The three principles that guide how electrons arrange themselves in an atom are the Aufbau principle, the Pauli exclusion principle, and Hund’s rule. Together, these rules explain why electrons fill orbitals in a specific, predictable order rather than randomly scattering around the nucleus. Understanding all three gives you the tools to write the electron configuration of any element on the periodic table.
The Aufbau Principle: Fill Low-Energy Orbitals First
The Aufbau principle (from the German word for “building up”) is the most straightforward of the three rules. It states that electrons occupy the lowest-energy orbitals available before moving to higher-energy ones. Think of it like filling a building from the ground floor up: you don’t skip to the fifth floor when there’s still room on the first.
The filling order goes: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and so on. Notice that 4s fills before 3d. This is because orbital energy depends on two things: the shell number (how far the orbital is from the nucleus) and the orbital shape. In atoms with more than one electron, these two factors combine so that some orbitals in a higher shell actually sit lower in energy than orbitals in the shell below.
A useful shortcut for predicting this order is the Madelung rule, sometimes called the (n+l) rule. You add the shell number (n) and the orbital type number (l), where s = 0, p = 1, d = 2, and f = 3. Orbitals fill in order of increasing (n+l). When two orbitals have the same sum, the one with the smaller shell number fills first. For example, 3d has n+l = 3+2 = 5, while 4p has n+l = 4+1 = 5, so 3d fills before 4p because its shell number is lower.
The Pauli Exclusion Principle: No Identical Electrons
Proposed by physicist Wolfgang Pauli in 1925, this principle sets a hard limit on how many electrons can share the same space. The rule: no two electrons in an atom can have the same set of four quantum numbers. Quantum numbers are essentially an address system for electrons, describing the shell, the orbital shape, the orbital orientation, and the spin direction. If two electrons already match on the first three numbers (meaning they’re in the same orbital), they must differ on the fourth, which is spin. Since spin only has two possible values (often described as “up” and “down”), each orbital can hold a maximum of two electrons, and those two must spin in opposite directions.
This is why the 1s orbital holds only 2 electrons, the three 2p orbitals hold a combined 6, and the five 3d orbitals hold a combined 10. The Pauli exclusion principle is the reason atoms have layers of electron shells at all. Without it, every electron would simply collapse into the single lowest-energy orbital, and chemistry as we know it wouldn’t exist.
Hund’s Rule: Spread Out Before Pairing Up
Hund’s rule governs what happens when you have multiple orbitals at the same energy level, called degenerate orbitals. The p sublevel, for instance, contains three orbitals of equal energy, and the d sublevel contains five. Hund’s rule says that electrons fill each of these orbitals singly, all with the same spin direction, before any orbital gets a second electron.
Picture three empty seats on a bus. Most people sit in their own row before doubling up with a stranger. Electrons behave similarly because they repel each other (they’re all negatively charged), so spreading out minimizes that repulsion. The “same spin” part matters too: atoms with the maximum number of parallel-spinning electrons in a sublevel are more stable than atoms where spins are randomly mixed.
For a practical example, consider nitrogen with seven electrons. After filling 1s² and 2s², you have three electrons left for the 2p sublevel. Rather than putting two in one 2p orbital and one in another, each of the three 2p orbitals gets one electron, all spinning the same direction: 2p¹ 2p¹ 2p¹. Oxygen, with one more electron, is forced to start pairing: one 2p orbital now holds two electrons while the other two still hold one each.
How the Three Principles Work Together
Writing an electron configuration means applying all three rules simultaneously. Take iron (26 electrons) as an example. The Aufbau principle tells you to fill in order: 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d⁶. The Pauli exclusion principle ensures you never put more than two electrons in any single orbital. And Hund’s rule tells you how those six 3d electrons arrange themselves across the five d orbitals: four orbitals get one electron each (all with the same spin), and the remaining two electrons pair into one orbital with opposite spins.
For quick notation, you can replace the inner electrons with the symbol of the nearest preceding noble gas in brackets. Iron becomes [Ar] 4s² 3d⁶, where [Ar] stands for the first 18 electrons. Sodium becomes [Ne] 3s¹, and potassium becomes [Ar] 4s¹. This shorthand highlights the valence electrons, the outermost ones that actually participate in chemical bonding.
Notable Exceptions to the Rules
The three principles predict configurations accurately for most elements, but a handful of transition metals break the pattern. The two most well-known exceptions are chromium (element 24) and copper (element 29). The Aufbau principle predicts chromium should be [Ar] 4s² 3d⁴ and copper should be [Ar] 4s² 3d⁹. In reality, both steal one electron from the 4s orbital to achieve a more stable d sublevel arrangement:
- Chromium: [Ar] 4s¹ 3d⁵ (half-filled d sublevel)
- Copper: [Ar] 4s¹ 3d¹⁰ (completely filled d sublevel)
Half-filled and fully filled d sublevels carry extra stability. This stability is significant enough to override the normal filling order, pulling an electron from 4s into 3d. Similar exceptions appear elsewhere in the periodic table, particularly in the heavier transition metals and the lanthanides, but chromium and copper are the two you’re most likely to encounter in a chemistry course.
Why These Principles Matter for Chemistry
Electron configuration isn’t just an abstract exercise. The arrangement of electrons, particularly those in the outermost shell (valence electrons), determines how an element behaves chemically. Alkali metals like sodium and potassium each have a single valence electron, which they lose easily, making them highly reactive. Halogens like fluorine and chlorine are one electron short of a full outer shell, so they aggressively grab electrons from other atoms. Noble gases have completely filled valence shells, which is why they rarely react with anything.
The periodic table itself is organized around these filling patterns. Each row corresponds to filling a new principal energy level, and each block (s-block, p-block, d-block, f-block) corresponds to the type of orbital being filled. Once you understand the Aufbau principle, the Pauli exclusion principle, and Hund’s rule, the structure of the entire periodic table stops being something you memorize and becomes something you can derive.