Electron Configuration Explained: Aufbau Principle, Pauli Exclusion and Hund's Rule

The shape of the periodic table and the chemistry of each element come down to how electrons are arranged inside the atom. An electron configuration records which orbitals an atom's electrons occupy and how many are in each. It looks like a code at first, but three rules are enough to write the configuration of most elements yourself.

Basic terms: shells, subshells and orbitals

The state of an electron is described by quantum numbers. For writing configurations you need only a few ideas.

• Shell (principal quantum number n): 1, 2, 3 and so on. Higher shells are farther from the nucleus and higher in energy.
• Subshell (s, p, d, f): divisions within a shell according to orbital shape. Shell n contains n kinds of subshell: shell 1 has only 1s, shell 2 has 2s and 2p, shell 3 has 3s, 3p and 3d.
• Orbital: a region where an electron is likely to be found. An s subshell has one orbital, p has three, d has five and f has seven.

Each orbital holds at most two electrons, so the maximum occupancy is 2 for s, 6 for p, 10 for d and 14 for f.

A configuration is written as the subshell label followed by a superscript electron count, such as 1s² 2s² 2p⁴. That is oxygen, with eight electrons: two in 1s, two in 2s and four in 2p.

Rule 1: the Aufbau principle

The Aufbau principle (from the German for "building up") states that in a ground-state atom, electrons fill the lowest-energy orbitals first. The catch is that orbital energies do not follow shell number exactly. For example, 4s fills before 3d.

The usual filling order is:

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p

A handy way to remember it is the n + l rule, also called the Madelung rule. Give s, p, d and f the l values 0, 1, 2 and 3.

1. Fill subshells in order of increasing n + l.
2. When two subshells have the same n + l, fill the one with smaller n first.

4s has n + l = 4 + 0 = 4, while 3d has 3 + 2 = 5, so 4s comes first. 3d and 4p (4 + 1 = 5) tie, so 3d, with the smaller n, goes first. Many textbooks show this as a diagram of diagonal arrows.

The periodic table itself encodes this order. Reading across each row from the top left, you pass through the s-block, then the f-block where present, then the d-block and finally the p-block, which is exactly the filling sequence.

Rule 2: the Pauli exclusion principle

The Pauli exclusion principle says that no two electrons in an atom can have the same set of four quantum numbers. For configurations, this means an orbital can hold at most two electrons, and they must have opposite spins. That is why an orbital box contains one up arrow (↑) and one down arrow (↓) when it is full.

Rule 3: Hund's rule

Hund's rule says that when several orbitals have the same energy, electrons occupy them singly, with parallel spins, before any of them pair up. Think of passengers boarding a bus with empty double seats: people take an empty pair for themselves before anyone sits next to a stranger. Electrons repel each other, so spreading out into separate orbitals gives a lower energy.

Drawing orbital box diagrams

Take nitrogen, with seven electrons. Its configuration is 1s² 2s² 2p³, and the orbital boxes look like this:

• 1s: [↑↓]
• 2s: [↑↓]
• 2p: [↑ ] [↑ ] [↑ ]

Following Hund's rule, the three 2p electrons occupy separate boxes with the same spin, so nitrogen has three unpaired electrons.

Oxygen, with eight electrons, is 1s² 2s² 2p⁴:

• 2p: [↑↓] [↑ ] [↑ ]

The fourth 2p electron has to pair up, leaving two unpaired electrons. That paired electron is the reason nitrogen has a higher ionization energy than oxygen, an exception discussed in the periodic trends guide.

Noble gas shorthand

Configurations get long for larger atoms. Written in full, iron (26 electrons) is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶

The first part, 1s² 2s² 2p⁶ 3s² 3p⁶, is identical to the configuration of argon (18 electrons), so it can be replaced by the noble gas symbol in square brackets:

[Ar] 4s² 3d⁶

This is noble gas notation. The bracketed part represents the core electrons, which rarely take part in chemistry; what follows are the valence electrons that decide the element's behavior. More examples:

Line up the shorthand for elements in one group and the outer configuration repeats: sodium is [Ne]3s¹, potassium [Ar]4s¹ and rubidium [Kr]5s¹. That repetition is why elements in a group behave alike.

There are two conventions for ordering the subshells. Some write them in filling order, [Ar] 4s² 3d⁶; others in order of shell number, [Ar] 3d⁶ 4s². Both describe the same configuration.

Exceptions: chromium and copper

Applying the Aufbau principle mechanically gives [Ar] 4s² 3d⁴ for chromium (24 electrons) and [Ar] 4s² 3d⁹ for copper (29). The measured ground states are different:

• Chromium: [Ar] 4s¹ 3d⁵
• Copper: [Ar] 4s¹ 3d¹⁰

One 4s electron moves into 3d, leaving the d subshell exactly half full (d⁵) or completely full (d¹⁰). The usual shorthand explanation is that half-filled and filled subshells are especially stable. More precisely, 4s and 3d are so close in energy that the gain in exchange energy among same-spin electrons, together with reduced repulsion, outweighs the cost of promoting one 4s electron.

Molybdenum ([Kr] 5s¹ 4d⁵), silver ([Kr] 5s¹ 4d¹⁰) and gold ([Xe] 4f¹⁴ 5d¹⁰ 6s¹) show similar exceptions, and palladium ([Kr] 4d¹⁰) has no outer s electron at all. Exceptions multiply in heavier elements, where orbital energies crowd together and relativistic effects come into play. Chromium and copper are the ones most often tested, but remember that the filling rules are a very good approximation rather than a law without exceptions.

Configurations of ions

To form a cation, remove electrons from the outermost shell (highest n) first. Although 4s filled before 3d, it also empties before 3d.

• Fe: [Ar] 3d⁶ 4s² → Fe²⁺: [Ar] 3d⁶ → Fe³⁺: [Ar] 3d⁵
• Cu: [Ar] 3d¹⁰ 4s¹ → Cu⁺: [Ar] 3d¹⁰ → Cu²⁺: [Ar] 3d⁹

For anions, add electrons. Chlorine ([Ne] 3s² 3p⁵) gains one electron to become Cl⁻ ([Ne] 3s² 3p⁶), the same configuration as argon.

Practice: write your own

Follow these steps and you can write the configuration of almost any element.

1. Use the atomic number to find the number of electrons in the neutral atom.
2. Find the preceding noble gas and write its symbol in brackets.
3. Walk across the periodic table from the cell after that noble gas to your element, filling s, then f, then d, then p as you pass through each block.
4. Check whether the element is one of the chromium- or copper-type exceptions.

Selenium (34) is a good example. The preceding noble gas is argon (18). The remaining 16 electrons go 2 into 4s, 10 into 3d and 4 into 4p, giving [Ar] 3d¹⁰ 4s² 4p⁴. The 4p⁴ ending tells you immediately that selenium is in group 16 with oxygen. Compare your answers with the configurations shown on each element page to practise.