction of undecayed nuclei of a given radionuclide always decays per unit time. This share is called decay constant and designate. IN general view this law is expressed by an exponential relationship:

N N0 et ,

where N is the number of nuclei that decayed during time;N 0 is the initial number of nuclei

radionuclide; e = 2.718; is the decay constant, and the corresponding half-life depends only on the stability of the nuclei.

This law, expressing the decrease in the number of nuclei of atoms of a radioactive substance over time, is called the law of radioactive decay (Fig. 4).

Rice. 4. Radioactive decay graph:

N 0 – initial amount of radioactive substance; T 1/2 – half-life of the substance

A radionuclide can transform into another radionuclide, which leads to the formation of so-called radioactive chains.

For any moment in time

	N 1N 0		e 1 t;
		N0 (e 1 t e 2 t )

where N 1 and N 2 are the number of nuclei of the parent and daughter radionuclides; N 0 is the number of nuclei of the parent radionuclide in starting moment time; 1 and 2 – decay constants of the parent and daughter radionuclides.

To characterize the stability of the nuclei of a radioactive substance with respect to decay, the concept of “half-life” is used. Half life radioactive substances - a period of time during which, as a result of radioactive decay, the number of nuclei of a given radioactive substance is halved. Accordingly, the intensity of the ionizing radiation emitted by this radioactive substance is halved. Between constant

decay () and half-life (T 1/2) there is a relationship

					0,693 .
The reciprocal of the decay constant is called the average
lifetime of a radioactive nucleus:
				T 1/ 2		1.443 T 1/ 2.

The half-life for various radionuclides ranges from fractions of a second to billions of years. Accordingly, radioactive substances are divided into short-lived (hours, days) and long-lived (many years).

For example: 214 84 Po (T 1/2 = 1.6 10–4 s); 238 92 U (T 1/2 = 4.47 1010 years).

Half-life is one of the main characteristics of radioactive substances, which is taken into account when practical application. Thus, in gamma therapy, preference is given to radioactive substances with a long half-life.

For example: 137 55 Cs (T 1/2 = 30 years); 27 60 Co (T 1/2 = 5.25 years).

When introducing radioactive substances into the body for diagnostic purposes, they strive to minimize the dose of radiation to organs and

Nuclear binding energy
Binding energy

Nuclear binding energy – the minimum energy required to split a nucleus into its constituent nucleons (protons and neutrons). The nucleus is a system of bound nucleons, consisting of Z protons (mass of a proton in a free state m p) and N neutrons (mass of a neutron in a free state m n). In order to split a nucleus into its component nucleons, a certain minimum energy W, called binding energy, must be expended. In this case, a nucleus at rest with mass M transforms into a set of free resting protons and neutrons with a total mass Zm p + Nm n. The energy of a nucleus at rest is Mc 2. Energy of released nucleons at rest (Zm p + Nm n)с 2. In accordance with the law of conservation of energy Mc 2 + W = (Zm p + Nm n)c 2. Or W = (Zm p + Nm n)c 2 - Ms 2. Since W > 0, then M< (Zm p + Nm n), т.е. масса, начального ядра, в котором нуклоны связаны, меньше суммы масс свободных нуклонов, входящих в его состав.
W increases with increasing number A of nucleons in the nucleus (A = Z + N). It is convenient to deal with the specific binding energy ε = W/A, i.e. average binding energy per nucleon. For most nuclei ε ≈ 8 MeV (1 MeV = 1.6·10 -13 J). To break a chemical bond, energy is needed 10 6 times less.

In order for atomic nuclei to be stable, protons and neutrons must be held inside the nuclei by enormous 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 represent a manifestation of the most intense type of interaction known in physics - the so-called strong interaction. Nuclear forces are approximately 100 times greater than electrostatic forces and tens of orders of magnitude greater than the forces of gravitational interaction between nucleons. Important feature nuclear forces is their short-range nature. Nuclear forces manifest themselves noticeably, as Rutherford’s experiments on the scattering of α-particles showed, only at distances on the order of the size of the nucleus (10–12–10–13 cm). At large distances, the action of relatively slowly decreasing Coulomb forces manifests itself.

