Principal quantum numberP P P

(Physics. Optics. Quantum physics. Structure and physical properties substances)

quantum numbers and fine structure spectra

Principal quantum numberP denotes the number of the energy level of an electron in an atom. The value of the principal quantum number P= 1 corresponds to the ground state of the electron with the lowest energy. Principal quantum number P describes only circular (Bohr) orbits. If at...
(Physical foundations theory of optical and X-ray spectroscopy)

Barnett's experience. Experience of Einstein and de Haas. Experience of Stern and Gerlach. Spin. Quantum numbers of orbital and spin momentum

It is known that the magnetization of a substance in a magnetic field is due to the preferential orientation or induction in an external magnetic field of microscopic molecular currents arising from the movement of electrons along closed microscopic orbits within each molecule (atom). For quality...
(Physics. Optics. Quantum physics. Structure and physical properties of matter)

Quantum-mechanical model of the hydrogen atom (results of solving the Schrödinger equation). Quantum numbers of the hydrogen atom

Quantum mechanics, without involving Bohr's postulates, makes it possible to obtain a solution to the problem of energy levels both for a hydrogen atom and a hydrogen-like system, and for more complex atoms. Let us consider a hydrogen-like atom containing a single external electron. The electric field created by...
(Physics. Optics. Quantum physics. Structure and physical properties of matter)

General characteristics of quantum numbers

Principal quantum number

ncharacterizes the energy of an electron in an atom and the size electron orbital. It also corresponds to the number of the electron layer on which the electron is located. A set of electrons in an atom with the same value of the principal quantum numberncalled electron layer ( energy level). n- takes values 1, 2, 3, …, ¥ . Energy levels are indicated in capital Latin letters:

Differences in the energies of electrons belonging to different sublevels of a given energy level reflect side (orbital) quantum number l. Electrons in an atom the same values n and lconstitute energy sublevel(electron shell). Maximum number of electrons in a shell N l :

N l = 2(2l + 1). (5.1)

The side quantum number takes integer values ​​0, 1, … ( n- one). Usually lindicated not by numbers, but by letters:

Orbital

- the space around the nucleus, in which the electron is most likely to be found.

Side (orbital) quantum number lcharacterizes various energy state electrons on given level, the shape of the orbital, the orbital angular momentum of the electron.

Thus, an electron, having the properties of a particle and a wave, moves around the nucleus, forming an electron cloud, the shape of which depends on the value l. So if l= 0, (s-orbital), then the electron cloud has spherical symmetry. Atl= 1 (p-orbital) the electron cloud has the shape of a dumbbell. d orbitals have different shape: dz 2 - dumbbell located along the Z axis with a torus in the X - Y plane, d x 2 - y 2 - two dumbbells located along the X and Y axes; dxy, dxz, dyz,- two dumbbells at 45 o to the corresponding axes (Fig. 5.1).

Rice. 5.1. E-cloud shapes for different states electrons in atoms

Magnetic quantum number

m l characterizes the orientation of the orbital in space, and also determines the value of the projection of the orbital angular momentum on the Z axis.m l takes values ​​from +l before - l, including 0. Total number valuesm l is equal to the number of orbitals in a given electron shell.

Magnetic spin quantum number m s characterizes the projection of the proper angular momentum of the electron on the Z axis and takes the values ​​+1/2 and –1/2 in units h/2p(h is the Planck constant).

Principle (prohibition) of Pauli

An atom cannot have two electrons with all four identical quantum numbers.

The Pauli principle determines the maximum number of electrons N n , on the electronic layer with the numbern:

N n = 2n 2 . (5.2)

On the first electron layer there can be no more than two electrons, on the second - 8, on the third - 18, etc.

Hund's rule

The energy levels are filled in such a way that the total spin is maximum.

For example, three p-electrons in the orbitals of the p-shell are arranged as follows:

Thus, each electron occupies one p-orbital.

Examples of problem solving

. Characterize by quantum numbers the electrons of a carbon atom in an unexcited state. Present your answer in the form of a table.

Decision. Electronic formula carbon atom: 1s 2 2s 2 2p 2 . There are two carbon atoms in the first layer s -electron with antiparallel spins, for whichn= 1. For two s - electrons of the second layern= 2. The spins of the two p-electrons of the second layer are parallel; for themm s = +1/2.

electron number

Characterize by quantum numbers the outer electrons of the oxygen atom in the ground state. Present your answer in the form of a table.

