The positive charge of the nucleus of an atom is equal. Atomic nucleus: nuclear charge

CORE CHARGE

Moseley's Law. The electric charge of the nucleus is formed by the protons that make up its composition. Number of protons Z they call it charge, meaning that the absolute value of the charge of the nucleus is equal to Ze. The nuclear charge coincides with the serial number Z element in periodic table Mendeleev's elements. The charges of atomic nuclei were first determined by the English physicist Moseley in 1913. By measuring the wavelength using a crystal λ characteristic X-ray radiation for the atoms of certain elements, Moseley discovered regular change wavelength λ for elements following each other in the periodic table (Fig. 2.1). Moseley interpreted this observation as dependence λ from some atomic constant Z, varying by one from element to element and equal to one for hydrogen:

where and are constants. From experiments on the scattering of X-ray quanta by atomic electrons and α -particles with atomic nuclei it was already known that the charge of the nucleus is approximately equal to half atomic mass and therefore close to the atomic number of the element. Since the emission of characteristic X-ray radiation is a consequence electrical processes in the atom, Moseley concluded that the atomic constant found in his experiments, which determines the wavelength of characteristic X-ray radiation and coincides with the atomic number of the element, can only be the charge of the atomic nucleus (Moseley's law).

Rice. 2.1. X-ray spectra of atoms of neighboring elements obtained by Moseley

The measurement of X-ray wavelengths is carried out with great accuracy, so that on the basis of Moseley's law, the atom's belonging to a chemical element is established absolutely reliably. At the same time, the fact that the constant Z in the last equation is the charge of the nucleus, although substantiated by indirect experiments, ultimately rests on a postulate - Moseley's law. Therefore, after Moseley’s discovery, nuclear charges were repeatedly measured in scattering experiments α -particles based on Coulomb's law. In 1920, Chadwig improved the technique for measuring the proportion of scattered α -particles and received the charges of the nuclei of copper, silver and platinum atoms (see table 2.1). Chadwig's data leaves no doubt about the validity of Moseley's law. In addition to these elements, the experiments also determined the charges of the nuclei of magnesium, aluminum, argon and gold.

Table 2.1. Results of Chadwick's experiments

Definitions. After Moseley's discovery, it became clear that the main characteristic of an atom is the charge of the nucleus, and not its atomic mass, as chemists of the 19th century assumed, because the charge of the nucleus determines the number of atomic electrons, and therefore Chemical properties atoms. The reason for the differences between the atoms of chemical elements is precisely that their nuclei have a different number of protons in their composition. On the contrary, a different number of neutrons in the nuclei of atoms with the same number of protons does not change the chemical properties of the atoms in any way. Atoms that differ only in the number of neutrons in their nuclei are called isotopes chemical element.

Belkin I.K. The charge of the atomic nucleus and Mendeleev’s periodic system of elements // Quantum. - 1984. - No. 3. - P. 31-32.

By special agreement with the editorial board and editors of the journal "Kvant"

Modern ideas about the structure of the atom arose in 1911 - 1913, after Rutherford's famous experiments on the scattering of alpha particles. In these experiments it was shown that α -particles (their charge is positive), falling on a thin metal foil, are sometimes deflected by large angles and even thrown back. This could only be explained by the fact that the positive charge in the atom is concentrated in a negligibly small volume. If we imagine it in the form of a ball, then, as Rutherford established, the radius of this ball should be approximately 10 -14 -10 -15 m, which is tens and hundreds of thousands of times smaller sizes atom as a whole (~10 -10 m). Only near such a small positive charge can there exist electric field, capable of discarding α -a particle traveling at a speed of about 20,000 km/s. Rutherford called this part of the atom the atomic nucleus.

This is how the idea arose that an atom of any substance consists of a positively charged nucleus and negatively charged electrons, the existence of which in atoms was established earlier. Obviously, since the atom as a whole is electrically neutral, the charge of the nucleus must be numerically equal to the charge of all the electrons present in the atom. If we denote the charge modulus of an electron by the letter e (elementary charge), then the charge q i kernel should be equal q i = Ze, Where Z- an integer equal to the number of electrons in an atom. But what is the number Z? What is the charge? q am I the core?

