Quantum numbers and their physical meaning

Much of quantum mechanics is beyond comprehension, much seems fantastic.The same applies to the quantum numbers, the nature of which is mysterious today.The article describes the concept, types and general principles of work with them.

General characteristics

Whole or half-integer quantum numbers have the physical quantities determined by various discrete values ​​characterizing the quantum system (molecule, atom, the nucleus), and elementary particles.Their use is closely linked to the existence of Planck's constant.Readability occurring processes in the microcosm, reflects the quantum numbers and their physical meaning.They were first introduced to describe the regularities of spectra of atoms.But the physical sense and discrete individual values ​​were disclosed only in quantum mechanics.
set that defines exhaustively the state of the system is called complete.All states are responsible for the possible values ​​of this set form a complete system of states.The quantum numbers in Chemistry with

degrees of freedom of the electron determines its three-dimensional position and the internal degree of freedom - spin.

configurations of electrons and atoms

located in the nucleus of an atom and the electrons, between which there are forces of electrostatic nature.The energy will be increased to the extent that it reduces the distance between the nucleus and the electron.It is believed that the potential energy is equal to zero if it is removed from the core is infinite.This state is used as the reference point.This determines the relative energy of the electron.

electron shell, is a set of energy levels.Belonging to one of them expressed the principal quantum number n.

main number

It refers to a specific energy level with a set of orbitals that have similar values, consisting of positive integers: n = 1, 2, 3, 4, 5 ... When an electron is transferred from one to another stage changesthe principal quantum number.Note that not all the levels are filled with electrons.When filling the shell of the atom, implemented the principle of lowest energy.His fortune in this case referred to the unexcited or ground state.

Orbital number

In each level there are orbitals.Those who have a similar energy to form a sub-layer.This assignment is done using the orbital (or as it is called - side) quantum number l, which takes integer values ​​from zero to n - 1. Since the electron, having the principal and orbital quantum numbers n and l, may be from l= 0 and ending with l = n - 1.

This shows the nature of the movement and the level of the relevant sub-level energy.When l = 0 and all values ​​of n, the electron cloud will have a spherical shape.Its radius is directly proportional to n.If l = 1, the electron cloud will take the form of infinity or eight.The greater the value of l, the form will become more difficult, and the electron energy - grow.

Magnetic numbers

Ml is the projection of the orbital (side) of the angular momentum on a particular magnetic field direction.It shows the spatial orientation of the orbitals in which the same number l.Ml may have different values ​​2l + 1 from -l to + l.Other
magnetic quantum number is called spin - ms, which is the intrinsic angular momentum of the movement.To understand this, one can imagine the rotation of the electron as it around its own axis.Ms can be -1/2, +1/2, 1.
general for any of the electron spin of the absolute value of s = 1/2, and ms is its projection on the axis.


Pauli principle: an atom can not be two electrons with the same 4 quantum numbers.At least one of them must be different.
Rule compilation of formulas atoms.

  1. principle of minimum energy.According to him, first fill levels and sub-levels that are closer to the core, according to the rules Klechkovskii.
  2. Position element indicates how the electrons are distributed over the energy levels and sublevels:
  • number coincides with the charge of the atom and the number of its electrons;
  • batch number corresponds to the number of energy levels;
  • group number coincides with the number of valence electrons in an atom;
  • subgroup shows their distribution.

elementary particles and nuclei

quantum numbers of elementary particle physics are their intrinsic characteristics that determine the patterns of interaction and transformation.In addition to the spin s, it is the electric charge Q, which all elementary particles is zero or an integer, positive or negative;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 antiparticle - zero and minus one;isotopic spin with a whole or half-integer;strangeness S and others.These quantum numbers apply to both elementary particles and atomic nuclei.
Broadly referred to as physical quantities that determine the motion of a particle or system and are stored.However, it is not necessary that they belong to the discrete spectrum of all possible values.