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Why doesn’t every electron in an atom simply drop into the lowest-energy orbital, the 1s, close to the nucleus? If that happened, every element would behave much the same, there’d be no periodic table, and chemistry as we know it wouldn’t exist. The reason it doesn’t happen is one of the deepest rules in physics: the Pauli exclusion principle. This article explains it without heavy mathematics.
The principle
The Austrian physicist Wolfgang Pauli proposed it in 1925 to explain patterns in atomic spectra. In the form chemists use:
No two electrons in the same atom can have the same set of four quantum numbers.
A practical consequence follows immediately:
Each orbital can hold at most two electrons, and those two must have opposite spins.
Pauli received the Nobel Prize in Physics in 1945 for this discovery.
The four quantum numbers, briefly
Every electron in an atom is described by four quantum numbers, a bit like an address. See quantum numbers explained.
| Quantum number | Specifies | Example values |
|---|---|---|
| n (principal) | shell | 1, 2, 3… |
| l (angular momentum) | subshell type (s, p, d, f) | 0 to n − 1 |
| mₗ (magnetic) | particular orbital | −l to +l |
| mₛ (spin) | spin direction | +½ or −½ |
The first three quantum numbers specify an orbital. Only one quantum number is left to distinguish electrons within that orbital: spin. Since spin has only two possible values (+½ and −½, often drawn as ↑ and ↓), only two electrons can share an orbital, and they must differ in spin.
Example: the two electrons in helium
| Electron | n | l | mₗ | mₛ |
|---|---|---|---|---|
| 1 | 1 | 0 | 0 | +½ |
| 2 | 1 | 0 | 0 | −½ |
A third electron can’t join the 1s orbital: it would have to repeat one of these sets exactly. So lithium’s third electron must go into the next available orbital, 2s.
What “spin” means
Electron spin is a quantum property with no perfect everyday equivalent. It’s an intrinsic angular momentum that makes each electron behave like a tiny magnet. It was demonstrated in 1922 by the Stern–Gerlach experiment, in which a beam of silver atoms split into exactly two beams in a magnetic field, showing that the magnetic property of their outer electron comes in only two orientations.
Calling it “spin” is convenient, but the electron isn’t literally a spinning ball; it’s better to think of spin as a built-in property, like charge.
How Pauli builds the periodic table
Because each orbital holds only two electrons, electrons must fill orbitals in higher and higher shells as atoms get bigger. The capacities follow directly:
| Subshell | Orbitals | Maximum electrons |
|---|---|---|
| s | 1 | 2 |
| p | 3 | 6 |
| d | 5 | 10 |
| f | 7 | 14 |
And each shell n holds up to 2n² electrons: 2, 8, 18, 32. See shells vs subshells vs orbitals.
These numbers produce the widths of the periodic table’s blocks (2, 6, 10, 14 columns) and the lengths of its periods (2, 8, 8, 18, 18, 32, 32). Without the exclusion principle, all electrons would crowd into 1s, every atom would have similar chemistry, and the periodic table wouldn’t exist. See why is the periodic table shaped like that?
Pauli, Aufbau and Hund together
The three rules for writing configurations each play a different role:
- Aufbau: which orbital to fill next (lowest energy first).
- Pauli: how many electrons each orbital can take (two, opposite spins).
- Hund: how to distribute electrons among equal-energy orbitals (singly first, parallel spins).
Worked example: nitrogen
Nitrogen has 7 electrons.
- 1s: 2 electrons (↑↓), full by Pauli.
- 2s: 2 electrons (↑↓), full.
- 2p: 3 electrons, one in each of the three orbitals (↑ ↑ ↑) by Hund.
Configuration: 1s² 2s² 2p³. See how to draw orbital box diagrams.
Spotting violations
Which of these orbital diagrams break the Pauli principle?
- A box containing ↑↑ → violation: two electrons with the same spin in one orbital would share all four quantum numbers.
- A box containing ↑↓↑ → violation: three electrons in one orbital.
- Three 2p electrons drawn as ↑↓, ↑, (empty) → allowed by Pauli, but it breaks Hund’s rule; the ground state is ↑, ↑, ↑.
Why matter is solid
The exclusion principle has consequences far beyond atomic structure. When two atoms are pushed together, their electron clouds would have to overlap, squeezing electrons into the same regions and states. The exclusion principle forbids electrons from sharing states, so they’re forced into higher-energy ones. This creates a strong resistance to compression, sometimes called Pauli repulsion.
Together with electrical repulsion, this is why you can’t push your hand through a table, even though atoms are mostly empty space, and why solids and liquids are so hard to compress. See how small is an atom?
Stars that are held up by Pauli
In white dwarf stars, the remnants of stars like the Sun, gravity squeezes matter to enormous densities. What stops further collapse is electron degeneracy pressure: the electrons can’t all occupy the same low-energy states, so they resist being compressed. A teaspoon of white dwarf material has a mass of several tonnes.
If the star is massive enough, even this isn’t sufficient, and electrons combine with protons to form neutrons. The resulting neutron star is supported by neutron degeneracy pressure, because neutrons obey the same exclusion principle.
Which particles obey it?
The principle applies to particles called fermions, which have half-integer spin: electrons, protons, neutrons and quarks. It doesn’t apply to bosons (such as photons), which can crowd into the same state in unlimited numbers. That’s what makes lasers possible: huge numbers of photons in the same state.
Common misconceptions
- “Pauli means electrons avoid each other because they’re both negative.” Electrical repulsion is a separate effect. The exclusion principle would apply even to uncharged fermions such as neutrons.
- “Two electrons in an orbital must be spinning in opposite directions like tops.” Spin is a quantum property, not literal rotation.
- “An orbital can hold two electrons with the same spin if they’re far apart.” Not within one orbital; the four quantum numbers must differ.
Pauli in the lab
The exclusion principle isn’t only theory. It underlies techniques used in chemistry labs every day. In NMR spectroscopy and its medical cousin MRI, nuclear spins, which also come in a limited number of allowed orientations, are flipped by radio waves. In electron spin resonance (ESR), the same idea is applied to unpaired electrons, allowing chemists to detect free radicals. And the pairing of electrons into orbitals explains why most stable molecules have even numbers of electrons: pairing is energetically favourable once the principle limits each orbital to two.
Key takeaways
- No two electrons in an atom can have the same four quantum numbers.
- So each orbital holds at most two electrons, with opposite spins.
- This gives subshell capacities of 2, 6, 10 and 14, shell capacities of 2n², and the structure of the periodic table.
- It works with the Aufbau principle and Hund’s rule to determine electron configurations.
- The same principle makes matter resist compression and holds up white dwarfs and neutron stars.
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