Atomic nuclei are strongly bound systems of large number 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 a 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 system of nucleons decreases.
Calculation of nuclear binding energy
The binding energy of a nucleus is numerically equal to the work that must be expended to split a nucleus into individual nucleons, or the energy released during the synthesis of nuclei from nucleons.
A measure of the binding energy of a nucleus is the mass defect.
The formula for calculating the binding energy of a nucleus is Einstein's formula:
if there is some system of particles that has mass, then a change in the energy of this system leads to a change in its mass.
Here the binding energy of the nucleus is expressed by the product of the mass defect and the square of the speed of light.
IN nuclear physics the mass of particles is expressed in atomic mass units (amu)
in nuclear physics it is customary to express energy in electronvolts (eV):
Let's calculate the correspondence of 1 amu. electronvolts:
Now the calculation formula for binding energy (in electronvolts) will look like this:
EXAMPLE OF CALCULATION OF THE BINDING ENERGY OF THE NUCLEUS OF A HELIUM Atom (He)
>Topic 16. Atomic nucleus
Section 7. Elements of nuclear physics and particle physics
Questions:
1. Atomic nucleus. Mass defect. Binding energy of an atomic nucleus
2. Radioactive radiation. Law of radioactive decay.
3. Nuclear reactions. Nuclear reaction energy.
4. Elementary particles. Fundamental interaction.
5. Conclusion on discipline.
The atomic nucleus is the central part of the atom, in which all the positive charge and almost all the mass are concentrated.
The nuclei of all atoms are made up of particles called nucleons. Nucleons can be in two states - an electrically charged state and a neutral state. A nucleon in a charged state is called a proton. Proton (p) is the nucleus of the lightest chemical element– hydrogen. The proton charge is equal to the elementary positive charge, which is equal in magnitude to the elementary negative charge q e = 1.6 ∙ 10 -19 C., i.e. electron charge. A nucleon in a neutral (uncharged) state is called a neutron (n). The nucleon masses in both states differ little from each other, i.e. m n ≈ m p .
Nucleons are not elementary particles. They have a complex internal structure and consist of even smaller particles of matter - quarks.
The main characteristics of the atomic nucleus are charge, mass, spin and magnetic moment.
Core charge determined by the number of protons (z) included in the nucleus. The nuclear charge (zq) is different for different chemical elements. The number z is called the atomic number or charge number. The atomic number is the atomic number of a chemical element in periodic table elements of D. Mendeleev. The charge of the nucleus also determines the number of electrons in the atom. The number of electrons in an atom determines their distribution over energy shells and subshells and, consequently, all the physicochemical properties of the atom. The charge of the nucleus determines the specificity of a given chemical element.
Core mass The mass of the nucleus is determined by the number (A) of nucleons that make up the nucleus. The number of nucleons in a nucleus (A) is called the mass number. The number of neutrons (N) in the nucleus can be found if from total number nucleons (A) subtract the number of protons (z), i.e. N=F-z. In the periodic table, up to its middle, the number of protons and neutrons in the nuclei of atoms is approximately the same, i.e. (A-z)/z= 1, to the end of the table (A-z)/z= 1.6.
The nuclei of atoms are usually designated as follows:
X - symbol of a chemical element;
Z – atomic number;
A – mass number.
When measuring nuclear masses simple substances It has been discovered that most chemical elements are made up of groups of atoms. Having the same charge, the nuclei of different groups differ in mass. Varieties of atoms of a given chemical element, differing in nuclear masses, were called isotopes. Isotopic nuclei have the same number of protons, but a different number of neutrons (and; , ; ,).
In addition to isotope nuclei (z - same, A - different), there are nuclei isobars(z - different, A - the same). (And).
The masses of nucleons, atomic nuclei, atoms, electrons and other particles in nuclear physics are usually measured not in “KG”, but in atomic mass units (amu – otherwise called the carbon mass unit and denoted “e”). The atomic mass unit (1e) is taken to be 1/12 of the mass of a carbon atom 1e=1.6603 ∙ 10 -27 kg.
Nucleon masses: m p -1.00728 e, m n =1.00867 e.
We see that the mass of the nucleus expressed in “e” will be written as a number close to A.
Nuclear spin. Mechanical moment The momentum (spin) of the nucleus is equal to vector sum spins of the nucleons that make up the nucleus. The proton and neutron have a spin equal to L = ± 1/2ћ. In accordance with this, the spin of nuclei with an even number of nucleons (A is even) is an integer or zero. The spin of a nucleus with an odd number of nucleons (A odd) is half-integer.
