Writing Electron Configurations: Aufbau, Pauli and Hund

Filling the address book

You now know the "addresses" (orbitals) available to electrons. An electron configuration lists which orbitals an atom's electrons actually occupy in the ground state. For example, sodium is 1s² 2s² 2p⁶ 3s¹.

In each term such as 2p⁶, the 2 is n, the p is the sublevel, and the superscript 6 is the number of electrons in that sublevel.

Remember from Grade 11: you arranged the first 20 elements' electrons in shells of 2, 8, 8, 2. Electron configurations add the sublevel detail that explains why the fourth row of the periodic table suddenly gets 10 extra elements (the transition metals).

Three rules

1. Aufbau principle (German for "building up"): electrons fill the lowest-energy orbitals first.
2. Pauli exclusion principle: an orbital holds at most two electrons, with opposite spins.
3. Hund's rule: when electrons fill orbitals of equal energy (such as the three 2p orbitals), they go into separate orbitals with parallel spins first, and pair up only when every orbital in the sublevel has one electron. (Electrons repel each other, so they spread out.)

The filling order

In a multi-electron atom, sublevels in the same level have different energies: s < p < d < f. As a result the levels overlap, and 4s is lower in energy than 3d for the atoms where it is being filled. The order is:

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

A handy rule: sublevels fill in order of increasing n + l; when two have the same n + l, the one with lower n fills first (3d has n + l = 5, the same as 4p, but 3d has lower n, so 3d comes first).

Three ways to write a configuration

• Full configuration: every sublevel. Phosphorus (15 electrons): 1s² 2s² 2p⁶ 3s² 3p³.
• Condensed (noble-gas core) configuration: replace the core with the previous noble gas in square brackets. Phosphorus: [Ne] 3s² 3p³. The electrons after the core in the highest n level are the valence electrons (5 for phosphorus).
• Orbital box diagram: one box per orbital, arrows for electrons. This is the only form that shows unpaired electrons.

Ions

• Anions: add electrons in the normal filling order. Cl (17 e⁻): [Ne] 3s² 3p⁵, so Cl⁻ (18 e⁻) is [Ne] 3s² 3p⁶, the same as [Ar]. Atoms and ions with the same configuration are isoelectronic.
• Cations of main-group elements: remove the outermost electrons. Na⁺ is 1s² 2s² 2p⁶, isoelectronic with neon.
• Transition-metal cations: remove the 4s electrons before the 3d. Once 3d starts to fill, 4s electrons are the outermost (they are farther from the nucleus on average). Iron is [Ar] 4s² 3d⁶; Fe²⁺ is [Ar] 3d⁶ and Fe³⁺ is [Ar] 3d⁵.

Two famous exceptions

Chromium is [Ar] 4s¹ 3d⁵, not [Ar] 4s² 3d⁴. Copper is [Ar] 4s¹ 3d¹⁰, not [Ar] 4s² 3d⁹. A half-filled (d⁵) or completely filled (d¹⁰) d sublevel is especially stable, and 4s and 3d are so close in energy that moving one electron pays off. Elements below them (molybdenum, silver, gold) show similar patterns. Use the regular rules for everything else in this course.

Magnetism: a test of the rules

A substance with unpaired electrons is paramagnetic (pulled into a magnetic field). If all electrons are paired, it is diamagnetic. Measurements agree with the predictions: Zn ([Ar] 4s² 3d¹⁰, all paired) is diamagnetic, while Fe³⁺ ions (3d⁵, five unpaired electrons) are strongly paramagnetic.