The force acting between an electron and the nucleus of an atom. Nuclear forces: properties

In physics, the concept of "force" denotes the 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 forces. The first of them corresponds to nuclear forces acting inside atomic nuclei.

What unites the cores?

It is generally known that the nucleus of an atom is tiny, four to five decimal orders of magnitude smaller than the size of the atom itself. This raises an obvious question: why is it so small? After all, atoms, 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 an accident?

Meanwhile, it is known that it is electrical forces that keep negatively charged electrons near atomic nuclei. What is the force or forces that hold the core particles together? This task is performed by nuclear forces, which are a measure of strong interactions.

Strong nuclear force

If there were only gravitational and electrical forces in nature, i.e. the ones we encounter in Everyday life, then atomic nuclei, often consisting of many positively charged protons, would be unstable: the electrical forces pushing protons apart will be many million times stronger than any gravitational forces attracting them to each other. 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 the phenomenon that is known as the strong nuclear interaction. Nuclear forces are its manifestation.

The figure above shows that the two opposite forces in the nucleus are the electrical repulsion between positively charged protons and the nuclear force that pulls protons (and neutrons) together. If the number of protons and neutrons is not too different, then the second forces are superior to the first.

Are protons analogs of atoms, and nuclei analogs of molecules?

What particles are nuclear forces acting between? 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 are quite simple. But in molecules, the distance between atoms is comparable to the size of atoms, so the intrinsic complexity of the latter comes into play. Diverse and difficult situation caused by 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. Likewise, the distance between protons and neutrons in a nucleus is comparable to their size - and just like molecules, the properties of the nuclear forces holding nuclei together are much more complex than the mere attraction of protons and neutrons.

There is no nucleus without a neutron, except for hydrogen

It is known that the kernels of some chemical elements stable, while in others they continuously decay, and the range of rates of this decay is very wide. Why do the forces that hold the nucleons in nuclei cease to act? Let's see what we can learn from simple considerations about the properties of nuclear forces.

One is that all nuclei, with the exception of the most abundant isotope hydrogen (which has only one proton), contain neutrons; that is, there is no nucleus with several protons that do not contain neutrons (see figure below). So it's clear that neutrons play an important role in helping protons stick together.

In fig. the above shows light stable or nearly stable nuclei together with a neutron. The latter, like tritium, is shown with a dotted line, indicating that they will eventually decay. Other combinations with a small number of protons and neutrons do not form nuclei at all, or form extremely unstable nuclei. In addition, alternative names often given to some of these objects are shown in italics; For example, the helium-4 nucleus is often referred to as the alpha particle, a name given to it when it was originally discovered in the first studies of radioactivity in the 1890s.

Neutrons as proton shepherds

On the contrary, there is no nucleus made only of neutrons without protons; most light nuclei such as oxygen and silicon have roughly the same number of neutrons and protons (Figure 2). Large nuclei with large masses, like gold and radium, have slightly more neutrons than protons.

This says two things:

1. Not only are neutrons needed to keep the protons together, but the protons are also needed to keep the neutrons together.

2. If the number of protons and neutrons becomes very large, then the electrical repulsion of the protons must be compensated for by adding a few additional 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 indicates stable nuclei. Any shift from the black line up or down means a decrease in the life of the nuclei - near it, the life of the nuclei is millions of years or more, as the blue, brown or yellow regions move inward ( different colors corresponds to different mechanisms of nuclear decay), their lifetimes are getting shorter, down to fractions of a second.

Note that stable kernels have P and N roughly equal for small P and N, but N gradually becomes more than 1.5 times larger than P. 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. With a large number of them, the known nuclei are in principle unstable (although they can exist for millions of years). Apparently, the above-mentioned mechanism of stabilization of protons in nuclei due to the addition of neutrons to them in this region does not have one hundred percent efficiency.

How the size of an atom depends on the mass of its electrons

How do the considered forces affect the structure of the atomic nucleus? Nuclear forces primarily affect its size. Why are nuclei so small compared to atoms? To find out, let's start with the simplest nucleus, which has both a proton and a neutron: it is the second most common isotope of hydrogen, the atom of which contains one electron (like all hydrogen isotopes) and a nucleus of one proton and one neutron. This isotope is often called "deuterium" and its nucleus (see Figure 2) is sometimes called "deuteron." How can we explain what holds the deuteron together? Well, you can imagine that it is not that different from an ordinary hydrogen atom, which also contains two particles (a proton and an electron).