From Rutherford's experiments, which made it possible to determine the size of the nucleus, it is, in principle, possible to determine the magnitude of the nuclear charge. After all, the electric field that rejects α -particle depends not only on the size, but also on the charge of the nucleus. And Rutherford actually estimated the charge of the nucleus. According to Rutherford, the charge on the nucleus of an atom of a chemical element is approximately equal to half of its relative atomic mass A, multiplied by the elementary charge e, that is

\(~Z = \frac(1)(2)A\).

But, oddly enough, the true charge of the nucleus was established not by Rutherford, but by one of the readers of his articles and reports - the Dutch scientist Van den Broek (1870-1926). It’s strange because Van den Broek by education and profession was not a physicist, but a lawyer.

Why did Rutherford, when estimating the charges of atomic nuclei, correlate them with atomic masses? The fact is that when in 1869 D.I. Mendeleev created the periodic system of chemical elements, he arranged the elements in increasing order of their relative atomic masses. And over the past forty years everyone has become accustomed to the fact that the most important characteristic of a chemical element - its relative atomic mass, which is what distinguishes one element from another.

Meanwhile, it was at this time, at the beginning of the 20th century, that difficulties arose with the system of elements. During the study of the phenomenon of radioactivity, a number of new radioactive elements. And there seemed to be no place for them in the Mendeleev system. It seemed that the Mendeleev system required changes. Van den Broek was especially concerned about this. Over the course of several years, they were offered several options for an expanded system of elements, in which there would be enough space not only for undiscovered stable elements (D.I. Mendeleev himself “took care” of the places for them), but also for radioactive elements too. Van den Broek published the last version in early 1913, it had 120 places, and uranium occupied cell number 118.

Also in 1913, the results of the latest research on scattering were published α -particles at large angles, carried out by Rutherford's collaborators Geiger and Marsden. Analyzing these results, Van den Broek made a crucial discovery. He found that the number Z in the formula q i = Ze not equal to half relative mass atom of a chemical element, but its atomic number. And, moreover, the serial number of the element in the Mendeleev system, and not in his, Van den Broek’s, 120-place system. It turns out that the Mendeleev system did not need to be changed!

From Van den Broek’s idea it follows that every atom consists of an atomic nucleus, the charge of which is equal to the serial number of the corresponding element in the Mendeleev system, multiplied by the elementary charge, and electrons, the number of which in the atom is also equal to the serial number of the element. (A copper atom, for example, consists of a nucleus with a charge of 29 e, and 29 electrons.) It became clear that D.I. Mendeleev intuitively arranged the chemical elements in increasing order not of the atomic mass of the element, but of the charge of its nucleus (although he did not know about this). Consequently, one chemical element differs from another not by its atomic mass, but by the charge of the atomic nucleus. The charge of the nucleus of an atom is main characteristic chemical element. There are atoms completely various elements, but with the same atomic masses (they have a special name - isobars).

The fact that it is not atomic masses that determine the position of an element in a system is also evident from the periodic table: in three places the rule of increasing atomic mass is violated. Thus, the relative atomic mass of nickel (No. 28) is less than that of cobalt (No. 27), of potassium (No. 19) it is less than that of argon (No. 18), of iodine (No. 53) less than that of tellurium ( No. 52).

The assumption about the relationship between the charge of the atomic nucleus and the atomic number of the element easily explained the rules of displacement during radioactive transformations, discovered in the same 1913 (“Physics 10”, § 103). In fact, when emitted by the nucleus α -particle, the charge of which is equal to two elementary charges, the charge of the nucleus, and therefore its serial number (now usually called the atomic number) should decrease by two units. When emitting β -particle, that is, a negatively charged electron, it should increase by one unit. This is exactly what the rules of displacement are.

Van den Broek's idea very soon (literally in the same year) received its first, albeit indirect, experimental confirmation. Somewhat later, its correctness was proven by direct measurements of the charge of the nuclei of many elements. It's clear that she played important role V further development physics of the atom and the atomic nucleus.

At the heart of any science lies something small and important. In biology it is a cell, in linguistics it is a letter and a sound, in engineering it is a cog, in construction it is a piece of sand, and for chemistry and physics the most important thing is the atom and its structure.

This article is intended for persons over 18 years of age

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An atom is the smallest particle of everything that surrounds us, which carries all the necessary information, a particle that determines characteristics and charges. For a long time scientists thought that it was indivisible, one, but over the course of long hours, days, months and years, studies, research and experiments were carried out, which proved that the atom also has its own structure. In other words, this microscopic ball is made up of even smaller components that affect the size of its core, properties and charge. The structure of these particles is as follows:

  • electrons;
  • nucleus of an atom.

