# Pauli exclusion principle explained

• I
• Silviu
In summary, the Pauli exclusion principle states that electrons in an atom must occupy different energy levels and have opposite spins. The Aufbau principle, which involves adding electrons to orbitals of increasing energy, is a useful way to determine electronic configurations. However, the actual state of the electrons is a linear combination of different orbitals and the electrons cannot be labeled or distinguished from each other. This means that the third electron in an atom does not "know" the spins of the first two electrons, but rather the overall state of the electrons already takes into account all energy levels being occupied.
Silviu
Hello! I am a bit confused about the Pauli exclusion principle. Let's say I have 3 electrons. Due to energy considerations the first 2 go to the ground state, and they can be only 2 electrons there, because the position wavefunction has only one option ##\psi_{100}## (and again due to energy configurations it chooses the symmetrical state) and the spin picks the anti-symmetrical so that it respect the fermions statistics overall. Hence, as there is no free state here, the 3rd electron goes to the next energy level ##\psi_{200}##. What confuses me is, how does the 3rd electron know the spins of the first 2? The 2 electrons in the ground state, don't need to have a precise value of the z component of the spin, it can be a linear combination of up and down. Of course, upon measurement, if one of them turns out to be up, the other one is necessary down, but for a random atom, before any measurement the up and down positions of the spin (in the z direction) are not occupied yet, as they are not measured, so how is the 3rd electron prevented to go there? I.e. the state (1,0,0,up) and (1,0,0,down) are not taken, as the 2 electrons are a linear combinations of them.

The Aufbau principle, where the atom is built up by adding electrons to occupy orbitals of ever increasing energy is a nice heuristic, very helpful to figure out electronic configurations. But Nature doesn't proceed like that.

What you have to consider in the case you describe is that you have three electrons, and you have to figure out what combinations of orbitals are possible, such that the total wave function is anti-symmetric with respect to the exchange of two electrons (Pauli principle). You will find that the lowest energy result corresponds to two electrons in the lowest energy spatial wf, with opposite spin, and one electron in a higher-energy orbital, with arbitrary spin (many solutions are possible here).

Note that I didn't say "the first and second electron" and so on, because that would not result in a wf with a definite exchange parity. The results is one where each electron can be in any of the orbitals, a linear combination of each electron being in each state. You can look up Slater determinant to figure out what these wave functions can look like.

DrChinese
Silviu said:
how does the 3rd electron know the spins of the first 2?

Electrons don't have labels; you can't pick out individual electrons and say that one is the "first", one is the "second", one is the "third", and match up each label with an orbital. Electrons are indistinguishable; that means that all you can say about the state in your example is that there are two electrons in the lowest energy level and one electron in the next higher energy level. In other words, you don't have three one-electron states where one of the three has to "know" that it can't be in the lowest energy-level; you have one three-electron state that already "knows" all of the energy levels being occupied.

bhobba, dlgoff and DrChinese

## 1. What is the Pauli exclusion principle?

The Pauli exclusion principle is a fundamental principle in quantum mechanics that states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. This means that two electrons cannot be in the same energy level of an atom at the same time, for example.

## 2. Who discovered the Pauli exclusion principle?

The Pauli exclusion principle was first proposed by Austrian physicist Wolfgang Pauli in 1925. It was later experimentally confirmed by Italian physicist Enrico Fermi in 1926.

## 3. What are some real-world applications of the Pauli exclusion principle?

The Pauli exclusion principle is essential to our understanding of atomic and molecular structure, as well as the behavior of electrons in materials. It also plays a crucial role in the stability of matter and the formation of chemical bonds.

## 4. How does the Pauli exclusion principle relate to the periodic table of elements?

The Pauli exclusion principle explains the arrangement of electrons in the electronic structure of atoms, which in turn determines the properties and behavior of elements. For example, the filling of electron orbitals according to the Pauli exclusion principle is what gives rise to the periodicity observed in the periodic table.

## 5. Can the Pauli exclusion principle be violated?

No, the Pauli exclusion principle is a fundamental law of nature and has been extensively tested and confirmed by experiments. It is a crucial principle in quantum mechanics and is considered to be one of the most well-established physical principles in science.

• Quantum Physics
Replies
17
Views
2K
• Quantum Physics
Replies
15
Views
2K
• Quantum Physics
Replies
2
Views
906
• Quantum Physics
Replies
2
Views
1K
• Quantum Physics
Replies
1
Views
790
• Quantum Physics
Replies
6
Views
1K
• Quantum Physics
Replies
11
Views
1K
• Quantum Physics
Replies
18
Views
1K
• Quantum Physics
Replies
3
Views
841
• Quantum Physics
Replies
12
Views
1K