Decision. The electronic formula of the oxygen atom is: 1s 2 2s 2 2p 4 . This atom has 6 electrons in its outer layer. s 2 2p 4 . The values ​​of their quantum numbers are given in the table.

electron number

. Characterize by quantum numbers five electrons in the 4d state . Present your answer in the form of a table.

Decision. According to Hund's rule, electrons in quantum cells are arranged as follows:

The values ​​of the main, side and spin quantum numbers for electrons are the same and equal n=4, l=2, m s =+1/2. The considered electrons differ in the values ​​of quantum numbersm l .

electron number

Calculate the maximum number of electrons in the electron layer withn = 4.

Decision. The maximum number of electrons that have a given value of the principal quantum number is calculated using formula (5.2). Therefore, there can be no more than 32 electrons in the third energy level.

Calculate the maximum number of electrons in the electron shell with l = 3.

The maximum number of electrons in the shell is determined by expression (5.1). Thus, the maximum number of electrons in an electron shell with l= 3 equals 14.

Tasks for independent solution

5.1.Characterize by quantum numbers the electrons of the boron atom in the ground state. Present your answer in the form of a table:

electron number

electron number




5.2Characterize by quantum numbers d are the electrons of the iron atom in the ground state. Present your answer in tabular form:

The location of the 3d electrons of the iron atom in orbitals:

The values ​​of the quantum numbers of these electrons are:

electron number

Six 3d -electrons of an iron atom are arranged in orbitals as follows The quantum numbers of these electrons are given in the table electron number




5.3.What are the possible values ​​of the magnetic quantum number ml , if the orbital quantum numberl = 3?

m l= +3; +2; +1; 0, - 1, - 2, - 3.




5.4.Characterize by quantum numbers the electrons in the second electron layer:



Present your answer in the form of a table:

electron number

Answer. Electronic configuration 2s 2 2p 5 . The main quantum number for everyone electrons is 2. For s-electrons l= 0, for p-electronsl= 1. electron number

Bohr's model of the atom was an attempt to reconcile the ideas of classical physics with the emerging laws of the quantum world.

E. Rutherford, 1936: How are the electrons arranged in the outer part of the atom? I regard Bohr's original quantum theory of the spectrum as one of the most revolutionary that has ever been made in science; and I don't know of any other theory that has more success. He was at that time in Manchester and, firmly believing in nuclear structure of the atom, which became clear in scattering experiments, tried to understand how to arrange the electrons in order to obtain the known spectra of atoms. The basis of his success lies in the introduction of completely new ideas into the theory. He introduced into our ideas the idea of ​​a quantum of action, as well as an idea that is alien to classical physics, that an electron can orbit around the nucleus without emitting radiation. When putting forward the theory of the nuclear structure of the atom, I was fully aware that, according to the classical theory, electrons should fall on the nucleus, and Bohr postulated that for some unknown reason this does not happen, and on the basis of this assumption, as you know, he was able to explain the origin of the spectra. Using quite reasonable assumptions, he solved step by step the problem of the arrangement of electrons in all atoms of the periodic table. There were many difficulties here, since the distribution had to match the optical and x-ray spectra elements, but in the end Bohr was able to suggest an arrangement of electrons that made sense periodic law.
As a result of further improvements, mainly introduced by Bohr himself, and modifications made by Heisenberg, Schrödinger and Dirac, the whole mathematical theory and the ideas of wave mechanics were introduced. Quite apart from these further refinements, I regard Bohr's writings as greatest triumph human thought.
To understand the significance of his work, one should consider at least the extraordinary complexity of the spectra of the elements and imagine that within 10 years all the main characteristics of these spectra were understood and explained, so that now the theory optical spectra so complete that many consider it a settled issue, similar to how it was a few years ago with sound.

By the middle of the 1920s, it became obvious that N. Bohr's semiclassical theory of the atom could not give an adequate description of the properties of the atom. In 1925–1926 In the works of W. Heisenberg and E. Schrödinger, a general approach was developed for describing quantum phenomena - quantum theory.