The latter can also be divided into very elementary parts, which in science are called protons and neurons, of which there is a clear number in each specific case.

The number of protons that are in the nucleus indicates the structure of the shell, which consists of electrons. This shell, in turn, contains everything necessary properties a certain material, substance or object. Calculating the sum of protons is very simple - it is enough to know the serial number of the smallest part of the substance (atom) in the well-known periodic table. This value is also called the atomic number and is denoted Latin letter"Z". It is important to remember that protons have a positive charge, and in writing this value is defined as +1.

Neurons are the second component of the nucleus of an atom. This is an elementary subatomic particle that does not carry any charge, unlike electrons or protons. Neurons were discovered in 1932 by J. Chadwick, for which, 3 years later, he received Nobel Prize. In textbooks and scientific works they are denoted by the Latin symbol "n".

The third component of the atom is the electron, which is in monotonous motion around the nucleus, thus creating a cloud. This particle is the lightest of all known modern science, which means that its charge is also the smallest. The electron is denoted by the letter from −1.

It is the combination of positive and negative particles in the structure that makes an atom an uncharged or neutrally charged particle. The nucleus, in comparison with the overall size of the entire atom, is very small, but it is in it that all the weight is concentrated, which indicates its high density.

How to determine the charge of an atomic nucleus?

To determine the charge of the nucleus of an atom, you need to have a good understanding of the structure of the atom itself and its nucleus, understand the basic laws of physics and chemistry, and also be armed with the periodic table of Mendeleev to determine the atomic number of a chemical element.

  1. Knowledge that a microscopic particle of any substance has in its structure a nucleus and electrons, which create a shell in the form of a cloud near it. The nucleus, in turn, includes two types of elementary indivisible particles: protons and neurons, each of which has its own properties and characteristics. Neurons do not have an electronic charge in their arsenal. This means that their charge is neither equal nor greater or less than zero. Protons, unlike their counterparts, carry a positive charge. In other words, their electric charge can be designated as +1.
  2. Electrons, which are an integral part of every atom, also carry a certain type of electric charge. They are negatively charged elementary particles, and in writing they are defined as −1.
  3. To calculate the charge of an atom, you need knowledge about its structure (we just remembered necessary information), the number of elementary particles in the composition. And in order to find out the amount of charge of an atom, you need to mathematically add the number of some particles (protons) to others (electrons). Usually, the characteristics of an atom indicate that it is electron neutral. In other words, the value of electrons is equal to the number of protons. The result is this: the charge value of such an atom is zero.
  4. An important nuance: there are situations when the number of positively and negatively charged elementary particles in the nucleus may not be equal. This means that the atom becomes an ion with a positive or negative charge.

Designation of the nucleus of an atom in scientific field looks like Ze. It’s quite simple to decipher: Z is the number assigned to an element in the well-known periodic table; it is also called an ordinal or charge number. And it indicates the number of protons in the nucleus of an atom, and e is just the charge of the proton.

In modern science there are nuclei with different meaning charges: from 1 to 118.

Another important concept that young chemists need to know is mass number. This concept indicates the total charge of nucleons (these are the smallest components of the nucleus of an atom of a chemical element). And you can find this number if you use the formula: A = Z + N where A is the desired mass number, Z is the number of protons, and N is the value of neutrons in the nucleus.

What is the charge on the nucleus of a bromine atom?

To demonstrate in practice how to find the charge of an atom required element(in our case, bromine), you should turn to the periodic table of chemical elements and find bromine there. Its atomic number is 35. This means that its nuclear charge is 35, since it depends on the number of protons in the nucleus. And the number of protons is indicated by the number under which the chemical element stands in Mendeleev’s great work.

