Much of quantum mechanics remains beyond comprehension; much seems fantastic. The same applies to quantum numbers, the nature of which is mysterious even today. The article describes the concept, types and general principles of working with them.
general characteristics
Whole or half-integer quantum numbers in physical quantities determine all kinds of discrete values that characterize quantum systems (molecule, atom, nucleus) and elementary particles. Their application is closely related to the existence of the Planck constant. The discreteness of processes occurring in the microworld reflect quantum numbers and their physical meaning. They were first introduced in order to describe the laws of the spectra of an atom. But the physical meaning and discreteness of individual quantities were disclosed only in quantum mechanics.
The set, which determines the exhaustive state of this system, is called complete. 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 an internal degree of freedom - spin.
Electron and atom configurations
In the atom are the nucleus and electrons, between which there are forces of an electrostatic nature. Energy will increase as the distance between the nucleus and the electron decreases. It is believed that the potential energy will be zero if it is infinitely distant from the core. This condition is used as a reference. Thus, the relative energy of the electron is determined.
The electron shell is a set of energy levels. Belonging to one of them is expressed by the main quantum number n.
Prime number
It refers to a certain energy level with a set of orbitals, which have similar values, consisting of natural numbers: n = 1, 2, 3, 4, 5 ... When an electron moves from one stage to another, the main quantum number changes . Keep in mind that not all levels are filled with electrons. When filling the shell of an atom, the principle of least energy is realized. In this case, his condition is called unexcited or basic.
Orbital numbers
Each level has orbitals. Those with similar energies form a sublevel. Such assignment is made using the orbital (or as it is also called - side) quantum number l, which takes the values of integers from zero to n - 1. So the electron having the main and orbital quantum numbers n and l can be equal to starting l = 0 and ending with l = n - 1.
This shows the nature of the movement 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 will take the form of infinity or figure eight. The larger the value of l, the more complex the shape will become, and the electron energy will increase.
Magnetic numbers
Ml is the projection of the orbital (secondary) angular momentum onto one direction or another 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 2l + 1, from -l to + l.
Another magnetic quantum number is called spin - ms, which is the proper moment of the number of motion. To understand this, one can imagine the rotation of an electron around its own axis. Ms can be -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 onto the axis.
Pauli principle: two electrons with 4 similar quantum numbers cannot be in an atom. At least one of them must be excellent.
The rule of making formulas of atoms.
- The principle of minimum energy. First, levels and sublevels that are closer to the core are filled in according to the rules of Klechkovsky.
- 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;
- a periodic number corresponds to the number of energy levels;
- the group number coincides with the number of valence electrons in the atom;
- subgroup shows their distribution.
Elementary particles and nuclei
Quantum numbers in elementary particle physics are their internal characteristics, which determine the interactions and laws of transformations. In addition to spin s, this is an electric charge Q, which for all elementary particles is equal to zero or an integer, negative or positive; baryon charge B (in the particle - zero or one, in the antiparticle - zero or minus one); lepton charges, where Le and Lm are equal to zero, one, and in the antiparticle - zero and minus one; isotopic spin with an integer or half integer number; Strangeness S and others. All these quantum numbers are applied both to elementary particles and to atomic nuclei.
In the broad sense of the word, they are called physical quantities that determine the motion of a particle or system and which are conserved. However, it is not necessary that they belong to a discrete spectrum of all kinds of values.