In fig. it was shown above that in the hydrogen atom the nucleus and the electron are very far from each other, 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 size. This partly explains why nuclear forces are much more complex than forces in the atom.

It is known that electrons have a small mass compared to protons and neutrons. Hence it follows that

• the mass of an atom is essentially close to the mass of its nucleus,
• the size of an atom (essentially the size of an electron cloud) is inversely proportional to the mass of electrons and inversely proportional to the total electromagnetic force; uncertainty principle quantum mechanics plays a decisive role.

And if nuclear forces are similar to electromagnetic

What about the deuteron? It, like an atom, is made of two objects, but they have almost the same mass (the masses of a neutron and a proton differ only by about one 1500th part), so both particles are equally important in determining the mass of the deuteron and its size ... Now suppose 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 value was the same (at a certain distance) as the electromagnetic force, then this would mean that since a proton is about 1850 times heavier than an electron, then a deuteron (and indeed any nucleus) must be at least a thousand times smaller than hydrogen.

What gives taking into account the significant difference between nuclear and electromagnetic forces

But we already guessed that the nuclear force is much greater than the electromagnetic force (at the same distance), because if it is not, it would not be able to prevent the electromagnetic repulsion between the protons until the nucleus decays. So the proton and neutron under its action come closer together even more densely. And therefore it is not surprising that the deuteron and other nuclei are not just one thousand, but one hundred thousand times less than atoms! Again, this is only because

• protons and neutrons are almost 2000 times heavier than electrons,
• at these distances, the large nuclear force between protons and neutrons in the nucleus is many times greater than the corresponding electromagnetic forces (including the electromagnetic repulsion between protons in the nucleus.)

This naive guess gives a roughly 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 similar to electromagnetic, but with a greater attractive or repulsive ability, should evidently manifest itself in everyday life, but we do not see anything like it. So something in this force must be different from electrical forces.

Short range of nuclear power

What distinguishes them is that the nuclear forces that keep the atomic nucleus from decay 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, can also be the size of a moderately large nucleus, only several 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 dayton; if you spread them to greater distance they will hardly feel any attraction at all. In fact, if you place them too close together, 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.

Physical mechanism of nuclear interaction

Any material process, including the interaction between nucleons, must 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, now and then appearing and immediately 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, find themselves at a distance of about 10 -15 m, an exchange of pions occurs, similar to the exchange of valence electrons in atoms during the formation of molecules, and an attraction arises between 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 repulsion rather than attraction between the nucleons.

Nuclear forces: the structure of the nucleus from the simplest to the largest

Summarizing all of the above, we can note:

• strong nuclear force is much, much weaker than electromagnetism at distances much larger than the size of a typical nucleus, so we do not encounter it in everyday life; but
• at short distances, comparable to the nucleus, it becomes much stronger - the force of attraction (provided that the distance is not too short) is able to overcome the electrical repulsion between the protons.

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 outline of nuclear physics has been well studied for decades, many important details are still being actively explored.

Introduction

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 the 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 hence their own magnetic field. When charged particles move in a magnetic field, the Lorentz force acts on them, which is directed perpendicular to the particle velocity vector and the magnetic induction vector. Obviously, the Coulomb force and the Lorentz force are not enough, for the electron to remain in its orbital, the repulsive force between the electron and the proton is also required. Modern quantum concepts do not give a clear answer, what exactly is caused by the quantization of the orbitals and, consequently, the energies of the electron in the atom. Within the framework of this article, we will consider the reasons for quantization and obtain equations describing the behavior of an electron in an atom. Let me remind you that according to modern ideas the position of an electron in an atom is described by the probabilistic Schrödinger equation. We will receive a purely mechanical equation, which will make it possible to determine the position of the electron at any moment in time, which will show the inconsistency of the Heisenberg principle.

Balance of power

Figure 1 shows all the forces that act in an atom.

Figure 1 - forces acting on an electron in a hydrogen atom

Let's write down Newton's second law for the system of forces shown in the figure.

Let us write the system of equations for the projections of these forces on the XYZ coordinate axes.

(2)

Here the angle is the angle between the radius vector r (t) and the XY plane,

angle - the angle between the X axis and the projection of the radius vector r (t) on the XY plane.

Let us write down each force in system (2) in terms of well-known formulas, taking into account their projections on the axes.

Pendant Strength

, (3)

where is the electrical constant equal to

- modulus of charge of an electron or proton

- coordinates of the electron in the selected coordinate system

Potential force of gravitational waves

More information about this power can be found in the monograph

(4)

Are the masses of the electron and proton, respectively.

