A diagram explaining the Pauli Exclusion Principle.

Pauli Exclusion Principle

The Pauli exclusion principle is a cornerstone of Quantum Mechanics, and plays a huge role in shaping the structure of matter as we know it.

A diagram explaining the Pauli Exclusion Principle tells us that when the maximum number of electrons are in an orbital (which is two electrons), then they must spin in opposite directions. in order to have the 4 quantum numbers be different in the 2s orbital, the electrons must spin in different directions. This is because the n, l, and ml are all the same when referring to the same orbital (in this case 2s), so the ms number MUST be different to ensure that the two electrons do not have the same 4 quantum numbers. Source: Expii

At its heart, the Pauli exclusion principle states that no two identical fermions (particles like electrons, protons, and neutrons that have half-integer spin) can occupy the same quantum state within a quantum system at the same time.

Each electron in an atom is described by four quantum numbers:

  • n (energy level),
  • ℓ (orbital shape),
  • mℓ (orbital orientation),
  • and ms (spin).

No Two Identical Electrons

The Pauli exclusion principle says that no two electrons in the same atom can have the exact same set of all four quantum numbers.

So, in any given orbital (which can hold two electrons), the two electrons must have opposite spins – one with +½ and one with −½.

This principle explains why electrons fill up orbitals in a specific order and why the periodic table has its structure.

It is the reason why matter has volume. Because electrons cannot all collapse into the lowest energy state, they stack up in layers, giving atoms their size and shape.

This principle is also why white dwarf stars do not collapse under their own gravity. Instead, their electrons resist being squeezed into the same state, creating what is called electron degeneracy pressure.

All Rules Have an Exception

However, not all particles are subject to the principle.

A series of images show, from left to right, increasing density as those rubidium atoms begin to form a BEC. Image: NIST/JILA/CU-Boulder - NIST Image
In the 1920s, Satyendra Nath Bose and Albert Einstein first conceived of a strange form of matter in which individual atoms clump together and behave like a single super atom. But scientists Eric A. Cornell and Carl E. Wieman only demonstrated it seven decades later, in ultracold rubidium atoms. Here, a series of images show, from left to right, increasing density as those rubidium atoms begin to form a BEC. Image: NIST/JILA/CU-Boulder – NIST Image

Particles with an integer spin (bosons) are not subject to the Pauli exclusion principle.

Any number of identical bosons can occupy the same quantum state, such as the photons produced by a laser or the atoms found in a Bose–Einstein condensate.

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