Everything in the world, such as people, books, stars, is made up of atoms. The diameter of an average atom is eight billionths of an inch (1 inch equals 2.54 centimeters). To visualize how small this value is, let's say that the thickness of a book page is 500,000 atoms.
Each such tiny atom has a nucleus, consisting of protons and neutrons bound together. Electrons revolve around the nucleus in their orbits. They revolve around the core in the same way that the planets revolve around the Sun.
Atoms are thus made up of particles: protons, neutrons, and electrons. These particles are held together by electromagnetic forces. The electromagnetic force is one of the four main forces acting in the universe. Negatively charged electrons are attracted to positively charged protons in the nucleus of an atom. Therefore, electrons rotate stably in their orbits. The same electromagnetic force makes lightning flash.
Another force is gravity. It attracts material objects to each other and is directly proportional to their masses. This force keeps the planets in their orbits and makes a picture that has fallen from the wall fall to the floor. The force of gravity is more noticeable than the electromagnetic force, but the latter is much stronger. The electric forces of attraction and repulsion between charged particles in an atom are many times greater than the gravitational force between them.
Forces acting in the nucleus of an atom are called the forces of intranuclear interaction. These forces compress the protons and neutrons of the atomic nucleus into a dense ball. The fourth type of force is the weak force of intranuclear interaction. They are really very weak and become noticeable only in the process of radioactive decay of the nucleus during the emission of elementary particles.
In physics, the concept of "force" denotes a measure of the interaction of material formations with each other, including the interaction of parts of matter (macroscopic bodies, elementary particles) with each other and with physical fields (electromagnetic, gravitational). In total, four types of interaction in nature are known: strong, weak, electromagnetic and gravitational, and each has its own type of force. The first of them corresponds to the nuclear forces acting inside the atomic nuclei.
It is well known that the nucleus of an atom is tiny, its size is four to five decimal orders smaller than the size of the atom itself. This raises the obvious question: why is it so small? For atoms, which are made up of tiny particles, are still much larger than the particles they contain.
In contrast, nuclei do not differ much in size from the nucleons (protons and neutrons) from which they are made. Is there a reason for this or is it a coincidence?
Meanwhile, it is known that it is electrical forces that keep negatively charged electrons near atomic nuclei. What force or forces hold the particles of the nucleus together? This task is performed by nuclear forces, which are a measure of strong interactions.
If in nature there were only gravitational and electric forces, i.e. those that we encounter in everyday life, then atomic nuclei, often consisting of many positively charged protons, would be unstable: the electrical forces pushing the protons away from each other would be many millions of times stronger than any gravitational forces pulling them towards each other. friend. Nuclear forces provide an attraction even stronger than electrical repulsion, although only a shadow of their true magnitude appears in the structure of the nucleus. When we study the structure of the protons and neutrons themselves, we see the true possibilities of what is known as the strong nuclear force. Nuclear forces are its manifestation.
The figure above shows that the two opposing forces in the nucleus are the electrical repulsion between positively charged protons and the nuclear force, which pulls the protons (and neutrons) together. If the number of protons and neutrons is not too different, then the second forces outnumber the first.
Between which particles do nuclear forces act? First of all, between nucleons (protons and neutrons) in the nucleus. In the end, they also act between particles (quarks, gluons, antiquarks) inside a proton or neutron. This is not surprising when we recognize that protons and neutrons are intrinsically complex.
In an atom, tiny nuclei and even smaller electrons are relatively far apart compared to their size, and the electrical forces that hold them in the atom operate quite simply. But in molecules, the distance between atoms is comparable to the size of atoms, so the intrinsic complexity of the latter comes into play. The varied and complex situation caused by the partial compensation of intra-atomic electrical forces gives rise to processes in which electrons can actually move from one atom to another. This makes the physics of molecules much richer and more complex than that of atoms. Similarly, the distance between protons and neutrons in a nucleus is comparable to their size - and just like with molecules, the properties of nuclear forces that hold nuclei together are much more complex than the simple attraction of protons and neutrons.
It is known that the nuclei of some chemical elements are stable, while in others they continuously decay, and the range of rates of this decay is very wide. Why, then, do the forces that hold nucleons in nuclei cease to operate? Let's see what we can learn from simple considerations about what are the properties of nuclear forces.