X- Proportionality factor numerically equal to square the speed of light.

As you know, the Lorentz force is calculated as follows

The vector product (5) can be represented in components on the axis orthogonal to the 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 a hydrogen atom is caused by a ring current of truly elementary particles moving in it, in accordance with the Bio-Savard-Laplace law obtained for a ring with a current, we write down the components of the magnetic induction vector:

(7)

angle is the angle of the circular contour

- proton radius

- 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.

- instantaneous curvature of the trajectory

- the speed of the electron relative to the origin

Is the normal vector to the trajectory of the electron

The instantaneous curvature of the trajectory is determined by the expression

- the first and second time derivatives of the radius vector.

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 in time, i.e.

The unit normal vector to the trajectory of the electron motion is determined by the expression

(11)

Expanding the vector products through the components of the vector on the coordinate axis, writing down the radius vector through its components, substituting expressions (9), (10), and (11) into (8), we obtain the components 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:

It is not possible to find an analytical solution to this system. The solution can be obtained by numerical methods for solving systems differential equations second order. The solution is shown in the video below.

The energy levels of an electron are determined by the whole number of resonant standing waves (a trail of antinodes behind the electron) arising along the trajectory of the electron's motion. If the energy of a photon absorbed by an electron corresponds to the energy required to form a whole number of standing waves, the motion 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 a picture of the absorption of a photon by an electron and then its emission. Photons, the energy of which does not lead to the emergence of a whole number of antinodes along the trajectory of the electron's motion, are not captured, because no resonance wave is formed and no absorption-radiation pattern is observed.

Inside the core, there are:

1) electric forces of repulsion between protons and

2) nuclear forces between nucleons (repulsion - at small and attraction - at large distances).

It was found that the nuclear forces are the same for both types of nucleons. The nuclear attraction between the protons significantly exceeds the electrical repulsion, as a result of which the proton is firmly held in the composition of the nucleus.

The core is surrounded by a potential barrier due to nuclear forces. The exit from the nucleus of a nucleon and a system of nucleons (for example, alpha particles) is possible either by the "tunnel effect", or by obtaining energy from the outside. In the first case, a spontaneous radioactive decay of the nucleus occurs, in the second, a forced nuclear reaction... Both processes allow making some judgments about the size of the kernel. Valuable information on the length of the potential barrier around nuclei was obtained in the study of scattering by nuclei of various bombarding particles - electrons, protons, neutrons, etc.

Studies have shown that the nuclear forces of attraction between nucleons decrease very quickly 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, on the basis of experimental data is expressed by the estimated 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 particle density decreases to the boundaries of the nucleus to zero, then in this case

These formulas show that the "effective" volume of the 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 the nuclei is very high; for example, for a nucleus with a mass radius

The state of a nucleon in different places inside the nucleus can be characterized by the amount of energy that must be expended in order 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 nucleon is located in the volume of the nucleus.

The interaction of nucleons in a nucleus can be compared with a similar interaction of atoms in crystal lattices metals, where

electrons play an essential role as "transmitters of interaction".

The difference lies in the fact that in nuclei, "transmitters of interaction" between nucleons are heavier particles - pi-mesons (or pions), whose mass is 273 times more mass 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 pi-mesons. Inside the nucleus, where the particles are at relatively small distances from each other, the pi-meson cloud actively participates in nuclear processes, causing the interaction and mutual transformations of nucleons.

Everything in the world, for example people, books, stars, is made 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 made up of interconnected protons and neutrons. Electrons revolve around the nucleus in their orbits. They revolve around the core in the same way as planets revolve around the Sun.

What are atoms made of?

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 basic forces at work in the universe. Negatively charged electrons are attracted to the positively charged protons of the atomic nucleus. Therefore, electrons rotate steadily in their orbits. The same electromagnetic force makes lightning flash.

Another force is the force of gravity. It attracts material objects to each other and is directly proportional to their masses. This force keeps the planets in orbits and makes the painting that fell from the wall to 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 a huge number of times greater than the force of gravity between them.

Intranuclear forces

In the nucleus of the atom, there are forces called the forces of intranuclear interaction. These forces press the protons and neutrons of the atomic nucleus into a tight ball. The fourth type of forces is the weak forces of intranuclear interaction. They are really very weak and become noticeable only in the process of radioactive decay of the nucleus with the emission of elementary particles.