The quantum physics

Status Description

(x,y,z,p x ,p y ,p z)

State change over time

=∂H/∂p, = -∂H/∂t,

measurements

x, y, z, p x , p y , p z

ΔхΔp x ~
∆y∆p y ~
∆z∆p z ~

Determinism

Statistical theory

|(x,y,z)| 2

Hamiltonian H = p 2 /2m + U(r) = 2 /2m + U(r)

The state of a classical particle at any moment of time is described by setting its coordinates and momenta (x,y,z,p x ,p y ,p z ,t). Knowing these values ​​at the time t, it is possible to determine the evolution of the system under the action of known forces at all subsequent moments of time. The coordinates and momenta of the particles are themselves quantities that can be directly measured experimentally. In quantum physics, the state of a system is described by the wave function ψ(x, y, z, t). Because for a quantum particle, it is impossible to simultaneously accurately determine the values ​​of its coordinates and momentum, then it makes no sense to talk about the movement of the particle along a certain trajectory, you can only determine the probability of finding the particle at a given point in this moment time, which is determined by the square of the modulus wave function W ~ |ψ(x,y,z)| 2.
The evolution of a quantum system in the nonrelativistic case is described by a wave function that satisfies the Schrödinger equation

where is the Hamilton operator (the operator of the total energy of the system).
In the nonrelativistic case − 2 /2m + (r), where t – particle mass, is the momentum operator, (x,y,z) is the potential energy operator of the particle. Set the law of particle motion in quantum mechanics it means to determine the value of the wave function at each moment of time at each point in space. AT steady state the wave function ψ(x, y, z) is a solution to the stationary Schrödinger equation ψ = Eψ. Like every connected system in quantum physics, the nucleus has a discrete spectrum eigenvalues energy.
Status since the most energy the bonds of the nucleus, i.e., with the lowest total energy E, are called the main. States with higher total energy are excited states. The lowest energy state is assigned a zero index and the energy E 0 = 0.

E0 → Mc 2 = (Zm p + Nm n)c 2 − W 0 ;

W 0 is the binding energy of the nucleus in the ground state.
Energies E i (i = 1, 2, ...) of excited states are measured from the ground state.

Scheme of the lower levels of the 24 Mg nucleus.

The lower levels of the kernel are discrete. As the excitation energy increases, the average distance between the levels decreases.
An increase in the level density with increasing energy is a characteristic property of many-particle systems. It is explained by the fact that with an increase in the energy of such systems, the number various ways distribution of energy between nucleons.
quantum numbers- integer or fractional numbers that determine the possible values physical quantities characterizing a quantum system - an atom, an atomic nucleus. Quantum numbers reflect the discreteness (quantization) of physical quantities characterizing the microsystem. A set of quantum numbers that exhaustively describe a microsystem is called complete. So the state of the nucleon in the nucleus is determined by four quantum numbers: the main quantum number n (can take values ​​1, 2, 3, ...), which determines the energy E n of the nucleon; orbital quantum number l = 0, 1, 2, …, n, which determines the value L the orbital angular momentum of the nucleon (L = ћ 1/2); the quantum number m ≤ ±l, which determines the direction of the orbital momentum vector; and the quantum number m s = ±1/2, which determines the direction of the nucleon spin vector.

quantum numbers

n	Principal quantum number: n = 1, 2, … ∞.
j	The quantum number of the total angular momentum. j is never negative and can be integer (including zero) or half-integer depending on the properties of the system in question. The value of the total angular momentum of the system J is related to j by the relation J 2 = ћ 2 j(j+1). = + where and are the orbital and spin angular momentum vectors.
l	Quantum number of orbital angular momentum. l can only take integer values: l= 0, 1, 2, … ∞, The value of the orbital angular momentum of the system L is related to l relation L 2 = ћ 2 l(l+1).
m	The projection of the total, orbital, or spin angular momentum onto a preferred axis (usually the z-axis) is equal to mћ. For the total moment m j = j, j-1, j-2, …, -(j-1), -j. For the orbital moment m l = l, l-1, l-2, …, -(l-1), -l. For the spin moment of an electron, proton, neutron, quark m s = ±1/2
s	Quantum number of spin angular momentum. s can be either integer or half-integer. s is a constant characteristic of the particle, determined by its properties. The value of the spin moment S is related to s by the relation S 2 = ћ 2 s(s+1)
P	Spatial parity. It is equal to either +1 or -1 and characterizes the behavior of the system when mirror reflection P=(-1) l .