One is that all nuclei, with the exception of the most common isotope of hydrogen (which has only one proton), contain neutrons; that is, there is no nucleus with multiple protons that does not contain neutrons (see figure below). So it's clear that neutrons play an important role in helping protons stick together.
On fig. light stable or nearly stable nuclei are shown above along with the neutron. The latter, like tritium, are shown with dotted lines, indicating that they eventually decay. Other combinations with a small number of protons and neutrons do not form nuclei at all, or form extremely unstable nuclei. Also shown in italics are alternative names often given to some of these objects; For example, the helium-4 nucleus is often referred to as an α particle, the name given to it when it was originally discovered in early radioactivity research in the 1890s.
Conversely, there is no nucleus made only of neutrons without protons; most light nuclei, such as oxygen and silicon, have about the same number of neutrons and protons (Figure 2). Large nuclei with large masses, like those of gold and radium, have somewhat more neutrons than protons.
This says two things:
1. Not only are neutrons needed to keep protons together, but protons are needed to keep neutrons together too.
2. If the number of protons and neutrons becomes very large, then the electrical repulsion of the protons must be compensated by adding a few extra neutrons.
The last statement is illustrated in the figure below.
The figure above shows stable and nearly stable atomic nuclei as a function of P (number of protons) and N (number of neutrons). The line shown with black dots denotes stable nuclei. Any shift from the black line up or down means a decrease in the life of nuclei - near it, the life of nuclei is millions of years or more, as the blue, brown or yellow regions move inward (different colors correspond to different mechanisms of nuclear decay), their life becomes shorter and shorter, down to fractions of a second.
Note that stable nuclei have P and N approximately equal for small P and N, but N gradually becomes larger than P by more than one and a half times. We also note that the group of stable and long-lived unstable nuclei remains in a rather narrow band for all values of P up to 82. For a larger number of them, the known nuclei are in principle unstable (although they can exist for millions of years). Apparently, the above-mentioned mechanism for stabilizing protons in nuclei by adding neutrons to them in this region is not 100% efficient.
How do the considered forces influence the structure of the atomic nucleus? Nuclear forces primarily affect its size. Why are nuclei so small compared to atoms? To figure this out, let's start with the simplest nucleus that has both a proton and a neutron: it's the second most common isotope of hydrogen, an atom that contains one electron (like all hydrogen isotopes) and a nucleus of one proton and one neutron. This isotope is often referred to as "deuterium" and its nucleus (see Figure 2) is sometimes referred to as "deuteron." How can we explain what holds the deuteron together? Well, one can imagine that it is not that different from an ordinary hydrogen atom, which also contains two particles (a proton and an electron).
On fig. above shows that in a hydrogen atom, the nucleus and electron are very far apart, in the sense that the atom is much larger than the nucleus (and the electron is even smaller.) But in the deuteron, the distance between the proton and the neutron is comparable to their sizes. This partly explains why nuclear forces are much more complex than the forces in an atom.
It is known that electrons have a small mass compared to protons and neutrons. Hence it follows that
What about the deuteron? It, like the atom, is made of two objects, but they are almost the same mass (the masses of the neutron and proton differ only by parts by about one 1500th part), so both particles are equally important in determining the mass of the deuteron and its size. . Now suppose that the nuclear force pulls the proton towards the neutron in the same way as the electromagnetic forces (this is not entirely true, but imagine for a moment); and then, by analogy with hydrogen, we expect the size of the deuteron to be inversely proportional to the mass of the proton or neutron, and inversely proportional to the magnitude of the nuclear force. If its magnitude was the same (at a certain distance) as that of the electromagnetic force, then this would mean that since the proton is about 1850 times heavier than the electron, then the deuteron (and indeed any nucleus) must be at least a thousand times smaller than hydrogen.
But we have already guessed that the nuclear force is much greater than the electromagnetic force (at the same distance), because if it were not, it would not be able to prevent the electromagnetic repulsion between protons until the nucleus decays. So the proton and neutron under its action come closer together even more closely. And therefore it is not surprising that the deuteron and other nuclei are not just one thousand, but one hundred thousand times smaller than atoms! Again, this is only because
This naive guess gives an approximately correct answer! But this does not fully reflect the complexity of the interaction between a proton and a neutron. One of the obvious problems is that a force like the electromagnetic one, but with more attractive or repulsive power, should be obvious in everyday life, but we do not observe anything like that. So something about this force must be different from electrical forces.
