Much in quantum mechanics remains beyond understanding, much seems 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
Integer or half-integer quantum numbers for physical quantities determine all possible discrete values that characterize systems of quanta (molecule, atom, nucleus) and elementary particles. Their application is closely related to the existence of Planck's constant. The discreteness of the processes occurring in the microcosm reflects quantum numbers and their physical meaning. They were first introduced in order to describe the regularities of the spectra of the atom. But the physical meaning and discreteness of individual quantities were revealed only in quantum mechanics.
The set, which exhaustively determines the state of this system, was called the complete set. All states responsible for possible values from such a set form a complete system of states. Quantum numbers in chemistry with the degrees of freedom of an electron define it in three spatial coordinates and an internal degree of freedom -spin.
Electron configurations in atoms
In an atom there are a nucleus and electrons, between which there are forces of an electrostatic nature. The 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 far from the nucleus. This state is used as the starting point. 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.
Main number
It refers to a certain energy level with a set of orbitals that have similar values, consisting of natural numbers: n=1, 2, 3, 4, 5… When an electron moves from one step to another, the main quantum number changes. It should be taken into account that not all levels are filled with electrons. When filling the shell of an atom, the principle of least energy is realized. His state in this case is called unexcited or basic.
Orbital numbers
Each level has orbitals. Those of them with similar energy form a sublevel. Such an assignment is made using the orbital (or, as it is also called, side) quantum number l, which takes on the values of integers from zero to n - 1. So an electron that has the main and orbital quantum numbers n and l can be equal, starting with l=0 and ending with l=n - 1.
This shows the nature of the movement of the respectivesublevel 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. At 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 energy of the electron will increase.
Magnetic numbers
Ml is the projection of the orbital (side) angular momentum onto one or another direction of the magnetic field. It shows the spatial orientation of those orbitals in 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 intrinsic moment of the momentum. To understand this, one can imagine the rotation of an 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 s=1/2, and ms means its projection onto the axis.
Pauli's principle: an atom cannot contain two electrons with 4 similar quantum numbers. At least one of them must be excellent.
The rule for formulating atoms.
- Principle of minimum energy. According to it, levels and sublevels that are closer to the core are first filled, according to the rules of Klechkovsky.
- The position of the element indicates how the electrons are distributed over energy levels and sublevels:
- the number matches the charge of the atom and the number of its electrons;
- periodic number corresponds to the number of levelsenergy;
- group number is the same as 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 interactions and regularities of transformations. In addition to the spin s, this is the electric charge Q, which for all elementary particles is equal to zero or an integer, negative or positive; baryon charge B (in a particle - zero or one, in an 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 integer or half-integer; strangeness S and others. All of these quantum numbers apply to both elementary particles and atomic nuclei.
In the broad sense of the word, they are called physical quantities that determine the motion of a particle or system and are conserved. However, it is not at all necessary that they belong to a discrete spectrum of possible values.
