Aufbau Principle, Pauli Exclusion and Hund's Rule Explained

Electrons fill an atom's orbitals according to three rules that together predict the electronic structure of every element. The Aufbau principle says electrons occupy the lowest-energy orbital available first. The Pauli exclusion principle limits each orbital to two electrons with opposite spins. Hund's rule says electrons spread out singly across equal-energy orbitals before pairing up.

These rules matter because an atom's electron arrangement decides its position in the periodic table, its valency and how it bonds. Get the configuration right and trends like ionisation energy and atomic size start making sense; get it wrong and every prediction built on it collapses.

Key Concepts

• Aufbau principle (German for "building up"): orbitals fill in order of increasing energy: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p … Note that 4s fills before 3d.
• (n + l) rule: the orbital with the lower (n + l) value fills first; on a tie, the lower n wins. For 4s: n + l = 4 + 0 = 4; for 3d: 3 + 2 = 5, so 4s fills first.
• Pauli exclusion principle: no two electrons in an atom can have all four quantum numbers identical, so an orbital holds at most two electrons, with opposite spins (↑↓).
• Hund's rule: in degenerate (equal-energy) orbitals such as the three 2p orbitals, electrons occupy separate orbitals with parallel spins before any pairing occurs.
• Orbital capacity: s holds 2, p holds 6, d holds 10, f holds 14 electrons.
• Half-filled/full subshell stability: chromium is [Ar] 3d⁵ 4s¹ (not 3d⁴ 4s²) and copper is [Ar] 3d¹⁰ 4s¹ (not 3d⁹ 4s²) because half-filled and fully filled d subshells are extra stable.

Formulas

• Maximum electrons in shell n: 2n². For n = 3: 2 × 9 = 18 electrons maximum.
• Maximum electrons in a subshell: 2(2l + 1). For d (l = 2): 2 × 5 = 10.

These count capacities; the actual filling order comes from the (n + l) rule above.

Worked Example

Write the electronic configuration of Fe²⁺ (iron, atomic number 26, has lost 2 electrons) and count its unpaired electrons.

1. Neutral Fe (Z = 26): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶, or [Ar] 4s² 3d⁶.
2. For cations, remove electrons from the highest n first: the 4s electrons leave before 3d. So Fe²⁺ = [Ar] 3d⁶.
3. Apply Hund's rule to the five 3d orbitals: first five electrons go singly (↑ ↑ ↑ ↑ ↑), the sixth pairs up (↑↓ ↑ ↑ ↑ ↑).
4. Count unpaired: 4 orbitals hold single electrons.

Fe²⁺ is [Ar] 3d⁶ with 4 unpaired electrons.

Common Misconceptions

• 3d fills before 4s because 3 < 4. The (n + l) rule, not the shell number alone, decides: 4s (n + l = 4) is lower in energy than 3d (n + l = 5) for potassium and calcium, so it fills first.
• Ions lose their outermost-shell electrons by shell number. Transition-metal cations lose ns electrons before (n−1)d electrons — Fe²⁺ loses 4s, not 3d.
• Hund's rule is about opposite spins pairing. Opposite-spin pairing is the Pauli principle; Hund's rule is about spreading electrons singly with parallel spins first.

Real-World Applications

• Configurations explain the periodic table's blocks (s, p, d, f) and element positions.
• Unpaired electrons predict magnetism: Fe²⁺ with 4 unpaired electrons is paramagnetic.
• Chemists predict valency, oxidation states and bond types from valence configurations.
• The Cr and Cu exceptions explain their unusual chemistry and colours.
• Spectroscopy and ionisation-energy trends are interpreted using these rules.

Build up from the lowest energy (Aufbau), cap each orbital at two opposite-spin electrons (Pauli), and spread electrons singly before pairing (Hund). Remember the 4s-before-3d order and the Cr/Cu exceptions, and you can write any configuration confidently.