Magnetic moment of the nucleus. The magnetic moment of the nucleus (P m i) of the nucleus in comparison with the magnetic moment of the electrons filling the electron shells of the atom is very small. On magnetic properties atom, the magnetic moment of the nucleus does not affect. The unit of measurement of the magnetic moment of nuclei is the nuclear magneton μ i = 5.05.38 ∙ 10 -27 J/T. It is 1836 times less than the magnetic moment of the electron - Bohr magneton μ B = 0.927 ∙ 10 -23 J/T.
The proton's magnetic moment is 2.793 μi and is parallel to the proton's spin. The magnetic moment of the neutron is 1.914 μi and is antiparallel to the neutron spin. The magnetic moments of nuclei are of the order of a nuclear magneton.
To split a nucleus into its constituent nucleons, a certain amount of work must be done. The amount of this work is a measure of the binding energy of the nucleus.
The binding energy of a nucleus is numerically equal to the work that must be done to split a nucleus into its constituent nucleons and without informing them kinetic energy.
During the reverse process of nuclear formation, the same energy should be released from the constituent nucleons. This follows from the law of conservation of energy. Therefore, the binding energy of the nucleus is equal to the difference between the energy of the nucleons that make up the nucleus and the energy of the nucleus:
ΔE = E nuk – E i. (1)
Taking into account the relationship between mass and energy (E = m ∙ c 2) and the composition of the nucleus, we rewrite equation (1) as follows:
ΔE = ∙ s 2 (2)
Magnitude
Δm = zm p +(A-z)m n – M i, (3)
The difference between the masses of the nucleons that make up the nucleus and the mass of the nucleus itself is called the mass defect.
Expression (2) can be rewritten as:
ΔE = Δm ∙ s 2 (4)
Those. mass defect is a measure of the binding energy of the nucleus.
In nuclear physics, the mass of nucleons and nuclei is measured in amu. (1 amu = 1.6603 ∙ 10 27 kg), and energy is usually measured in MeV.
Considering that 1 MeV = 10 6 eV = 1.6021 ∙ 10 -13 J, we find the energy value corresponding to the atomic mass unit
1.a.e.m. ∙ s 2 = 1.6603 ∙10 -27 ∙9 ∙10 16 = 14.9427 ∙ 10 -11 J = 931.48 MeV
Thus, the nuclear binding energy in MeV is equal to
ΔE light = Δm ∙931.48 MeV (5)
Considering that the tables usually give not the mass of nuclei, but the mass of atoms, for practical calculation of the mass defect, instead of formula (3)
use another
Δm = zm Н +(A-z)m n – M а, (6)
That is, the mass of the proton was replaced by the mass of a light hydrogen atom, thereby adding z electron masses, and the mass of the nucleus was replaced by the mass of the atom M a, thereby subtracting these z electron masses.
The binding energy per nucleon in the nucleus is called the specific binding energy
The dependence of the specific binding energy on the number of nucleons in the nucleus (on the mass number A) is given in Fig. 1.
Analysis of the graph shows:
1. Nucleons are more tightly bound in the nuclei of the elements in the middle part periodic table (30<А< 100), для этих ядер ≈8,7 МэВ.
2. For nuclei with a mass number A > 100, the specific binding energy decreases with increasing number of nucleons (A); for nuclei at the end of the periodic table ≈7.5 MeV.
3. For nuclei with mass number A< 30 удельная энергия связи с уменьшением числа нуклонов (А) уменьшается; для ядер начала периодической таблицы ≈ 1 - 3 МэВ.
4. For light nuclei, the specific binding energy exhibits characteristic maxima and minima: for odd-odd nuclei (,); the maximum is for even-even nuclei (,).
The analysis of the graph shows that it is energetically favorable for the lightest nuclei to merge with each other into heavier ones (the energy increases). On the contrary, the heaviest nuclei are energetically favored by the process of fission into fragments (lighter nuclei)
Topic 17. Radioactive radiation
Research shows that atomic nuclei are stable formations. This means that in the nucleus there is a certain bond between the nucleons. The study of this connection can be carried out without involving information about the nature and properties of nuclear forces, but based on the law of conservation of energy.
Let's introduce definitions.
The binding energy of a nucleon in the nucleus called physical quantity, equal to the work that must be done to remove a given nucleon from the nucleus without imparting kinetic energy to it.
Full nuclear binding energy is determined by the work that needs to be done to split a nucleus into its constituent nucleons without imparting kinetic energy to them.
