Electron Spin: What the Spin Quantum Number Really Means

Three quantum numbers describe an electron’s orbital: its shell (n), its shape (l) and its orientation (mₗ). But electrons have one more property that no orbital picture shows: spin. It’s written as the fourth quantum number, mₛ, and it can only take two values, +½ or −½. Spin seems like a small detail, drawn as up and down arrows in orbital diagrams, but without it, the periodic table would look completely different, and magnets wouldn’t exist. This article explains what spin is, how it was discovered, and why it matters in chemistry.

The spin quantum number

Symbol	Allowed values	Common notation
mₛ	+½ or −½	↑ (“spin up”) and ↓ (“spin down”)

Every electron has spin, and it’s always one of just these two values relative to any chosen direction. There’s no “slightly up” or “in between”. See quantum numbers explained.

How spin was discovered

The Stern–Gerlach experiment (1922)

Otto Stern and Walther Gerlach passed a beam of silver atoms through a non-uniform magnetic field. Each silver atom has one unpaired outer electron (5s¹); all its other electrons are paired. If the atom behaved like a tiny magnet that could point in any direction, the beam should have spread into a continuous smear.

Instead, the beam split cleanly into exactly two beams: one deflected up, one down. The tiny magnetic property of the electron came in only two orientations. This was a startling result that classical physics couldn’t explain.

Explaining atomic spectra

At about the same time, physicists were puzzling over fine structure in atomic spectra: some spectral lines, such as the famous yellow line of sodium, turned out to be closely spaced pairs (589.0 and 589.6 nm). In 1925, the young Dutch physicists George Uhlenbeck and Samuel Goudsmit proposed that the electron has an intrinsic angular momentum, which they called spin, with two possible orientations. Its interaction with the electron’s orbital motion splits energy levels slightly, doubling the lines.

In 1928, Paul Dirac combined quantum mechanics with Einstein’s relativity and found that spin emerges naturally from the equations. It isn’t an add-on; it’s a fundamental feature of the electron.

What spin is (and isn’t)

It’s tempting to imagine the electron as a tiny ball spinning on its axis, like the Earth. That picture helps explain why spin produces magnetism (a spinning charge would create a magnetic field), but it doesn’t hold up:

• The electron has no measurable size, so there’s nothing to rotate.
• If it were a spinning ball of the right size, its surface would have to move faster than light to produce the observed angular momentum.
• Spin only ever takes two values, unlike any spinning object.

The best way to think of spin is as an intrinsic property of the electron, like its mass or charge. It’s a quantum form of angular momentum that makes each electron behave like a tiny magnet, with a magnetic moment of about one Bohr magneton.

Protons and neutrons also have spin ½, and so do many atomic nuclei, a fact that underlies NMR spectroscopy.

Spin and the Pauli exclusion principle

The Pauli exclusion principle says no two electrons in an atom can have the same four quantum numbers. Two electrons in the same orbital share n, l and mₗ, so they must differ in mₛ:

• one electron with mₛ = +½ (↑)
• one with mₛ = −½ (↓)

Because spin has only two values, each orbital can hold at most two electrons. This single fact produces subshell capacities of 2, 6, 10 and 14, shell capacities of 2n², and the shape of the periodic table. See the Pauli exclusion principle.

Spin and Hund’s rule

When electrons occupy a set of equal-energy orbitals (such as the three 2p orbitals), they go in singly with parallel spins before pairing. Parallel spins reduce electron repulsion and gain a quantum stabilisation called exchange energy. See Hund’s rule.

That’s why nitrogen’s three 2p electrons are drawn ↑ ↑ ↑, not ↑↓ ↑ _.

Spin and magnetism

Each electron’s spin makes it a tiny magnet.

• Paired electrons (↑↓) have opposite spins; their magnetic effects cancel.
• Unpaired electrons leave a net magnetic moment, so the substance is paramagnetic (attracted to magnets).
• If all electrons are paired, the substance is diamagnetic (very weakly repelled).
• In iron, cobalt and nickel, unpaired spins on neighbouring atoms line up spontaneously, giving ferromagnetism: permanent magnets.

See paramagnetic vs diamagnetic and how to count unpaired electrons.

Spin in chemical bonds

A covalent bond usually contains two electrons with opposite spins (a spin pair). Pairing lets both electrons occupy the same bonding orbital, concentrated between the nuclei. This is why most stable molecules have an even number of electrons, all paired.

Species with an unpaired electron, called radicals, are usually highly reactive, because the unpaired electron readily pairs with an electron from another species. Examples include chlorine atoms that destroy ozone, and the nitrogen monoxide molecule. See ionic vs covalent bonds.

Oxygen is a famous exception: O₂ has two unpaired electrons with parallel spins in its ground state, which is why liquid oxygen is attracted to a magnet and why oxygen reacts more slowly with many substances than you might expect from its reactivity.

Applications of spin

NMR spectroscopy and MRI

Nuclei such as ¹H and ¹³C have spin. In a strong magnetic field, their two spin states have slightly different energies, and radio waves can flip them. The exact frequency depends on the chemical environment, which is how NMR spectroscopy reveals molecular structure. MRI scanners use the same physics to image hydrogen nuclei in the body’s water and fat.

ESR (electron spin resonance)

ESR (also called EPR) flips the spins of unpaired electrons using microwaves. It detects and studies radicals and transition metal ions, for example in enzymes, in irradiated foods, and in dating archaeological materials.

Spintronics

Modern computer hard drives read data using the giant magnetoresistance effect, which depends on electron spin (Albert Fert and Peter Grünberg received the 2007 Nobel Prize in Physics for its discovery). Researchers are developing spintronic devices that use spin, not just charge, to store and process information.

Common misconceptions

• “Spin means the electron rotates.” It’s an intrinsic quantum property, not literal rotation.
• “Up and down are absolute directions.” They’re relative to whatever direction is used to measure spin, such as an applied magnetic field.
• “Spin only matters for magnetism.” It controls how many electrons fit in each orbital, and therefore the whole structure of the periodic table.

Key takeaways

• The spin quantum number mₛ can only be +½ or −½, drawn as ↑ and ↓.
• Spin was revealed by the Stern–Gerlach experiment and by fine structure in spectra, and explained by Dirac’s relativistic quantum theory.
• Spin is an intrinsic property, making each electron a tiny magnet, not a literally spinning ball.
• Because spin has two values, each orbital holds two electrons (Pauli), and Hund’s rule favours parallel spins.
• Spin explains magnetism, electron pairing in bonds, radicals, and techniques such as NMR, MRI and ESR.