Along with this set of quantum numbers, the state of the nucleon in the nucleus can also be characterized by another set of quantum numbers n, l, j, jz . The choice of a set of quantum numbers is determined by the convenience of describing a quantum system.
The existence of conserved (invariant in time) physical quantities for a given system is closely related to the symmetry properties of this system. So if isolated system does not change during arbitrary rotations, then it retains the orbital angular momentum. This is the case for the hydrogen atom, in which the electron moves in the spherically symmetric Coulomb potential of the nucleus and is therefore characterized by a constant quantum number l. An external perturbation can break the symmetry of the system, which leads to a change in the quantum numbers themselves. A photon absorbed by a hydrogen atom can transfer an electron to another state with different values ​​of quantum numbers. The table lists some quantum numbers used to describe atomic and nuclear states.
In addition to quantum numbers reflecting the space-time symmetry of the microsystem, essential role play the so-called internal quantum numbers of particles. Some of them, such as spin and electric charge, are conserved in all interactions, others are not conserved in some interactions. So the quantum number strangeness, which is conserved in the strong and electromagnetic interactions, is not conserved in weak interaction, which reflects the different nature of these interactions.
atomic nucleus in each state is characterized by the total angular momentum . This moment in the rest frame of the nucleus is called nuclear spin.
For the kernel, following rules:
a) A is even J = n (n = 0, 1, 2, 3,...), i.e. an integer;
b) A is odd J = n + 1/2, i.e. half-integer.
In addition, one more rule has been experimentally established: for even-even nuclei in the ground state Jgs = 0. This indicates mutual compensation of nucleon moments in the ground state of the nucleus – special property internucleon interaction.
The invariance of the system (hamiltonian) with respect to spatial reflection - inversion (replacement → -) leads to the parity conservation law and the quantum number parity R. This means that the nuclear Hamiltonian has the corresponding symmetry. Indeed, the nucleus exists due to the strong interaction between nucleons. In addition, an essential role in nuclei is also played by electromagnetic interaction. Both of these types of interactions are invariant to spatial inversion. This means that nuclear states must be characterized by a certain parity value P, i.e., be either even (P = +1) or odd (P = -1).
However, between nucleons in the nucleus there are also non-parity-preserving weak forces. The consequence of this is that a (usually insignificant) admixture of a state with the opposite parity is added to the state with a given parity. The typical value of such an impurity in nuclear states is only 10 -6 -10 -7 and in most cases can be ignored.
The parity of the nucleus P as a system of nucleons can be represented as the product of the parities of individual nucleons p i:

P \u003d p 1 p 2 ... p A ,

moreover, the parity of the nucleon p i in the central field depends on the orbital momentum of the nucleon , where π i is the internal parity of the nucleon, equal to +1. Therefore, the parity of a nucleus in a spherically symmetric state can be represented as the product of the orbital parities of nucleons in this state:

Nuclear level diagrams usually indicate the energy, spin, and parity of each level. The spin is indicated by a number, and the parity is indicated by a plus sign for even levels and a minus sign for odd levels. This sign is placed to the right of the top of the number indicating the spin. For example, the symbol 1/2 + denotes an even level with spin 1/2, and the symbol 3 - denotes an odd level with spin 3.

Isospin of atomic nuclei. Another characteristic of nuclear states is isospin I. Core (A, Z) consists of A nucleons and has a charge Ze, which can be represented as the sum of nucleon charges q i , expressed in terms of projections of their isospins (I i) 3

is the projection of the isospin of the nucleus onto axis 3 of the isospin space.
Total isospin of the nucleon system A

All states of the nucleus have the value of the isospin projection I 3 = (Z - N)/2. In a nucleus consisting of A nucleons, each of which has isospin 1/2, isospin values ​​are possible from |N - Z|/2 to A/2

|N - Z|/2 ≤ I ≤ A/2.

The minimum value I = |I 3 |. Maximum value I is equal to A/2 and corresponds to all i , directed in one direction. It has been experimentally established that the excitation energy of a nuclear state is the higher, the higher more value isospin. Therefore, the isospin of the nucleus in the ground and low-excited states has a minimum value

I gs = |I 3 | = |Z - N|/2.

The electromagnetic interaction breaks the isotropy of the isospin space. The interaction energy of a system of charged particles changes during rotations in isospace, since during rotations the charges of particles change and in the nucleus part of the protons passes into neutrons or vice versa. Therefore, the actual isospin symmetry is not exact, but approximate.

Potential well. For description connected states particles, the concept of a potential well is often used. Potential well - a limited region of space with a reduced potential energy of a particle. The potential well usually corresponds to the forces of attraction. In the area of ​​action of these forces, the potential is negative, outside - zero.