What distinguishes them is that the nuclear forces that keep the atomic nucleus from decaying are very important and large for protons and neutrons that are at a very short distance from each other, but at a certain distance (the so-called "range" of force), they fall very fast, much faster than electromagnetic. The range, it turns out, could also be the size of a moderately large nucleus, only a few times larger than a proton. If you place a proton and a neutron at a distance comparable to this range, they will be attracted to each other and form a deuteron; if they are further apart, they will hardly feel any attraction at all. In fact, if they are placed too close to each other, so that they start to overlap, they will actually repel each other. This is where the complexity of such a concept as nuclear forces manifests itself. Physics continues to develop continuously in the direction of explaining the mechanism of their action.
Any material process, including the interaction between nucleons, must also have material carriers. They are the quanta of the nuclear field - pi-mesons (pions), due to the exchange of which there is an attraction between nucleons.
According to the principles of quantum mechanics, pi-mesons, appearing and then disappearing, form around the “naked” nucleon something like a cloud called a meson coat (remember the electron clouds in atoms). When two nucleons surrounded by such coats are at a distance of the order of 10 -15 m, an exchange of pions occurs similar to the exchange of valence electrons in atoms during the formation of molecules, and attraction arises between the nucleons.
If the distances between nucleons become less than 0.7∙10 -15 m, then they begin to exchange new particles - the so-called. ω and ρ-mesons, as a result of which there is not an attraction between the nucleons, but a repulsion.
Summarizing all of the above, it can be noted:
So, this force matters only at distances comparable to the size of the nucleus. The figure below shows the form of its dependence on the distance between nucleons.
Large nuclei are held together by more or less the same force that holds the deuteron together, but the details of the process become more complex and difficult to describe. They are also not fully understood. Although the basic outlines of nuclear physics have been well understood for decades, many important details are still being actively explored.
Inside the kernel are:
1) electrical repulsive forces between protons and
2) nuclear forces between nucleons (repulsion - at small and attraction - at large distances).
It has been established that the nuclear forces are the same for both types of nucleons. The nuclear attraction between protons greatly exceeds the electrical repulsion, as a result of which the proton is firmly held in the composition of the nucleus.
The nucleus is surrounded by a potential barrier due to nuclear forces. The exit from the nucleus of the nucleon and the system of nucleons (for example, alpha particles) is possible either by the "tunnel effect" or by obtaining energy from outside. In the first case, a spontaneous radioactive decay of the nucleus occurs, in the second - a forced nuclear reaction. Both processes make it possible to make some judgments about the size of the kernel. Valuable information about the length of the potential barrier around nuclei was obtained by studying the scattering by nuclei of various bombarding particles - electrons, protons, neutrons, etc.
Studies have shown that the nuclear forces of attraction between nucleons decrease very rapidly with increasing distance between them. The average radius of action of nuclear forces, which can be interpreted in the same way as a certain conditional (“effective”) size of the nucleus, is expressed on the basis of experimental data by the estimation formula
If we assume that nuclei with a large number of nucleons consist of a core, where the particles are uniformly distributed over the volume, and a spherical shell, in which the density of particles decreases towards the boundaries of the nucleus to zero, then in this case
These formulas show that the "effective" volume of a nucleus is directly proportional to the number of nucleons; therefore, the nucleons in all nuclei are packed on average with almost the same density.
The density of nuclei is very high; for example, for a nucleus with a mass radius
The state of a nucleon in various places inside the nucleus can be characterized by the amount of energy that must be expended to extract this nucleon from the nucleus. It is called the binding energy of a given nucleon in the nucleus. In the general case, this energy is different for protons and neutrons and may depend on where the given nucleon is located in the volume of the nucleus.
The interaction of nucleons in the nucleus can be compared with the similar interaction of atoms in the crystal lattices of metals, where
electrons play a significant role as "transmitters of interaction".
The difference lies in the fact that in nuclei the "transmitters of interaction" between nucleons are heavier particles - pi-mesons (or pions), whose mass is 273 times greater than the mass of an electron. It is believed that nucleons continuously generate and absorb pi-mesons according to the scheme
so that each nucleon is surrounded by a cloud of virtual pions. Inside the nucleus, where the particles are located at relatively small distances from each other, the pi-meson cloud actively participates in nuclear processes, causing the interaction and mutual transformations of nucleons.
