PAULIS EXCLUSION PRINCIPLE, FERMIONS AND BOSONS

This fundamental law of quantum physics was set out for the first time by the physicist Wolfgang Pauli in 1925.
All of the particles of the same type have an identical nature but can have different properties. For example, the electrons in an atom have different energies (associated with their orbits). Each particle thus possesses a certain number of its own properties which form "the state of the particle". Amongst these properties we can cite:

• the mass at rest (identical for each particle of a given type)
• the electric charge Q which amounts to +1 for the proton, -1 for the electron, 0 for the neutron.
• the spin which corresponds to the internal kinetic moment, that is to say in general terms to the rotation of the particle around its own axis.

From this one question arises:
Two identicle particles (two electrons for example) can they exist in the same physical state, that is to say have the same energy, the same localisation, etc?
The response to this question cleaves the world of particles into two completely separate camps.

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• on the one side, mutually exclusive particles: they cannot be in the same place having exactly the same properties. These are FERMIONS (after the italian physicist Enrico Fermi). Electrons and nucleons are fermions.

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• on the other side, particles which are capable of resembling each other with several in the same physical state: These are BOSONS (after the indian physicist Satyendranath Bose). The photon is a boson. An ensemble of photon in the same state constitutes what we call a laser beam.

Two identical fermions cannot therefore coexist in the same place and in the same state: this prohibition is called Paulis exclusion principle. This principle doesn't apply to bosons.

In an atom, two electrons (fermions) can have the same energy on the condition that their spins are different. This explains the progressive filling of the periodic table of Mendéléiev, that is to say the electronic structure of atoms.
Each electronic orbit is composed of a given number of available quantic spaces; each cannot be occupied by anything other than a single electron. For example the first orbital or electronic layer (the closest to the nucleus) cannot contain anything other than at most two electrons with the same energy but with opposite spin (+1/2 and -1/2).
 
 

Notice that  all fermions have spins with a half values whereas  all bosons have whole number spins.

The fact that this exclusion principle applies to fermions is fundamental for us:
in effect, this makes fermions "real" particles of matter. If we force them to approach each other very, very close, by virtue of this exclusion principle, fermions will violently repel each other (quantum pressure) because they cannot coexist in the same space. Matter is thus distributed in space.
Fermions are though very individualistic particles, the opposite of bosons which are very gregarious!
As for bosons, we see that they  behave as mediator particles of the fundamental forces of nature.
 

Quantum formalisation: the mathematical atom
 

Since the middle of the 1930s, the atom has become a mathematical description which is very difficult to transcribe into images.
Quantum physics is integrally founded on what we call a formalism, that is to say a collection of principles, of mathematical concepts, of equations and of precisely established rules.This formalism leads to a representation of all physical systems, no matter what their nature (wave like or particle like), by mathematical entities, vectors of state, which have the property of being able to be added together: the sum of two possible states of a physical system gives rise to another possible state of the system. This fundamental principle, called the SUPERIMPOSITION PRINCIPLE, constitutes the foundation of quantum formalism.

Another fundamental concept is that of the wave function defined thus (the non mathematical can skip this paragraph with the utmost urgency!):
 

So that it's said!

That is the new vision of the atom valid since the 30s.