Electron Configuration — Aufbau, Pauli and Hund Explained
Electron configuration is the address list of every electron in an atom. Get it right and the periodic table, valency, magnetic behaviour and colour of transition-metal compounds all follow. Three rules decide the answer, and they are applied in a fixed order. This guide states each one plainly and works six configurations completely, including the two "exceptions" that are actually predictable.
The three rules, in the order you use them
2. Pauli exclusion principle — no two electrons in an atom may have all four quantum numbers the same, so an orbital holds at most two electrons, with opposite spins.
3. Hund's rule of maximum multiplicity — within a set of equal-energy (degenerate) orbitals, put one electron in each before pairing any, and keep those single electrons with parallel spins.
The filling order — and the (n + l) rule behind it
You do not have to memorise that sequence. It follows from the (n + l) rule:
- The orbital with the lower (n + l) fills first.
- If two orbitals have the same (n + l), the one with the lower n fills first.
Check the famous case: for 4s, n + l = 4 + 0 = 4; for 3d, n + l = 3 + 2 = 5. Four is less than five, so 4s fills before 3d. Now compare 3d (n + l = 5) with 4p (4 + 1 = 5): a tie, broken by the lower n, so 3d fills before 4p. Two comparisons reproduce the whole awkward part of the sequence.
Capacities follow from Pauli: s holds 2, p holds 6, d holds 10, f holds 14 — because each subshell has (2l + 1) orbitals and each orbital holds 2 electrons.
Worked example 1 — Nitrogen (Z = 7), and Hund's rule
Fill in order: 1s takes 2, 2s takes 2, leaving 3 electrons for 2p.
N: 1s² 2s² 2p³
Hund's rule decides how those three sit. The 2p subshell has three orbitals of equal energy (2px, 2py, 2pz), so each gets one electron with parallel spin. Nitrogen therefore has 3 unpaired electrons, not 1. That is why it is paramagnetic and why it forms three bonds.
Worked example 2 — Iron (Z = 26)
1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶ — check the count: 2 + 2 + 6 + 2 + 6 + 2 + 6 = 26 ✓
Written with the noble-gas core: Fe: [Ar] 3d⁶ 4s²
Note the convention: you fill 4s before 3d, but you write 3d before 4s, because configurations are written in order of increasing n. Both orders are correct in their own place, and confusing them is a genuine source of lost marks.
Applying Hund's rule to 3d⁶: five orbitals, so the first five electrons go in singly and the sixth pairs up — leaving 4 unpaired electrons.
Worked example 3 — Chromium (Z = 24) and Copper (Z = 29)
Straight Aufbau predicts Cr = [Ar] 3d⁴ 4s² and Cu = [Ar] 3d⁹ 4s². The observed configurations are:
Cr: [Ar] 3d⁵ 4s¹ (18 + 5 + 1 = 24 ✓)
Cu: [Ar] 3d¹⁰ 4s¹ (18 + 10 + 1 = 29 ✓)
Reason: 4s and 3d lie very close in energy here, and a half-filled (d⁵) or completely filled (d¹⁰) d subshell is extra stable — the electrons are symmetrically distributed and the exchange energy between parallel-spin electrons is maximised. Promoting one 4s electron costs less than that stability gain, so the atom takes the trade.
Chromium ends up with 6 unpaired electrons (five in 3d, one in 4s) — the highest of any element in the first transition series.
Worked example 4 — Bromine (Z = 35)
[Ar] is 18 electrons; 17 remain. Fill 4s² (2), then 3d¹⁰ (10), then 4p⁵ (5): 2 + 10 + 5 = 17 ✓
Br: [Ar] 3d¹⁰ 4s² 4p⁵
Seven electrons sit in the outermost shell (4s² 4p⁵), which is why bromine is a halogen in Group 17. The filled 3d¹⁰ is a completed inner shell and takes no part in normal bonding.
Worked example 5 — ions: Fe³⁺ and Ni²⁺
The rule for cations: remove electrons from the shell of highest principal quantum number n first — that is, 4s before 3d.
Fe is [Ar] 3d⁶ 4s². For Fe³⁺, remove the two 4s electrons and then one 3d electron:
Fe³⁺: [Ar] 3d⁵ (18 + 5 = 23 = 26 − 3 ✓)
Ni is [Ar] 3d⁸ 4s². For Ni²⁺, remove only the 4s pair:
Ni²⁺: [Ar] 3d⁸ (18 + 8 = 26 = 28 − 2 ✓)
Writing Fe³⁺ as [Ar] 3d³ 4s² — removing from 3d first — is one of the most frequently penalised errors in inorganic chemistry.
Turning the configuration into a magnetic moment
Count the unpaired electrons n and use the spin-only formula:
For Fe³⁺ ([Ar] 3d⁵, all five unpaired): μ = √(5 × 7) = √35 = 5.92 BM. For Ni²⁺ ([Ar] 3d⁸, two unpaired): μ = √(2 × 4) = √8 = 2.83 BM. A species with no unpaired electrons has μ = 0 and is diamagnetic. This one line is how a written configuration becomes an experimentally measurable number.
Common mistakes
- Filling 3d before 4s. The (n + l) rule settles it: 4s (4) fills before 3d (5).
- Removing 3d electrons before 4s when making a cation. Always take the outermost shell — 4s — first.
- Pairing electrons too early. Hund's rule fills every degenerate orbital singly first. p⁴ is not two pairs; it is one pair and two singles.
- Miscounting the electron total. Add the superscripts and check they equal Z (or Z − charge for an ion). This one check catches most errors.
- Treating Cr and Cu as random exceptions. They follow from half-filled and fully filled d-subshell stability, and examiners expect that reason, not just the fact.
- Forgetting the ion's charge convention. Cations lose electrons (Z − charge); anions gain them, so Cl⁻ has 18 electrons and the configuration of argon.
Where it appears in exams
| Exam | Typical question |
|---|---|
| CBSE/ICSE Class 11 | Write the configuration; state and apply the three rules; explain Cr and Cu |
| JEE / NEET | Unpaired electrons, spin-only magnetic moment, quantum numbers of the last electron |
| IIT-JAM / CUET-PG | Term symbols, d-block ion configurations, exchange energy arguments |
| GATE / CSIR-NET | High-spin vs low-spin complexes, lanthanide 4f configurations |
Check any element or ion in one click. Enter the atomic number or the symbol and the Electron Configuration calculator gives the full and noble-gas-core forms, the orbital diagram and the count of unpaired electrons — including the Cr and Cu exceptions.
Open the Electron Configuration Calculator →Atomic structure is the chapter everything else in chemistry rests on, so it is worth over-learning early. ABC Chemistry runs Class 11–12 chemistry coaching at the Gurugram centre and online classes across India, with home tuition available in Delhi-NCR — details at abcchemistry.in.