Electron configuration & quantum numbers
The idea
Four quantum numbers act as an address system for every electron in an atom: n sets the shell and overall energy, l the subshell shape (0 = s, 1 = p, 2 = d, 3 = f), ml the orbital orientation, and ms the spin. You already know the broad shell picture from introductory electron configuration; the university-level upgrade is using the Pauli exclusion principle (no two electrons share all four numbers), the aufbau filling order, and Hund's rule (spread out within a degenerate subshell before pairing) to write and defend configurations exactly.
The practical skill is reading configurations off the periodic table itself: the table's block structure is the filling order. Watch the 4s/3d crossover carefully. Neutral atoms fill 4s before 3d, but once 3d is occupied it drops below 4s in energy — so transition metals ionize by losing their 4s electrons first. The common error is stripping d electrons first because d filled last; that produces wrong magnetic predictions for nearly every transition-metal ion.
Configurations are testable, not bookkeeping trivia: the count of unpaired electrons predicts whether a species is paramagnetic (drawn into a magnetic field) or diamagnetic, and measured magnetism is how chemists confirm which electrons actually left.
Worked example
Write the ground-state electron configuration of Fe (Z = 26) and of Fe³⁺, and determine how many unpaired electrons each species has.
- Count electrons into subshells in aufbau order: 26 electrons give 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶, written compactly as [Ar] 4s² 3d⁶ since argon accounts for the first 18.
- Apply Hund's rule to the 3d⁶ set: six electrons in five d orbitals means one orbital holds a pair and four stay single — neutral Fe has 4 unpaired electrons.
- Form the cation by removing the three highest-energy electrons of the ion, not the last-filled subshell of the atom: both 4s electrons leave first, then one 3d, giving Fe³⁺ = [Ar] 3d⁵.
- A 3d⁵ subshell puts one electron in each of the five d orbitals, so Fe³⁺ has 5 unpaired electrons — strongly paramagnetic, which experiment confirms.
- Sanity-check: a half-filled d⁵ configuration has extra exchange stability, consistent with Fe³⁺ being one of the most common iron species in minerals and biology.
Answer. Fe is [Ar] 4s² 3d⁶ with 4 unpaired electrons; Fe³⁺ is [Ar] 3d⁵ with 5 unpaired electrons.
Check your understanding
- Why do transition metals lose 4s electrons before 3d when they ionize, even though 4s filled first in the neutral atom?
- How does Hund's rule follow from electron–electron repulsion and exchange energy rather than being an arbitrary convention?
- What experimental measurement would distinguish [Ar] 3d⁵ from [Ar] 4s² 3d³ for a 3+ ion, and what result would each predict?
- Where do the exceptions like Cr and Cu come from, and what does that tell you about how close in energy 4s and 3d really are?
Build the foundations first
Electron configuration & quantum numbers builds on these concepts. If any feel shaky, start there.