Let's give a few more examples to make it easier for young chemists to calculate the necessary data in the future:

  • The nuclear charge of the sodium atom (na) is 11, since it is under this number that it can be found in the table of chemical elements.
  • the charge of the phosphorus nucleus (the symbolic designation of which is P) has a value of 15, because that is how many protons are in its nucleus;
  • sulfur (with the graphic designation S) is a neighbor in the table of the previous element, therefore its nuclear charge is 16;
  • iron (and we can find it in the designation Fe) is number 26, which indicates the same number of protons in its nucleus, and therefore the charge of the atom;
  • carbon (aka C) is number 6 on the periodic table, which indicates the information we need;
  • magnesium has atomic number 12, and in international symbolism it is known as Mg;
  • chlorine in the periodic table, where it is written as Cl, is number 17, therefore its atomic number (which is what we need) is the same - 17;
  • calcium (Ca), which is so beneficial for young organisms, is found at number 20;
  • the charge of the nucleus of a nitrogen atom (with the written designation N) is 7, and it is in this order that it is presented in the periodic table;
  • barium is number 56, which is equal to it atomic mass;
  • the chemical element selenium (Se) has 34 protons in its nucleus, and this shows that this is exactly what the charge of the nucleus of its atom will be;
  • silver (or in written designation Ag) has an atomic number and atomic mass of 47;
  • if you need to find out the charge of the nucleus of a lithium atom (Li), then you need to turn to the beginning of Mendeleev’s great work, where it is numbered 3;
  • Aurum or our beloved gold (Au) has an atomic mass of 79;
  • for argon this value is 18;
  • Rubidium has an atomic mass of 37, while strontium has an atomic mass of 38.

It would take a very long time to list all the components of Mendeleev’s periodic table, because there are a lot of them (these components). The main thing is that the essence of this phenomenon is clear, and if you need to calculate the atomic number of potassium, oxygen, silicon, zinc, aluminum, hydrogen, beryllium, boron, fluorine, copper, fluorine, arsenic, mercury, neon, manganese, titanium, then you only need to refer to the table of chemical elements and find out the serial number of a particular substance.

Instructions

In the table of D.I. Mendeleev, as in a multi-story apartment building"" chemical elements, each of which occupies its own own apartment. Thus, each of the elements has a specific serial number indicated in the table. The numbering of chemical elements starts from left to right, and from top to bottom. In a table, horizontal rows are called periods, and vertical columns are called groups. This is important, because by group or period number you can also characterize some parameters atom.

An atom is a chemically indivisible, but at the same time consisting of smaller components, which can be classified as (positively charged particles), (negatively charged) (neutral particles). The bulk atom in the nucleus (due to protons and neutrons), around which electrons rotate. In general, the atom is electrically neutral, that is, the number of positive charges coincides with the number of negative ones, therefore, the number of protons is the same. Positive charge kernels atom takes place precisely due to protons.

Example No. 1. Determine the charge kernels atom carbon (C). We begin to analyze the chemical element carbon, focusing on the table of D.I. Mendeleev. Carbon is in "apartment" No. 6. Therefore, it kernels+6 due to 6 protons (positively charged particles) that are located in the nucleus. Considering that the atom is electrically neutral, this means there will also be 6 electrons.

Example No. 2. Determine the charge kernels atom aluminum (Al). Aluminum has a serial number - No. 13. Therefore, the charge kernels atom aluminum +13 (due to 13 protons). There will also be 13 electrons.

Example No. 3. Determine the charge kernels atom silver (Ag). Silver has a serial number - No. 47. This means the charge kernels atom silver + 47 (due to 47 protons). There are also 47 electrons.

note

In D.I. Mendeleev’s table, in one cell for each chemical element two are indicated numeric values. Do not confuse the atomic number and relative atomic mass of an element

An atom of a chemical element consists of kernels and electronic shell. The nucleus is the central part of the atom, in which almost all of its mass is concentrated. Unlike the electron shell, the nucleus has a positive charge.

You will need

  • Atomic number of a chemical element, Moseley's law

Instructions

Thus, charge kernels equal to the number of protons. In turn, the number of protons in the nucleus is equal to the atomic number. For example, the atomic number of hydrogen is 1, that is, the hydrogen nucleus consists of one proton and has charge+1. The atomic number of sodium is 11, charge his kernels equals +11.

During alpha decay kernels its atomic number is reduced by two due to the emission of an alpha particle ( kernels atom). Thus, the number of protons in a nucleus that has undergone alpha decay is also reduced by two.
Beta decay can occur in three different ways. In the case of beta-minus decay, the neutron turns into an antineutrino upon emission. Then charge kernels per unit.
In the case of beta-plus decay, a proton turns into a neutron, positron and nitrino, charge kernels decreases by one.
In case of electronic capture charge kernels also decreases by one.