From the law of conservation of energy it follows that when a nucleus is formed from its constituent nucleons, energy must be released equal to the binding energy of the nucleus. Obviously, the binding energy of a nucleus is equal to the difference between the total energy of the free nucleons that make up a given nucleus and their energy in the nucleus.
From the theory of relativity it is known that there is a relationship between energy and mass:
E = mс 2. (250)
If through ΔE St denote the energy released during the formation of a nucleus, then this release of energy, according to formula (250), should be associated with a decrease in the total mass of the nucleus during its formation from constituent particles:
Δm = ΔE St / from 2 (251)
If we denote by m p , m n , m I respectively, the masses of the proton, neutron and nucleus, then Δm can be determined by the formula:
Dm = [Zm р + (A-Z)m n]-m I . (252)
The mass of nuclei can be determined very accurately using mass spectrometers - measuring instruments, separating, using electric and magnetic fields, beams of charged particles (usually ions) with different specific charges q/m. Mass spectrometric measurements showed that, indeed, The mass of a nucleus is less than the sum of the masses of its constituent nucleons.
The difference between the sum of the masses of the nucleons making up the nucleus and the mass of the nucleus is called core mass defect(formula (252)).
According to formula (251), the binding energy of nucleons in the nucleus is determined by the expression:
ΔE SV = [Zm p+ (A-Z)m n - m I ]With 2 . (253)
The tables usually do not show the masses of nuclei m I, and the masses of atoms m a. Therefore, for the binding energy we use the formula:
ΔE SV =[Zm H+ (A-Z)m n - m a ]With 2 (254)
Where m H- mass of the hydrogen atom 1 H 1. Because m H more m r, by the electron mass m e , then the first term in square brackets includes the mass Z of electrons. But, since the mass of the atom m a different from the mass of the nucleus m I just by the mass Z of electrons, then calculations using formulas (253) and (254) lead to the same results.
Often, instead of the binding energy of nuclei, they consider specific binding energydE NE is the binding energy per one nucleon of the nucleus. It characterizes stability (strength) atomic nuclei, i.e. the more dE NE,the more stable the core . Specific binding energy depends on mass number A element. For light nuclei (A £ 12), the specific binding energy rises sharply to 6 ¸ 7 MeV, undergoing a number of jumps (see Figure 93). For example, for dE NE= 1.1 MeV, for -7.1 MeV, for -5.3 MeV. With a further increase in the mass number dE, the SV increases more slowly to a maximum value of 8.7 MeV for elements with A=50¸60, and then gradually decreases for heavy elements. For example, for it is 7.6 MeV. Let us note for comparison that the binding energy of valence electrons in atoms is approximately 10 eV (10 6 times less).
On the curve of specific binding energy versus mass number for stable nuclei (Figure 93), the following patterns can be noted:
a) If we discard the lightest nuclei, then in a rough, so to speak zero approximation, the specific binding energy is constant and equal to approximately 8 MeV per
nucleon. The approximate independence of the specific binding energy from the number of nucleons indicates the saturation property of nuclear forces. This property is that each nucleon can interact only with several neighboring nucleons.
b) The specific binding energy is not strictly constant, but has a maximum (~8.7 MeV/nucleon) at A= 56, i.e. in the region of iron nuclei, and decreases towards both edges. The maximum of the curve corresponds to the most stable nuclei. It is energetically favorable for the lightest nuclei to merge with each other, releasing thermonuclear energy. For the heaviest nuclei, on the contrary, the process of fission into fragments is beneficial, which occurs with the release of energy, called atomic.
The most stable are the so-called magic nuclei, in which the number of protons or the number of neutrons is equal to one of the magic numbers: 2, 8, 20, 28, 50, 82, 126. Double magic nuclei are especially stable, in which both the number of protons and number of neutrons. There are only five of these cores: , , , , .
Research shows that atomic nuclei are stable formations. This means that in the nucleus there is a certain bond between the nucleons.
The mass of nuclei can be very accurately determined using mass spectrometers - from measuring instruments that separate beams of charged particles (usually ions) with different specific charges Q/m using electric and magnetic fields. Mac spectrometric measurements have shown that The mass of a nucleus is less than the sum of the masses of its constituent nucleons. But since every change in mass (see § 40) must correspond to a change in energy, it follows that during the formation of a nucleus a certain energy must be released. The opposite also follows from the law of conservation of energy: to separate a nucleus into its component parts, it is necessary to expend the same amount of energy that is released during its formation. The energy that must be expended to split a nucleus into individual nucleons is called the binding energy of the nucleus (see § 40).
