Electronic Configuration

The d-block elements, commonly called transition metals, occupy Groups 3–12 in the periodic table and span periods 4 through 7. Their defining characteristic is that they possess partially filled d-orbitals either in their elemental state or in their commonly formed ions. The general electronic configuration is written as (n−1)d¹⁻¹⁰ ns¹⁻², where n is the principal quantum number of the outermost shell and (n−1)d represents the penultimate shell being filled. For the fourth-period transition metals, this means filling the 3d sub-shell while electrons also occupy the 4s orbital. A crucial principle governing d-block configurations is the extra stability associated with half-filled (d⁵) and completely filled (d¹⁰) sub-shells. These arrangements minimize electron–electron repulsion and maximize exchange energy—the quantum-mechanical stabilization that arises when electrons of parallel spin can exchange positions. This principle explains two famous exceptions to the expected aufbau filling order: chromium (Cr) and copper (Cu), which adopt configurations that deviate from simple predictions based on filling 4s before 3d. Understanding electronic configurations of transition metals is essential because these configurations directly determine magnetic properties (such as paramagnetism and diamagnetism), the range of oxidation states an element can exhibit, the ability to form complex ions with ligands, and the characteristic colours of transition metal compounds. Mastery of this concept underpins virtually all subsequent study of transition element chemistry.

Key takeaways
  • The Aufbau Principle and Sub-shell Energy Order
  • The General Formula (n−1)d¹⁻¹⁰ ns¹⁻²
  • Chromium: The d⁵ Exception
  • Copper: The d¹⁰ Exception
  • Configurations of Ions

The Aufbau Principle and Sub-shell Energy Order

Electrons fill orbitals in order of increasing energy. For elements up to Z = 20 (calcium), the 4s orbital is filled before 3d because 4s has slightly lower energy in neutral atoms with few d electrons. The filling order relevant to Period 4 transition metals is: [Ar] → 4s¹ (K) → 4s² (Ca) → 4s²3d¹ (Sc) → … → 4s²3d¹⁰ (Zn). Each step adds one electron to the 3d sub-shell while the 4s remains occupied with two electrons—except for the two famous exceptions.

The General Formula (n−1)d¹⁻¹⁰ ns¹⁻²

For Period 4 (n = 4): configuration = [Ar] 3d¹⁻¹⁰ 4s¹⁻². For Period 5 (n = 5): [Kr] 4d¹⁻¹⁰ 5s¹⁻². For Period 6 (n = 6): [Xe] 4f¹⁴ 5d¹⁻¹⁰ 6s¹⁻². The f-electrons in lanthanides are inner-core electrons and do not change the basic d-block formula. In all cases, (n−1)d electrons are being added to a sub-shell one principal level below the outermost s electrons.

Chromium: The d⁵ Exception

Expected (aufbau): [Ar] 3d⁴ 4s². Actual: [Ar] 3d⁵ 4s¹. Chromium promotes one 4s electron into the 3d sub-shell to achieve a half-filled 3d⁵ configuration. Each of the five 3d orbitals holds exactly one electron with parallel spins (Hund's rule maximized). The exchange energy gained by this arrangement—calculated as K × n(n−1)/2 where K is the exchange integral and n is the number of same-spin electrons—exceeds the energy cost of moving an electron from 4s to 3d. The result is a lower overall energy and therefore greater stability.

Copper: The d¹⁰ Exception

Expected (aufbau): [Ar] 3d⁹ 4s². Actual: [Ar] 3d¹⁰ 4s¹. Copper similarly promotes one 4s electron to complete the 3d sub-shell. A full d¹⁰ configuration achieves maximum exchange energy and also benefits from perfectly symmetrical electron density, which reduces inter-electron repulsion. The completely filled 3d¹⁰ sub-shell is exceptionally stable; this is why Cu⁺ ([Ar] 3d¹⁰) is a stable ion, though Cu²⁺ ([Ar] 3d⁹) is even more common in aqueous chemistry due to high hydration enthalpy.

Configurations of Ions

When transition metals form ions, the ns electrons are lost first (before (n−1)d electrons), even though the ns orbital was filled first. This is because in positive ions the 3d energy level drops below 4s, making 4s the higher-energy orbital. For example: Fe ([Ar] 3d⁶ 4s²) → Fe²⁺ ([Ar] 3d⁶) by loss of both 4s electrons; → Fe³⁺ ([Ar] 3d⁵) by further loss of one 3d electron. Fe³⁺ has a half-filled 3d⁵ configuration, explaining why it is particularly stable and commonly encountered.

