Sometimes it seems strange why atoms and molecules behave in a certain way. For example, why we cannot pass through walls, but infrared radiation passes through them. Everything can be explained by one principle - the Pauli exclusion principle.
Pauli's exclusion principle states that two electrons (or any two other fermions) cannot have the same quantum mechanical state in one atom or one molecule. In other words, no pair of electrons in an atom can have the same electron quantum numbers.
This principle was proposed by the Austrian physicist Wolfgang Pauli in 1925 to describe the behavior of electrons. In 1940, he extended the principle to all fermions in his spin-statistics theorem. Bosons - particles with an integer number of spins - do not follow the exclusion principle. Thus, identical bosons can occupy the same quantum state (as, for example, photons in lasers). The Pauli exclusion principle applies only to particles with half-integer spin.
It is easiest to think of spin as the rotation of a particle around its own axis. Of course, this is a gross oversimplification - and in reality it is impossible to say for sure whether something as small as an electron is actually spinning. Generally speaking, spin obeys the same mathematical laws of angular momentum as all rotating objects in classical physics. There are two important points to keep in mind here: the speed of rotation and the direction of the axis around which the particle rotates (up or down spin).
When Otto Stern and Walter Gerlach discovered spin in 1922, their experiments showed that the inherent angular momentum, or spin, of a particle like an electron was quantized, meaning it could only take on certain discrete values. The spin of composite particles, such as protons, neutrons, and atomic nuclei, is simply the sum of the spins and the orbital angular momentum of the particles they are composed of, which means they obey the same quantization conditions. Thus, spin is an absolutely quantum mechanical property of a particle and cannot be explained by classical physics.
It was later revealed that there are two subcategories of particles: integer-spin particles, known today as bosons - including photons, gluons, W- and Z-bosons - and hypothetical gravitons and particles with half-integer spin: fermions, which include electrons, neutrinos, muons and quarks that make up composite particles such as protons and neutrons. The difference between bosons and fermions can be described by the fact that the former have symmetric wave functions, while fermions have asymmetric wave functions. The concept of a particle with a half-integer spin is another example of the paradoxical nature of subatomic particles: roughly speaking, a fermion needs to be rotated around its axis twice before it takes its previous position.
The importance of this distinction for quantum theory is that the probability waves of bosons are "flipped" - or inverted - before they can interfere with each other, which, in fact, leads to their "herd" nature and collective behavior in lasers, superfluids liquids and superconductors. Fermions, however, do not flip their probability waves, which, among other things, leads to an "asocial" character.So it turns out that in quantum mechanics, you need to add the spins of particles very carefully and using special rules in addition to the angular momentum.
All of the above brings us to one of the most important principles in quantum mechanics - the Pauli exclusion principle. As mentioned above, it states that two identical fermions cannot occupy the same quantum state at the same time (although two electrons, for example, can acquire opposite spins in order to differentiate their quantum states). This principle can be described as follows: no two fermions in a quantum system can have the same values of all four quantum numbers at any time. The Pauli exclusion principle effectively explains the long-term existence of very high-density white dwarfs, as well as the existence of different types of atoms in the Universe, the large-scale stability of matter and its bulk.
To understand the importance of this principle, you need to know that, according to Bohr's model of the atom, electrons in an atom (existing in the same amount as protons in the nucleus of a particular atom so that the total charge is zero) can only occupy specific discrete orbital positions around the nucleus, which is also called the shell of the atom. The closer the electrons are to the nucleus, the stronger the electric force attracts the electron inward and the more energy is needed to "pull" it out of the paws of the nucleus. In the orbitals closest to the nucleus, only two electrons can fit - one with an upper spin, and one with a lower spin, in order to have different quantum states. The envelope with an energy level above can already accommodate eight, at a higher level - 18, at the next level - 32.
Pauli's exclusion principle dictates how electrons can be positioned inside an atom along its orbitals. The fact that two electrons cannot simultaneously occupy the same quantum state prevents them from "piling up" on top of each other, thereby explaining why matter occupies exclusively its place and does not allow other material objects to pass through itself, but at the same time time allows light and radiation to pass through itself.
This principle also explains the existence of different atoms in the periodic table and the diversity of the world around us. For example, when an atom receives a new electron, it always hits the lowest energy level available (the orbital farthest from the nucleus). Two atoms with "closed" shells cannot carry out a chemical bond with each other due to the fact that the electrons of one atom do not find available quantum states that they could occupy in another atom. So, the order of electrons, namely electrons in the most distant orbital, also affects the chemical properties of the element and the ability of atoms to interact with other atoms, and therefore, how molecules interact when forming gases, liquids or solids, and the way they combine in living organisms.
Pauli's exclusion principle is one of the most important principles in quantum physics, in large part because all three types of particles that make up all ordinary matter (electrons, protons, and neutrons) obey it. Interestingly, however, this principle is not supported by any physical forces known to science. When an electron enters an ion, it somehow already "knows" the quantum numbers of electrons located there, that is, it knows which atomic orbitals it can occupy and which it cannot.