Topic 1.5 Atomic Structure and Electron Configuration: write electron configurations for atoms and ions using the Aufbau principle, the Pauli exclusion principle, and Hund's rule, and relate them to the Coulombic model of the atom.

What this topic is asking

The College Board (Topic 1.5) wants you to describe the structure of the atom in terms of protons, neutrons and electrons, to apply the Coulombic model (the attraction between the nucleus and electrons), and to write electron configurations for atoms and ions using three rules: the Aufbau principle, the Pauli exclusion principle and Hund's rule.

The structure of the atom

Nearly all the mass is in the nucleus, but the electrons occupy nearly all the volume and determine chemical behavior. Electrons are held by the Coulombic attraction between their negative charge and the positive nucleus. Coulomb's law, $F \propto \dfrac{q_1 q_2}{r^2}$, tells you the attraction is stronger when the charges are larger and when the electron is closer to the nucleus. This single idea explains why inner electrons are harder to remove than outer ones, and it underlies the whole topic.

Energy levels, subshells and orbitals

Electrons occupy energy levels (shells), labelled by the principal quantum number $n = 1, 2, 3, \dots$. Each level is divided into subshells ($s$, $p$, $d$, $f$), and each subshell contains orbitals that each hold up to two electrons:

• $s$ subshell: 1 orbital, up to 2 electrons.
• $p$ subshell: 3 orbitals, up to 6 electrons.
• $d$ subshell: 5 orbitals, up to 10 electrons.
• $f$ subshell: 7 orbitals, up to 14 electrons.

Higher $n$ means, on average, farther from the nucleus and higher energy.

The three filling rules

A useful subtlety is that $4s$ fills before $3d$ on the way up, because at that point $4s$ is slightly lower in energy. But once the $3d$ orbitals are occupied, the $4s$ electrons are in the higher principal level and are removed first when the atom is ionized. This is why $\text{Fe}^{2+}$ is $[\text{Ar}]\,3d^6$, not $[\text{Ar}]\,3d^4\,4s^2$.

Writing configurations for ions

For a cation, remove electrons from the orbital with the highest principal quantum number $n$ first (the outermost shell), not necessarily the last one filled. For an anion, add electrons following the Aufbau order. The noble-gas shorthand, such as $[\text{Ne}]\,3s^2\,3p^4$ for sulfur, is accepted and saves time, as long as you can expand it.

The deeper point the College Board is testing is that configuration is governed by energy, and energy is governed by Coulomb's law. Electrons settle into the arrangement of lowest total energy: close to the nucleus where attraction is strong, but spread among orbitals to minimize the electron-electron repulsion that Hund's rule reflects. Photoelectron spectroscopy (Topic 1.6) lets you actually measure these energy levels, and periodic trends (Topic 1.7) are the patterns that emerge as configurations repeat down and across the table. Treating configuration as the energetic ground state, rather than a memorized pattern, is what lets you reason about ions, excited states and anomalies.

Try this

Q1. Write the noble-gas electron configuration of a neutral calcium atom (Ca, $Z = 20$). [1 point]

• Cue. $[\text{Ar}]\,4s^2$.

Q2. State how many unpaired electrons are in a nitrogen atom ($1s^2\,2s^2\,2p^3$) and justify using a filling rule. [2 points]

• Cue. Three; by Hund's rule the three $2p$ electrons occupy separate orbitals with parallel spins, so all three are unpaired.