The Key Equation

Config=[noble gas]  (n−1)d x ns y,x∈{1–10},  y∈{1,2}\text{Config} = [\text{noble gas}]\;(n-1)d^{\,x}\,ns^{\,y}, \quad x \in \{1\text{–}10\},\; y \in \{1,2\}
  • n — Principal quantum number (dimensionless): Identifies the period (outermost shell); for Period 4 transition metals n = 4.
  • (n-1)d^{x} — d sub-shell electrons (dimensionless): Electrons in the d sub-shell of the penultimate shell being progressively filled across the period; x ranges from 1 to 10.
  • ns^{y} — s sub-shell electrons (dimensionless): Electrons in the outermost s orbital; y = 2 for most elements, y = 1 for Cr and Cu due to half-filled/filled d stability.
  • [\text{noble gas}] — Noble gas core (dimensionless): Shorthand for the complete electron configuration of the preceding noble gas, representing the inner-shell electrons not involved in chemistry.

Worked Example

Problem. Write the full electronic configuration of manganese (Mn, Z = 25) and its Mn²⁺ ion. Identify how many unpaired electrons each species possesses.

Mn:[Ar]  3d5 4s2  (5 unpaired);Mn2+:[Ar]  3d5  (5 unpaired)\text{Mn}: [\text{Ar}]\;3d^5\,4s^2 \;(5\text{ unpaired}); \quad \text{Mn}^{2+}: [\text{Ar}]\;3d^5 \;(5\text{ unpaired})

Answer. Mn: [Ar] 3d⁵ 4s² with 5 unpaired electrons. Mn²⁺: [Ar] 3d⁵ with 5 unpaired electrons.

Figure
Diagram
d-Block Electronic Configurations: 4th Period Transition MetalsElement3d orbital occupancy (5 orbitals)4sConfig.Sc↑↑↓[Ar] 3d¹4s²Ti↑↑↑↓[Ar] 3d²4s²V↑↑↑↑↓[Ar] 3d³4s²Cr ★↑↑↑↑↑↑[Ar] 3d⁵4s¹Mn↑↑↑↑↑↑↓[Ar] 3d⁵4s²Fe↑↓↑↑↑↑↑↓[Ar] 3d⁶4s²Co↑↓↑↓↑↑↑↑↓[Ar] 3d⁷4s²Ni↑↓↑↓↑↓↑↑↑↓[Ar] 3d⁸4s²Cu ★↑↓↑↓↑↓↑↓↑↓↑[Ar] 3d¹⁰4s¹3d orbitals →Exception (Cr, Cu)Normal aufbau filling★ = promoted electron
Origins · 1 minNiels Bohr and how this was discovered
NB
Niels Bohr
1885–1962 · Danish

Bohr developed the quantum model of atomic structure (1913) that introduced discrete electron shells and quantized energy levels, providing the conceptual foundation on which modern orbital theory and electronic configuration rules are built. His correspondence principle and later work with Heisenberg helped transform these ideas into quantum mechanics. During World War II, Bohr escaped Nazi-occupied Denmark by boat to Sweden, then flew to Britain in a modified de Havilland Mosquito bomber—oxygen-starved for part of the flight because the helmet did not fit his large head—before ultimately joining the Manhattan Project under the alias 'Nicholas Baker'.

  • Variable Oxidation States of Transition Metals — The availability of both ns and (n−1)d electrons for removal directly causes the variable oxidation states characteristic of transition metals—a consequence of their electronic configurations.
  • Paramagnetism and Unpaired Electrons — The number of unpaired d electrons, determined from the electronic configuration using Hund's rule, directly determines the magnetic properties of transition metal ions and complexes.
  • Quantum Numbers and Atomic Orbitals — Electronic configurations are built using principal (n), angular momentum (l), magnetic (mₗ), and spin (mₛ) quantum numbers; understanding these is prerequisite to writing correct d-block configurations.
  • Complex Ions and Ligand Field Theory — The splitting of d-orbitals by ligands in complex ions, and the resulting colour and magnetic properties, depends critically on the number of d electrons established by the electronic configuration of the central metal ion.
  • Hund's Rule, Aufbau Principle and Pauli Exclusion — These three rules govern the order and manner in which orbitals are filled and are essential tools for correctly writing electronic configurations of d-block elements, including the exceptions Cr and Cu.