The particle energy E is the sum of its kinetic energy T ≥ 0 and potential energy U (it can be both positive and negative). If the particle is inside the well, then its kinetic energy T 1 is less than the depth of the well U 0 , particle energy E 1 = T 1 + U 1 = T 1 - U 0 In quantum mechanics, the energy of a particle in a bound state can only take on certain discrete values, i.e. there are discrete levels of energy. In this case, the lowest (main) level always lies above the bottom. potential hole. In order of magnitude, the distance Δ E between the levels of a particle of mass m in deep hole the width a is given by
ΔE ≈ ћ 2 / ma 2.
An example of a potential well is the potential well of an atomic nucleus with a depth of 40-50 MeV and a width of 10 -13 -10 -12 cm, in which various levels there are nucleons with an average kinetic energy of ≈ 20 MeV.

On the simple example particles in a one-dimensional infinite rectangular well, one can understand how a discrete spectrum of energy values ​​arises. In the classical case, a particle, moving from one wall to another, takes on any value of energy, depending on the momentum imparted to it. In a quantum system, the situation is fundamentally different. If a quantum particle is located in a limited region of space, the energy spectrum turns out to be discrete. Consider the case when a particle of mass m is in a one-dimensional potential well U(x) of infinite depth. The potential energy U satisfies the following boundary conditions

Under such boundary conditions, the particle, being inside the potential well 0< x < l, не может выйти за ее пределы, т. е.

ψ(x) = 0, x ≤ 0, x ≥ L.

Using the stationary Schrödinger equation for the region where U = 0,

we obtain the position and energy spectrum of the particle inside the potential well.

For an infinite one-dimensional potential well, we have the following:

The wave function of a particle in an infinite rectangular well (a), the square of the modulus of the wave function (b) determines the probability of finding a particle at various points in the potential well.

The Schrödinger equation plays the same role in quantum mechanics as Newton's second law plays in classical mechanics.
The most striking feature of quantum physics turned out to be its probabilistic nature.

The probabilistic nature of the processes occurring in the microcosm is fundamental property microworld.

E. Schrödinger: “The usual quantization rules can be replaced by other provisions that no longer introduce any “whole numbers”. Integrity is obtained in this case in a natural way by itself, just as the integer number of knots is obtained by itself when considering a vibrating string. This new representation can be generalized and, I think, is closely related to the true nature of quantization.
It is quite natural to associate the function ψ with some oscillatory process in the atom, in which the reality of electronic trajectories in recent times repeatedly questioned. At first, I also wanted to substantiate a new understanding of quantum rules using the indicated comparatively clear way, but then I preferred purely mathematical way, as it makes it possible to better clarify all the essential aspects of the issue. It seems to me essential that quantum rules are no longer introduced as a mysterious " integer requirement”, but are determined by the need for the boundedness and uniqueness of some specific spatial function.
I do not consider it possible, until more are successfully calculated in a new way. challenging tasks, consider in more detail the interpretation of the introduced oscillatory process. It is possible that such calculations will lead to a simple coincidence with the conclusions of conventional quantum theory. For example, when considering the relativistic Kepler problem according to the above method, if we act according to the rules indicated at the beginning, a remarkable result is obtained: half-integer quantum numbers(radial and azimuth)…
First of all, it is impossible not to mention that the main initial impetus that led to the appearance of the arguments presented here was de Broglie's dissertation, which contains many deep ideas, as well as reflections on the spatial distribution of "phase waves", which, as shown by de Broglie, each time corresponds to periodic or quasi-periodic motion of an electron, if only these waves fit on the trajectories integer once. The main difference from de Broglie's theory, which speaks of a rectilinearly propagating wave, is here that we are considering, if we use the wave interpretation, standing natural vibrations.

M. Laue: “The achievements of quantum theory accumulated very quickly. It had a particularly striking success in its application to radioactive decay by the emission of α-rays. According to this theory, there is a "tunnel effect", i.e. penetration through the potential barrier of a particle, the energy of which, according to the requirements classical mechanics, is not enough to pass through it.
G. Gamov gave in 1928 an explanation of the emission of α-particles, based on this tunnel effect. According to Gamow's theory, the atomic nucleus is surrounded by a potential barrier, but α-particles have a certain probability of "stepping over" it. Empirically found by Geiger and Nettol, the relationship between the radius of action of an α-particle and the half-period of decay was satisfactorily explained on the basis of Gamow's theory.