The hydrogen atom is the simplest in its structure. As you know, the hydrogen atom has a nucleus consisting of one proton and one electron located in the 1s orbital. Since the proton and electron have opposite charges, the Coulomb force acts between them. It is also known that the nuclei of atoms have their own magnetic moment and, consequently, their own magnetic field. When charged particles move in a magnetic field, they are affected by the Lorentz force, which is directed perpendicular to the particle velocity vector and the magnetic induction vector. It is obvious that the Coulomb force and the Lorentz force are not enough for the electron to remain in its orbit, a repulsive force between the electron and the proton is also necessary. Modern quantum concepts do not give a clear answer, what specifically caused the quantization of orbitals and, consequently, the energies of an electron in an atom. Within the framework of this article, we will consider the causes of quantization and obtain equations describing the behavior of an electron in an atom. Let me remind you that according to modern concepts, the position of an electron in an atom is described by the probabilistic Schrödinger equation. We will get a purely mechanical equation, which will make it possible to determine the position of the electron at any time, which will show the inconsistency of the Heisenberg principle.
Figure 1 shows all the forces that act in the atom.
Figure 1 - forces acting on an electron in a hydrogen atom
We write down Newton's second law for the system of forces shown in the figure.
Let us write down the system of equations for the projections of these forces onto the XYZ coordinate axes.
(2)
Here the angle is the angle between the radius vector r(t) and the XY plane,
angle – angle between the X axis and the projection of the radius vector r(t) onto the XY plane.
Let us describe each force in system (2) through known formulas, taking into account their projections on the axis.
, (3)
where is the electric constant equal to
is the charge modulus of an electron or proton
are the electron coordinates in the chosen coordinate system
More about this power can be found in the monograph
(4)
are the masses of the electron and proton, respectively.
X– The coefficient of proportionality is numerically equal to the square of the speed of light.
As you know, the Lorentz force is calculated as follows
Vector product (5) can be represented in components on the axis of an orthogonal coordinate system:
(6)
In the system of equations (6), it is necessary to determine the components of the magnetic induction vector 
.
Since the magnetic moment of the nucleus of the hydrogen atom is caused by the ring current of truly elementary particles moving in it, then, in accordance with the Biot-Savart-Laplace law obtained for a ring with current, we write down the components of the magnetic induction vector:
(7)
angle - this is the angle of bypassing the annular contour
is the proton radius
is the current strength in the proton ring circuit
– magnetic constant
As you know, the centrifugal force acts along the normal to the trajectory of the body and depends on the mass of the body, the curvature of the trajectory and the speed of movement.
is the instantaneous curvature of the trajectory
is the electron velocity relative to the origin
is the normal vector to the electron motion trajectory
The instantaneous curvature of the trajectory is given by
are the first and second derivatives of the radius vector with respect to time.
The speed of an electron is the root of the sum of the squares of its projections on the coordinate axes, which in turn are the first derivatives of the projections of the radius vector with respect to time, i.e.
The unit vector of the normal to the trajectory of the electron is determined by the expression
(11)
Expanding the vector products in terms of the vector components on the coordinate axes, writing the radius vector in terms of its components, substituting expressions (9), (10) and (11) into (8), we obtain the components of the centrifugal force in projections on the coordinate axes:
(12)
Having determined the projections of all forces included in the system of equations (2), it can be rewritten, taking into account the following expressions:
The resulting system looks like:
Finding an analytical solution to this system is not possible. The solution can be obtained by numerical methods for solving systems of second-order differential equations. The solution is shown in the video below.
The energy levels of an electron are determined by an integer number of resonant standing waves (a plume of antinodes behind the electron) that arise along the trajectory of the electron. If the energy of the photon absorbed by the electron corresponds to the energy necessary for the formation of a whole number of standing waves, the movement of the electron in them is repeated, making them resonant, thereby the photon is held by the electron for a certain time and we observe the picture of the absorption of the photon by the electron and then its emission. Photons, the energy of which does not lead to the appearance of a whole number of antinodes along the trajectory of the electron, are not captured, because no resonant wave is formed and no absorption-radiation pattern is observed.