Based on experimental data, we can conclude that protons and neutrons in the nucleus behave identically with respect to strong interaction, i.e., nuclear forces do not depend on the presence or absence of an electric charge on the particles.

The most important role in nuclear physics plays concept nuclear binding energy .

The binding energy of a nucleus is equal to the minimum energy that must be expended to completely split the nucleus into individual particles. From the law of conservation of energy it follows 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. Currently, physicists have learned to measure the masses of particles - electrons, protons, neutrons, nuclei, etc. - with very high accuracy. These measurements show that mass of any nucleus M Ialways less than the sum of the masses of its constituent protons and neutrons:

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

As an example, let's calculate the binding energy of a helium nucleus; for example, the ionization energy is 13.6 eV.

In tables it is customary to indicate specific binding energy , i.e. binding energy per nucleon. For a helium nucleus, the specific binding energy is approximately 7.1 MeV/nucleon. In Fig. 6.6.1 shows a graph of the specific binding energy versus mass number A. As can be seen from the graph, the specific binding energy of nucleons is not the same for different atomic nuclei. For light nuclei, the specific binding energy first increases steeply from 1.1 MeV/nucleon for deuterium to 7.1 MeV/nucleon for helium. Then, having undergone a series of jumps, the specific energy slowly increases to maximum value 8.7 MeV/nucleon for elements with mass number A= 50–60, and then decreases relatively slowly for heavy elements. For example, for uranium it is 7.6 MeV/nucleon.

The decrease in specific binding energy upon transition to heavy elements is explained by an increase in the energy of Coulomb repulsion of protons. In heavy nuclei, the bond between nucleons weakens, and the nuclei themselves become less strong.

In case stable lungs nuclei, where the role of the Coulomb interaction is small, the number of protons and neutrons Z And N turn out to be the same (, , ). Under the influence of nuclear forces, proton-neutron pairs are formed. But for heavy nuclei containing a large number of protons, due to the increase in the Coulomb repulsion energy, additional neutrons are required to ensure stability. In Fig. Figure 6.6.2 is a diagram showing the number of protons and neutrons in stable nuclei. For nuclei following bismuth ( Z> 83), due to large number For protons, complete stability turns out to be completely impossible.

From Fig. 6.6.1 it is clear that the most stable from an energy point of view are the nuclei of the elements in the middle part of the periodic system. This means that there are two possibilities for obtaining a positive energy yield from nuclear transformations:

1. division of heavy nuclei into lighter ones;

2. fusion of light nuclei into heavier ones.

Both of these processes release enormous amounts of energy. Currently, both processes have been carried out practically: fission reactions and thermonuclear reactions.

Let's do some estimations. Let, for example, a uranium nucleus be divided into two identical nuclei with mass numbers 119. For these nuclei, as can be seen from Fig. 6.6.1, specific binding energy is about 8.5 MeV/nucleon. The specific binding energy of the uranium nucleus is 7.6 MeV/nucleon. Consequently, the fission of a uranium nucleus releases energy equal to 0.9 MeV/nucleon or more than 200 MeV per uranium atom.

Let's now consider another process. Let, under certain conditions, two deuterium nuclei merge into one helium nucleus. The specific binding energy of deuterium nuclei is 1.1 MeV/nucleon, and the specific binding energy of helium nuclei is 7.1 MeV/nucleon. Consequently, the synthesis of one helium nucleus from two deuterium nuclei will release an energy equal to 6 MeV/nucleon or 24 MeV per helium atom.

It should be noted that the synthesis of light nuclei, compared to the fission of heavy nuclei, is accompanied by approximately 6 times greater energy release per nucleon.