Statistics. Pauli principle. The properties of quantum mechanical systems consisting of many particles are determined by the statistics of these particles. Classic systems, consisting of identical but distinguishable particles, obey the Boltzmann distribution

In a system of quantum particles of the same type, new features of behavior appear that have no analogues in classical physics. Unlike particles in classical physics, quantum particles are not only the same, but also indistinguishable - identical. One of the reasons is that in quantum mechanics, particles are described using wave functions, which allow one to calculate only the probability of finding a particle at any point in space. If the wave functions of several identical particles overlap, then it is impossible to determine which of the particles is at a given point. Since only the square of the modulus of the wave function has physical meaning, it follows from the particle identity principle that when two identical particles are interchanged, the wave function either changes sign ( antisymmetric state), or does not change sign ( symmetrical state).
Symmetric wave functions describe particles with integer spin - bosons (pions, photons, alpha particles ...). Bosons obey Bose-Einstein statistics

In one quantum state there can be an unlimited number of identical bosons at the same time.
Antisymmetric wave functions describe particles with half-integer spin - fermions (protons, neutrons, electrons, neutrinos). Fermions obey Fermi-Dirac statistics

The relationship between the symmetry of the wave function and spin was first pointed out by W. Pauli.

For fermions, the Pauli principle is valid - two identical fermions cannot simultaneously be in the same quantum state.

The Pauli principle determines the structure electron shells atoms, the filling of nucleon states in nuclei, and other features of the behavior of quantum systems.
With the creation of the proton-neutron model of the atomic nucleus, the first stage of development can be considered completed. nuclear physics, in which the basic facts of the structure of the atomic nucleus were established. The first stage began in the fundamental concept of Democritus about the existence of atoms - indivisible particles of matter. The establishment of the periodic law by Mendeleev made it possible to systematize atoms and raised the question of the reasons underlying this systematics. The discovery of electrons in 1897 by J. J. Thomson destroyed the concept of the indivisibility of atoms. According to the Thomson model, electrons are constituent elements all atoms. The discovery by A. Becquerel in 1896 of the phenomenon of uranium radioactivity and the subsequent discovery of the radioactivity of thorium, polonium and radium by P. Curie and M. Sklodowska-Curie showed for the first time that chemical elements are not eternal formations, they can spontaneously decay, turn into other chemical elements. In 1899, E. Rutherford found that atoms as a result radioactive decay can eject from their composition α-particles - ionized helium atoms and electrons. In 1911, E. Rutherford, generalizing the results of the experiment of Geiger and Marsden, developed a planetary model of the atom. According to this model, atoms consist of a positively charged atomic nucleus with a radius of ~10 -12 cm, in which the entire mass of the atom and negative electrons rotating around it is concentrated. The size of the electron shells of an atom is ~10 -8 cm. In 1913, N. Bohr developed the idea planetary model atom based on quantum theory. In 1919, E. Rutherford proved that protons are part of the atomic nucleus. In 1932, J. Chadwick discovered the neutron and showed that neutrons are part of the atomic nucleus. The creation in 1932 by D. Ivanenko and W. Heisenberg of the proton-neutron model of the atomic nucleus completed the first stage in the development of nuclear physics. All the constituent elements of the atom and the atomic nucleus have been established.

1869 Periodic system of elements D.I. Mendeleev

By the second half of the 19th century, chemists had accumulated extensive information on the behavior of chemical elements in various chemical reactions. It was found that only certain combinations of chemical elements form a given substance. Some chemical elements have been found to have roughly the same properties while their atomic weights vary greatly. D. I. Mendeleev analyzed the relationship between chemical properties elements and their atomic weight and showed that the chemical properties of the elements arranged with increasing atomic weights are repeated. This served as the basis for the periodic system of elements he created. When compiling the table, Mendeleev found that the atomic weights of some chemical elements fell out of the regularity he had obtained, and pointed out that the atomic weights of these elements were determined inaccurately. Later precise experiments showed that the originally determined weights were actually incorrect and the new results corresponded to Mendeleev's predictions. Leaving some places blank in the table, Mendeleev pointed out that there should be new yet undiscovered chemical elements and predicted their chemical properties. Thus, gallium (Z = 31), scandium (Z = 21) and germanium (Z = 32) were predicted and then discovered. Mendeleev left the task of explaining to his descendants periodic properties chemical elements. The theoretical explanation of Mendeleev's periodic system of elements, given by N. Bohr in 1922, was one of hard evidence the correctness of the emerging quantum theory.