Charge kernels can also be determined from the frequency of the spectral lines of the characteristic radiation of an atom. According to Moseley's law: sqrt(v/R) = (Z-S)/n, where v is the spectral characteristic radiation, R is the Rydberg constant, S is the screening constant, n is the principal quantum number.
Thus, Z = n*sqrt(v/r)+s.

Video on the topic

Sources:

  • how does the nuclear charge change?

An atom is the smallest particle of each element that carries its chemical properties. Both the existence and the structure of the atom have been the subject of speculation and study since ancient times. It was found that the structure of atoms is similar to the structure solar system: in the center is a core that takes up very little space, but contains almost all the mass; “planets” revolve around it - electrons carrying negative charges. How can you find the charge? kernels atom?

Instructions

Any atom is electrically neutral. But, since they carry negative charges, they must be balanced opposite charges. This is true. Positive charges carry particles called “protons” located in the nucleus of an atom. A proton is much more massive than an electron: it weighs as much as 1836 electrons!

The simplest case is the hydrogen atom of the first element of the Periodic Table. Looking at the table, you will see that it is number one, and its nucleus consists of a single proton, around which a single proton rotates. It follows that kernels hydrogen atom is +1.

The nuclei of other elements no longer consist only of protons, but also of so-called “neutrons”. As you can easily tell from the name itself, they do not carry any charge at all - neither negative nor positive. Therefore, remember: no matter how many neutrons are part of the atomic kernels, they affect only its mass, but not its charge.

Therefore, the amount of positive charge kernels of an atom depends only on how many protons it contains. But since, as already indicated, the atom is electrically neutral, its nucleus should contain the same number of protons that rotates around kernels. The number of protons is determined by the atomic number of the element in the Periodic Table.

Consider several elements. For example, the well-known and vital oxygen is in “cell” number 8. Therefore, its nucleus contains 8 protons, and the charge kernels will be +8. Iron occupies “cell” number 26, and, accordingly, has a charge kernels+26. And the metal - with serial number 79 - will have exactly the same charge kernels(79), with a + sign. Accordingly, an oxygen atom contains 8 electrons, an atom contains 26, and a gold atom contains 79.

Video on the topic

IN normal conditions the atom is electrically neutral. In this case, the nucleus of an atom, consisting of protons and neutrons, is positive, and electrons carry a negative charge. When there is an excess or deficiency of electrons, an atom turns into an ion.

Instructions

Chemical compounds can be molecular or ionic in nature. Molecules are also electrically neutral, and ions carry some charge. Thus, the ammonia molecule NH3 is neutral, but the ammonium ion NH4+ is positively charged. Bonds in the ammonia molecule formed according to the exchange type. The fourth hydrogen atom is added via a donor-acceptor mechanism, this is also a covalent bond. Ammonium is formed when ammonia reacts with acid solutions.

It is important to understand that the charge of the nucleus of an element does not depend on chemical transformations. No matter how many electrons you add or take away, the charge on the nucleus will remain the same. For example, an O atom, an O- anion, and an O+ cation are characterized by the same nuclear charge of +8. In this case, the atom has 8 electrons, the anion 9, and the cation 7. The nucleus itself can only be changed through nuclear transformations.

The most common type of nuclear reaction is radioactive decay, which can occur in the natural environment. The atomic mass of elements undergoing such decay is enclosed in square brackets. This means that the mass number is not constant and changes over time.

In the periodic table of elements D.I. Mendeleev silver has serial number 47 and the designation “Ag” (argentum). The name of this metal probably comes from the Latin “argos”, which means “white”, “shining”.

Instructions

Silver was known to mankind back in the 4th millennium BC. IN Ancient Egypt it was even called “white gold”. This metal occurs in nature both in native form and in the form of compounds, for example, sulfides. Silver nuggets are heavy and often contain impurities of gold, mercury, copper, platinum, antimony and bismuth.

Chemical properties of silver.

Silver belongs to the group of transition metals and has all the properties of metals. However, the activity of silver is low - in the electrochemical voltage series of metals it is located to the right of hydrogen, almost at the very end. In compounds, silver most often exhibits an oxidation state of +1.

Under normal conditions, silver does not react with oxygen, hydrogen, nitrogen, carbon, silicon, but interacts with sulfur, forming silver sulfide: 2Ag+S=Ag2S. When heated, silver interacts with halogens: 2Ag+Cl2=2AgCl↓.

