Hund’s rule is one of three basic principles that govern how electrons arrange themselves inside an atom. In plain terms, it says: when electrons are filling orbitals that have the same energy level, each orbital gets one electron before any orbital gets a second. And all those single electrons spin in the same direction. This simple pattern has real consequences for the magnetic and chemical behavior of elements across the periodic table.
German physicist Friedrich Hund first described this rule in 1925 while studying the spectra of transition metals from scandium to nickel. It is now taught in introductory chemistry courses worldwide, alongside two companion principles: the Aufbau principle and the Pauli exclusion principle.
How Hund’s Rule Works
Inside every atom, electrons occupy orbitals, which you can think of as regions of space where an electron is likely to be found. Some orbitals share the same energy level. The three p orbitals in any shell, for example, are all equal in energy. So are the five d orbitals. When electrons begin filling these equal-energy orbitals, Hund’s rule dictates the order: spread out first, pair up later.
Imagine three empty seats on a bus. If three passengers board one at a time, each picks an empty seat rather than sitting next to someone already there. Electrons do the same thing, and for a concrete physical reason: electrons repel each other because they all carry negative charge. Occupying separate orbitals keeps them farther apart on average, which lowers the overall energy of the atom. Lower energy means greater stability.
There’s a second part to the rule that’s easy to overlook. Every electron spins in one of two directions (often drawn as an up arrow or a down arrow). Hund’s rule requires that all the singly occupied orbitals contain electrons spinning the same way. This parallel spin arrangement creates what physicists call an antisymmetric spatial state, which pushes the electrons even farther apart and reduces their mutual repulsion further. The energy savings come not from the spins themselves but from how matching spins force the electrons into more separated positions in space.
Carbon, Nitrogen, and Oxygen: Step by Step
The 2p orbitals in the second shell of the periodic table offer the clearest demonstration. There are three of these orbitals, each able to hold two electrons.
Carbon (6 electrons): After filling the 1s and 2s orbitals with four electrons, carbon has two left for the 2p orbitals. Rather than stuffing both into a single p orbital, Hund’s rule places one in the first p orbital and one in the second, both spinning the same direction. Carbon therefore has two unpaired electrons.
Nitrogen (7 electrons): Nitrogen has three electrons for the 2p level. Each of the three p orbitals gets exactly one electron, all with parallel spins. This gives nitrogen three unpaired electrons and a perfectly half-filled 2p subshell.
Oxygen (8 electrons): With four electrons to place in three p orbitals, oxygen has no choice but to start pairing. One p orbital holds two electrons (with opposite spins, as required by the Pauli exclusion principle), while the other two orbitals each hold one. Oxygen ends up with two unpaired electrons.
How It Fits With the Other Two Rules
Electron configuration is governed by three principles working together. They answer different questions:
- Aufbau principle: Which energy levels fill first? Electrons occupy the lowest available energy level before moving to higher ones, like water filling a container from the bottom up.
- Pauli exclusion principle: How many electrons fit in one orbital? Exactly two, and they must have opposite spins. No two electrons in an atom can share the same set of four quantum numbers.
- Hund’s rule: How do electrons distribute across orbitals of equal energy? They spread out with parallel spins before pairing up.
The Aufbau principle tells you the order of energy levels. The Pauli exclusion principle sets the capacity of each orbital. Hund’s rule handles the situation where multiple orbitals sit at the same energy and you need to know which fills first. All three are needed to correctly write out any element’s electron configuration.
Why It Matters: Magnetism
Hund’s rule is the reason many elements are magnetic. Atoms with unpaired electrons are paramagnetic, meaning they are attracted to an external magnet. Because Hund’s rule maximizes the number of unpaired electrons in any subshell, it directly increases the magnetic character of elements that have partially filled orbitals.
Transition metals like vanadium, chromium, manganese, iron, cobalt, and nickel all have partially filled d orbitals. Hund’s rule spreads their d electrons across all five d orbitals before pairing begins, which is why these elements and their compounds are often strongly magnetic. Iron, with four unpaired d electrons in its ground state, is the most familiar example. If electrons paired up immediately instead of spreading out, far fewer elements would show magnetic behavior.
Half-Filled and Fully Filled Subshells
Hund’s rule also helps explain a quirk in the periodic table that surprises many chemistry students. Chromium and copper don’t follow the expected filling order. Chromium’s electron configuration is [Ar] 3d⁵ 4s¹ rather than the predicted [Ar] 3d⁴ 4s². Copper is [Ar] 3d¹⁰ 4s¹ instead of [Ar] 3d⁹ 4s². In both cases, the atom “borrows” an electron from the 4s orbital to achieve either a half-filled or fully filled d subshell.
A half-filled subshell, where every orbital holds exactly one electron with parallel spins, represents a particularly stable arrangement. So does a completely filled subshell. The extra stability comes from the same source Hund’s rule describes: the way electron repulsion is minimized when electrons are evenly distributed. Fully filled and half-filled subshells contribute nothing to the atom’s net angular momentum, creating a balanced, low-energy state.
The Physics Behind the Rule
At a deeper level, Hund’s rule is a consequence of how identical particles behave in quantum mechanics. Electrons are subject to the antisymmetrization requirement: the total description of two electrons must change sign if you swap them. When two electrons have parallel spins (a symmetric spin state), their spatial arrangement must be antisymmetric. In practical terms, this means the electrons avoid being in the same place, which reduces the energy cost of their electrical repulsion.
The key energy term that drives this is sometimes called exchange energy. It isn’t a new force. It’s a mathematical consequence of the way electron repulsion changes depending on whether the electrons occupy the same region of space or spread apart. When electrons have parallel spins and occupy different orbitals, the exchange contribution lowers the total energy. The larger the number of parallel-spin electrons, the more exchange stabilization the atom gains. This is why atoms in their ground states tend to have as many unpaired electrons as possible, exactly as Hund observed nearly a century ago.