atomic nucleus and periodic system elements

The basis for the successful construction of the periodic system of elements by Mendeleev and Logar Meyer was the idea that atomic weight can serve as a suitable constant for systematic classification elements. Modern atomic theory, however, has approached the interpretation of the periodic system without touching upon atomic weight at all. The place number of any element in this system and at the same time its chemical properties are uniquely determined positive charge atomic nucleus, or, what is the same, the number of negative electrons located around it. The mass and structure of the atomic nucleus play no part in this; so, at the present time, we know that there are elements, or rather types of atoms, which, with the same number and arrangement, outer electrons have significantly different atomic weights. Such elements are called isotopes. So, for example, in a galaxy of zinc isotopes, the atomic weight is distributed from 112 to 124. On the contrary, there are elements with significantly different chemical properties that exhibit the same atomic weight; they are called isobars. An example is the atomic weight of 124 found for zinc, tellurium and xenon.
For determining chemical element one constant is enough, namely, the number of negative electrons located around the nucleus, since all chemical processes flow among these electrons.
Number of protons n 2 , located in the atomic nucleus, determine its positive charge Z, and thereby the number of external electrons that determine the chemical properties of this element; some number of neutrons n 1 enclosed in the same core, in total with n 2 gives its atomic weight
A=n 1 +n 2 . Conversely, the serial number Z gives the number of protons contained in the atomic nucleus, and the difference between the atomic weight and the nuclear charge A - Z gives the number of nuclear neutrons.
With the discovery of the neutron, the periodic system received some replenishment in the region of small serial numbers, since the neutron can be considered an element with an ordinal number, zero. In the region of high ordinal numbers, namely from Z = 84 to Z = 92, all atomic nuclei are unstable, spontaneously radioactive; therefore, it can be assumed that an atom with a nuclear charge even higher than that of uranium, if it can only be obtained, should also be unstable. Fermi and his collaborators recently reported on their experiments, in which, when uranium was bombarded with neutrons, the appearance of radioactive element with serial number 93 or 94. It is quite possible that the periodic system has a continuation in this area as well. It only remains to add that Mendeleev's ingenious foresight provided for the framework of the periodic system so broadly that each new discovery, remaining within its scope, further strengthens it.

The wave function that is the solution of the Schrödinger equation is called orbital. To solve this equation, three quantum numbers are introduced ( n, l and m l )

Principal quantum numbern. it determines the energy of the electron and the size of the electron clouds. The energy of an electron mainly depends on the distance of the electron from the nucleus: the closer the electron is to the nucleus, the lower its energy. Therefore, we can say that the main quantum number n determine-

is the location of an electron on a particular energy level. The principal quantum number has the values ​​of a series of integers from 1 before ∞ . With the value of the principal quantum number equal to 1 (n = 1 ), the electron is in the first energy level, located at the minimum possible distance from the nucleus. The total energy of such an electron is the smallest.

The electron at the energy level farthest from the nucleus has the highest energy. Therefore, when an electron moves from a more distant energy level to a closer one, energy is released. Energy levels are indicated in capital letters according to the scheme:

Meaning n…. 1 2 3 4 5

Designation K L M N Q

Orbital quantum numberl . According to quantum mechanical calculations, electron clouds differ not only in size, but also in shape. The shape of the electron cloud is characterized by the orbital or side quantum number. The different form of electron clouds causes a change in the energy of an electron within the same energy level, i.e. its splitting into energy sublevels. Each shape of the electron cloud corresponds certain value mechanical moment of electron motion  , determined by the orbital quantum number:

A certain form of the electron cloud corresponds to a well-defined value of the orbital angular momentum of the electron's momentum  . As  can only take on discrete values ​​given by the quantum number l, then the shapes of electron clouds cannot be arbitrary: each possible value l corresponds to a well-defined form of the electron cloud.

Rice. 5. Graphical interpretation of the moment of electron motion, where μ - orbital angular momentum

electron motion

The orbital quantum number can take values ​​from 0 before n - 1 , Total n– values.

Energy sublevels are marked with letters:

Meaning l 0 1 2 3 4

Designation s p d f g

Magnetic quantum numberm l . It follows from the solution of the Schrödinger equation that electron clouds are oriented in a certain way in space. The spatial orientation of electron clouds is characterized by a magnetic quantum number.

