Quantum numbers and the shapes of s, p and d atomic orbitals; the aufbau principle, Pauli exclusion principle and Hund's rule used to write electronic configurations; and how electronic structure explains the s, p and d blocks and periodic trends in ionisation energy.

What this key area is asking

The SQA wants you to describe atomic structure using quantum numbers and orbitals, to know the shapes of s, p and d orbitals, to apply the aufbau principle, the Pauli exclusion principle and Hund's rule to write electronic configurations in spectroscopic notation, and to explain the s, p and d blocks and the periodic trends in ionisation energy. The chromium and copper exceptions and the ionisation-energy dips are reliable exam earners.

Quantum numbers and orbitals

The number of orbitals in each subshell is fixed: one s orbital, three p orbitals, five d orbitals and seven f orbitals. Their shapes matter:

• s orbitals are spherical and centred on the nucleus.
• p orbitals are dumbbell-shaped, with three orbitals ($p_x$, $p_y$, $p_z$) pointing along the three axes.
• d orbitals have more complex, four-lobed shapes (with one exception), and there are five of them; their splitting in a ligand field explains the colour of transition metal complexes.

The three filling rules

Electronic configurations are built by applying three rules in order:

Configurations are written in spectroscopic notation, for example iron ($Z = 26$) is $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^6\,4s^2$. Two important exceptions arise because a half-filled or fully filled d subshell is extra-stable: chromium is $[\text{Ar}]\,3d^5\,4s^1$ and copper is $[\text{Ar}]\,3d^{10}\,4s^1$.

Blocks of the periodic table

The shape of the periodic table follows directly from which subshell is being filled:

• The s block (groups 1 and 2) is where an s subshell is being filled.
• The p block (groups 13 to 18) is where a p subshell is being filled.
• The d block (the transition metals) is where a d subshell is being filled.

This is why the d block is ten elements wide (five d orbitals, two electrons each) and the p block is six wide.

Trends in ionisation energy

The first ionisation energy is the energy to remove one mole of electrons from one mole of gaseous atoms. Across a period it generally rises because the nuclear charge increases while the electrons are added to the same shell, pulling them in more tightly. Down a group it falls because the outer electron is in a higher shell, further from the nucleus and more screened.

Successive ionisation energies of a single element show large jumps when a complete shell is broken into, confirming the existence of shells.

Examples in context

Orbitals and configurations underpin much of the rest of the course. The colour of transition metal complexes depends on the splitting of the five d orbitals by ligands, so the d-orbital picture introduced here is essential later. The reactivity of group 1 metals follows directly from their single, easily lost outer s electron, while the stability of the noble gases follows from their filled subshells. Ionisation-energy data is routinely used as evidence: a graph of successive ionisation energies for an element reveals its group from the position of the largest jump, and the dips across a period are quoted as proof that subshells exist within shells.

Try this

Q1. State the maximum number of electrons that can occupy a single d subshell. [1 mark]

• Cue. Ten (five d orbitals, two electrons each).

Q2. Write the spectroscopic electronic configuration of a copper atom ($Z = 29$). [1 mark]

• Cue. $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^{10}\,4s^1$ (the copper exception).

Q3. State Hund's rule. [1 mark]

• Cue. Degenerate orbitals are filled singly with parallel spins before any electrons pair up.