Soluble silver nitrate AgNO3 is used for the qualitative determination of halide ions in solution – (Cl-), (Br-), (I-): (Ag+)+(Hal-)=AgHal↓. For example, when interacting with chlorine anions, silver gives an insoluble white precipitate AgCl↓.

Why silver products darken in the air?

The reason for the gradual decline of silver products is explained by the fact that silver reacts with hydrogen sulfide in the air. As a result, an Ag2S film is formed on the metal surface: 4Ag+2H2S+O2=2Ag2S+2H2O.

Nuclear charge () determines the location of a chemical element in the D.I. table. Mendeleev. The Z number is the number of protons in the nucleus. Cl is the charge of a proton, which is equal in magnitude to the charge of an electron.

Let us emphasize once again that the charge of the nucleus determines the number of positive elementary charges, the carriers of which are protons. And since the atom is a generally neutral system, the charge of the nucleus also determines the number of electrons in the atom. And we remember that an electron has a negative elementary charge. Electrons in an atom are distributed among energy shells and subshells depending on their number; therefore, the charge of the nucleus has a significant effect on the distribution of electrons among their states. The chemical properties of an atom depend on the number of electrons at the last energy level. It turns out that the charge of the nucleus determines the chemical properties of the substance.

Currently, it is customary to designate various chemical elements as follows: where X is the symbol of a chemical element in the periodic table, which corresponds to the charge.

Elements that have equal Z but different atomic masses (A) (this means that in the nucleus same number protons, but different quantities neutrons) are called isotopes. Thus, hydrogen has two isotopes: 1 1 H-hydrogen; 2 1 H-deuterium; 3 1 H-tritium

There are stable and unstable isotopes.

Nuclei with the same masses but different charges are called isobars. Isobars are mainly found among heavy nuclei, and in pairs or triads. For example, and.

Moseley was the first to indirectly measure the nuclear charge in 1913. He established a relationship between the frequency of characteristic X-ray radiation () and the nuclear charge (Z):

where C and B are constants independent of the element for the considered series of radiation.

The nuclear charge was directly determined by Chadwick in 1920 while studying the scattering of helium atom nuclei on metal films.

Kernel composition

The nucleus of a hydrogen atom is called a proton. Proton mass is equal to:

The nucleus is made up of protons and neutrons (together called nucleons). The neutron was discovered in 1932. The mass of the neutron is very close to the mass of the proton. A neutron has no electrical charge.

The sum of the number of protons (Z) and the number of neutrons (N) in the nucleus is called the mass number A:

Since the masses of the neutron and proton are very close, each of them is equal to almost an atomic unit of mass. The mass of electrons in an atom is much less than the mass of the nucleus, so it is believed that the mass number of the nucleus is approximately equal to the relative atomic mass of the element, if rounded to the nearest whole number.

Examples of problem solving

EXAMPLE 1

Exercise Nuclei are very stable systems, therefore, protons and neutrons must be held inside the nucleus by some force. What can you say about these forces?
Solution It can be immediately noted that the forces that bind nucleons are not gravitational, which are too weak. The stability of the nucleus cannot be explained by the presence of electromagnetic forces, since between protons, as particles carrying charges of the same sign, there can only be electric repulsion. Neutrons are electrically neutral particles.

Act between nucleons special kind forces called nuclear forces. These forces are almost 100 times stronger than electrical forces. Nuclear forces the most powerful of all known forces in nature. The interaction of particles in the nucleus is called strong.

The next feature of nuclear forces is that they are short-range. Nuclear forces become noticeable only at a distance of the order of cm, that is, at a distance the size of a nucleus.

EXAMPLE 2

Exercise What is the minimum distance that the nucleus of a helium atom, having a kinetic energy equal to a head-on collision, can approach the stationary nucleus of a lead atom?
Solution Let's make a drawing.

Let us consider the movement of the nucleus of a helium atom ( - particle) in an electrostatic field, which creates a stationary nucleus of a lead atom. - the particle moves towards the nucleus of the lead atom with a speed decreasing to zero, since repulsive forces act between similarly charged particles. The kinetic energy that the particle possessed will turn into the potential energy of interaction between the particle and the field (), which creates the nucleus of the lead atom:

We express the potential energy of a particle in an electrostatic field as:

where is the charge of the nucleus of a helium atom; - tension electrostatic field, which creates the nucleus of a lead atom.

From (2.1) - (2.3) we obtain: