Quantum numbers and their physical meaning

Much of quantum mechanics remains beyond the bounds of understanding, many seem fantastic. The same applies to quantum numbers, the nature of which is still mysterious today. The article describes the concept, types and general principles of working with them.

general characteristics

Whole or half-integral quantum numbers in physical quantities determine all possible discrete values that characterize quantum systems (a molecule, an atom, a nucleus) and elementary particles. Their application is closely related to the existence of the Planck constant. Discreteness, flowing in the microcosm of processes, reflect quantum numbers and their physical meaning. They were first introduced to describe the laws of atomic spectra. But the physical meaning and discreteness of the individual quantities were uncovered only in quantum mechanics.
A set that defines the exhaustive state of this system is called the complete one. All states responsible for possible values from such a set form a complete system of states. Quantum numbers in chemistry with degrees of freedom of an electron determine it in three spatial coordinates and the internal degree of freedom is spin.

The configurations of electrons and atoms

The nucleus and electrons are located in the atom, between which the forces of electrostatic nature act. Energy will increase as the distance between the nucleus and the electron decreases. It is assumed that the potential energy will be zero if it is removed from the nucleus indefinitely. This state is used as the origin. Thus, the relative energy of the electron is determined.

The electronic shell is a set of energy levels. Affiliation to one of them is expressed by the principal quantum number n.

Main number

It refers to a certain level of energy with a set of orbitals, in which similar values, consisting of natural numbers: n = 1, 2, 3, 4, 5 ... When the electron passes from one stage to another, the principal quantum number changes . It should be borne in mind that not all levels are filled with electrons. When the atomic shell is filled, the principle of least energy is realized. His condition in this case is called unexcited or basic.

Orbital numbers

In each level there are orbitals. Those of them with similar energy form a sublevel. Such a reference is made with the help of the orbital (or, as it is also called, secondary) quantum number l, which takes the values of integers from zero to n - 1. So an electron having a principal and orbital quantum numbers n and l can be equal, starting l = 0 and ending with l = n - 1.

This shows the nature of the motion of the corresponding sublevel and energy level. For l = 0 and any value of n, the electron cloud will have the shape of a sphere. Its radius will be directly proportional to n. For l = 1, the electron cloud takes the form of infinity or eight. The larger the value of l, the form will become more complicated, and the energy of the electron will increase.

Magnetic numbers

Ml is the projection of the orbital (spurious) angular momentum on one or another direction of the magnetic field. It shows the spatial orientation of those orbitals for which the number l is the same. Ml can have different values of 2l + 1, from -l to + l.
Another magnetic quantum number is called spin-ms, which is the eigenvalue of the number of motion. To understand this, one can imagine the rotation of the electron as it were around its own axis. Ms can be equal to -1/2, +1/2, 1.
In general, for any electron, the absolute value of the spin is s = 1/2, and ms means its projection to the axis.

The Pauli principle: there can not be two electrons in the atom with four analogous quantum numbers. At least one of them should be different.
The rule for composing atomic formulas.

1. The principle of minimum energy. It first filled the levels and sublevels, which are located closer to the core, according to the rules of Klechkovsky.
2. The position of the element indicates how the electrons are distributed over the energy levels and sublevels:

• The number coincides with the charge of the atom and the number of its electrons;
• The periodic number corresponds to the number of energy levels;
• The group number coincides with the number of valence electrons in the atom;
• The subgroup shows their distribution.

Elementary particles and nuclei

Quantum numbers in the physics of elementary particles are their internal characteristics, which determine the interactions and patterns of transformations. In addition to spin s, it is the electric charge Q, which for all elementary particles is zero or an integer, negative or positive; Baryon charge B (in particle - zero or one, in antiparticle - zero or minus one); Lepton charges, where Le and Lm are equal to zero, one, and in the antiparticle - to zero and minus one; Isotopic spin with integer or half-integer number; Strangeness S and others. All these quantum numbers are applied to both elementary particles and to atomic nuclei.
In the broadest sense of the word, they are called physical quantities that determine the motion of a particle or system and which persist. However, it is not at all necessary that they belong to the discrete spectrum of all possible values.