According to expression (40.9), the binding energy of nucleons in the nucleus
Where t r, t n, t i - respectively, the masses of the proton, neutron and nucleus. Tables usually do not show masses. T, nuclei, and masses T atoms. Therefore, for the binding energy of a nucleus they use the formula
where m n is the mass of the hydrogen atom. Since m n is greater than m p by the amount m e, then the first term in square brackets includes the mass Z electrons. But since the mass of the atom m differs from the mass of the nucleus m I just for the mass Z electrons, then calculations using formulas (252.1) and (252.2) lead to the same results. Magnitude
called nuclear mass defect. The mass of all nucleons decreases by this amount when an atomic nucleus is formed from them.
Often, instead of binding energy, specific binding energy is considered 8E a- binding energy per nucleon. It characterizes the stability (strength) of atomic nuclei, i.e. the greater dE St, the more stable the nucleus. Specific binding energy depends on mass number A element (Fig. 342). For light nuclei (A £ 12), the specific binding energy increases sharply to 6¸7 MeV, undergoing a number of jumps (for example, for 2 1 H dE св = 1.1 MeV, for 2 4 He - 7.1 MeV, for 6 3 Li - 5.3 MeV), then more slowly increases to a maximum value of 8.7 MeV for elements with A = 50¸60, and then gradually decreases for heavy elements (for example, for 238 92 U it is 7.6 MeV). Let us note for comparison that the binding energy of valence electrons in atoms is approximately 10 eV (10 b! times less).
The decrease in specific binding energy during the transition to heavy elements is explained by the fact that with an increase in the number of protons in the nucleus, their energy also increases Coulomb repulsion. Therefore, the bond between nucleons becomes less strong, and the nuclei themselves become less strong.
The most stable are the so-called magic nuclei, in which the number of protons or the number of neutrons is equal to one of the magic numbers: 2, 8, 20,28, 50, 82, 126. Double magic nuclei are especially stable, in which both the number of protons and number of neutrons (there are only five of these nuclei: 2 4 He, 16 8 O, 40 20 Ca, 48 20 Ca, 208 82 Ru.
From Fig. 342 it follows that the most stable from an energy point of view are the nuclei in the middle part of the periodic table. Heavy and light kernels are less stable. This means that the following processes are energetically favorable: 1) fission of heavy nuclei into lighter ones; 2) fusion of light nuclei with each other into heavier ones. Both processes release enormous amounts of energy; These processes are currently carried out practically: fission reactions and thermonuclear reactions.
Since most nuclei are stable, there is a special nuclear (strong) interaction between nucleons - attraction, which ensures the stability of nuclei, despite the repulsion of like-charged protons.
The binding energy of a nucleus is a physical quantity equal to the work that must be done to split a nucleus into its constituent nucleons without imparting kinetic energy to them.
From the law of conservation of energy it follows that during the formation of a nucleus the same energy must be released as must be expended during the splitting of the nucleus into its constituent nucleons. The binding energy of a nucleus is the difference between the energy of all the nucleons in the nucleus and their energy in the free state.
Binding energy of nucleons in an atomic nucleus:
where, are the masses of the proton, neutron and nucleus, respectively; - mass of a hydrogen atom; - atomic mass of this substance.
Mass corresponding to binding energy:
called nuclear mass defect. The mass of all nucleons decreases by this amount when a nucleus is formed from them.
Specific binding energy is the binding energy per nucleon: . It characterizes the stability (strength) of atomic nuclei, i.e. the more, the stronger the core.
The dependence of the specific binding energy on the mass number is shown in the figure. The nuclei in the middle part of the periodic table are the most stable (28<A<138). В этих ядрах составляет приблизительно 8,7 МэВ/нуклон (для сравнения, энергия связи валентных электронов в атоме порядка 10эВ, что в миллион раз меньше).
When moving to heavier nuclei, the specific binding energy decreases, since as the number of protons in the nucleus increases, the energy of their Coulomb repulsion increases (for example, for uranium it is 7.6 MeV). Therefore, the bond between nucleons becomes less strong, and the nuclei themselves become less strong.
Energetically favorable: 1) division of heavy nuclei into lighter ones; 2) fusion of light nuclei with each other into heavier ones. Both processes release enormous amounts of energy; these processes are now practically implemented; nuclear fission reactions and nuclear fusion reactions.