The magnetic quantum number can take any integer values, both positive and negative, ranging from - l to + l, and in total this number can take (2l+1) values ​​for a given l, including zero. For example, if l = 1, then there are three possible values m (–1,0,+1) orbital moment  , is a vector whose magnitude is quantized and determined by the value l. It follows from the Schrödinger equation that not only the quantity µ , but the direction of this vector, which characterizes the spatial orientation of the electron cloud, is quantized. Each direction of the vector given

length corresponds to a certain value of its projection onto the axis z characterizing some direction of the external magnetic field. The value of this projection characterizes m l .

Spin of an electron. The study of atomic spectra showed that three quantum numbers n, l and m l are not a complete description of the behavior of electrons in atoms. With the development of spectral research methods and an increase in the resolution of spectral instruments, a fine structure of the spectra was discovered. It turned out that the spectral lines split. To explain this phenomenon, a fourth quantum number was introduced, related to the behavior of the electron itself. This quantum number has been called back with the designation m s and taking only two values +½ and –½ depending on one of two possible orientations of the electron spin in a magnetic field. The positive and negative values ​​of a spin are related to its direction. Insofar as spin vector quantity, then it is conventionally denoted by an arrow pointing up or down ↓. Electrons having the same spin direction are called parallel, with opposite values ​​of spins - antiparallel.

The presence of a spin in an electron was proved experimentally in 1921 by W. Gerlach and O. Stern, who managed to split a beam of hydrogen atoms into two parts corresponding to the orientation of the electron spin. The scheme of their experiment is shown in fig. 6. When hydrogen atoms fly through a region of strong magnetic field, an electron of each atom interacts with magnetic field, and this causes the atom to deviate from its original rectilinear trajectory. The direction in which the atom deviates depends on the orientation of its electron's spin. The spin of an electron does not depend on external conditions and cannot be destroyed or changed.

Thus, it was finally established that the state of an electron in an atom is completely characterized by four quantum numbers n, l, m l . and m s ,

Rice. 6. Scheme of the Stern-Gerlach experiment

Quantum numbers are energy parameters that determine the state of an electron and the type atomic orbital on which it is located. Quantum numbers are necessary to describe the state of each electron in an atom. Only 4 quantum numbers. These are: the main quantum number - n , l , magnetic quantum number – m l and spin quantum number – m s .

The main quantum number is n .

The main quantum number - n - determines the energy level of the electron, the distance of the energy level from the nucleus and the size of the electron cloud. The principal quantum number takes any integer value, starting with n =1 ( n =1,2,3,…) and corresponds to the period number.

Orbital quantum number - l .

Orbital quantum number - l - determines geometric shape atomic orbital. The orbital quantum number takes any integer values, starting from l =0 ( l =0,1,2,3,… n -one). Regardless of the number of the energy level, each value of the orbital quantum number corresponds to an orbital of a special shape. A “set” of such orbitals with the same values ​​of the principal quantum number is called an energy level. Each value of the orbital quantum number corresponds to an orbital of a special shape. The value of the orbital quantum number l =0 matches s -orbital (1-in type). The value of the orbital quantum number l =1 match p -orbitals (3 types). The value of the orbital quantum number l =2 match d -orbitals (5 types). The value of the orbital quantum number l =3 match f -orbitals (7 types).

f-orbitals have even more complex shape. Each type of orbital is the volume of space in which the probability of finding an electron is maximum.

Magnetic quantum number - m l.

The magnetic quantum number - m l - determines the orientation of the orbital in space relative to the external magnetic or electric field. The magnetic quantum number takes any integer values ​​from -l to +l, including 0. This means that for each form of orbital there are 2l + 1 energetically equivalent orientations in space - orbitals.

For s-orbital:

l=0, m=0 – one equivalent orientation in space (one orbital).

For p-orbital:

l=1, m=-1,0,+1 – three equivalent orientations in space (three orbitals).

For d-orbital:

l=2, m=-2,-1,0,1,2 – five equivalent orientations in space (five orbitals).

For the f orbital:

l=3, m=-3,-2,-1,0,1,2,3 – seven equivalent orientations in space (seven orbitals).

Spin quantum number - m s .

The spin quantum number - m s - determines the magnetic moment that occurs when an electron rotates around its axis. The spin quantum number can take only two possible values+1/2 and -1/2. They correspond to two possible and opposite directions of one's own magnetic moment electron - spins. The following symbols are used to denote electrons with different spins: 5 and 6 .