Electronic Configuration of Atoms

What is Electronic Configuration?

The electronic configuration of an atom is the distribution of its electrons among the available shells, subshells and orbitals. Electronic configurations are written in a standard notation in which each occupied subshell is written in the form nl^x, where n is the principal quantum number, l the subshell symbol (s, p, d, f) and ^x the number of electrons in that subshell.

• Example: the electronic configuration of sodium is 1s²2s²2p⁶3s¹.
• Valence shell (outermost shell) is the shell with principal quantum number n.
• Penultimate shell is the shell with principal quantum number (n - 1).
• Anti-penultimate shell is the shell with principal quantum number (n - 2).

Example of Electronic Configuration

Ways to express electronic configuration

• Orbital notation (nl^x) - compact symbolic notation using subshell labels and superscripts to show electron counts. Example: Li (Z = 3) → 1s² 2s¹.
• Orbital diagram method - shows individual orbitals and electron spins (often with arrows). Example: Li (Z = 3):

• Condensed (noble-gas) form - uses the noble gas core to shorten the configuration. The noble gas in brackets represents the completed inner shells followed by the remaining outer subshells. Examples and further diagrams:

Rules used to build electronic configurations

• Aufbau principle: Electrons occupy orbitals of lowest energy first.
• Pauli exclusion principle: No two electrons in an atom can have the same set of four quantum numbers; thus an orbital holds a maximum of two electrons with opposite spins.
• Hund's rule: For degenerate orbitals (orbitals of the same energy), electrons occupy them singly with parallel spins as far as possible before pairing begins.
• n + l rule (Madelung rule): Orbitals are filled in the order of increasing (n + l) value; if two orbitals have the same (n + l), the one with lower n is filled first. Common filling order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s ...

Electronic configuration of ions

To write the electronic configuration of an ion, first write the configuration of the neutral atom and then add electrons for anions (negative charge) or remove electrons for cations (positive charge). Electrons are added or removed from the outermost shell (highest principal quantum number) first.

Example: Al (neutral): [Ne] 3s² 3p¹.

For chlorine: Cl : [Ne] 3s² 3p⁵.

For the chloride ion: Cl^- : [Ne] 3s² 3p⁶.

Note for transition elements: when cations form, electrons are removed first from the shell with the highest principal quantum number (the nth shell). For example, for the 3d series electrons are removed from 4s before 3d.

Exceptional configurations: Chromium and Copper

Some elements show departures from the simple Aufbau filling order because a half-filled or fully-filled d subshell gives extra stability. Important examples:

• Chromium (Z = 24) - expected: [Ar] 4s² 3d⁴, observed: [Ar] 4s¹ 3d⁵.
• Copper (Z = 29) - expected: [Ar] 4s² 3d⁹, observed: [Ar] 4s¹ 3d¹⁰.

Why these exceptions occur

Symmetrical electronic configuration

Half-filled and completely filled subshells (for example d⁵, d¹⁰, f⁷, f¹⁴) have greater symmetry and are relatively more stable. This extra stability can make it favourable to move an electron from the s subshell into the d subshell to achieve a half-filled or fully-filled d configuration.

Exchange energy

Electrons in degenerate orbitals with parallel spins can exchange positions. Each exchange lowers the energy; this lowering is the exchange energy. Configurations with more possible exchanges (parallel spins) have larger exchange stabilization. The extra stability from exchange energy contributes to the preference for half-filled or fully-filled subshells.

The enhanced stability of half-filled and fully-filled subshells arises from a combination of:

• relatively small shielding of the added electron,
• reduced Coulombic repulsion in a symmetric arrangement, and
• increased exchange energy due to parallel spins.

Magnetic properties and magnetic moment

The magnetic behaviour of an atom or ion depends on the number of unpaired electrons it contains.

• Diamagnetic species have no unpaired electrons (all electrons paired). They are weakly repelled by an external magnetic field. In this case the magnetic moment m = 0.
• Paramagnetic species have one or more unpaired electrons and are attracted (weakly) by a magnetic field.

The spin-only magnetic moment (in Bohr magnetons, BM) for a species with n unpaired electrons is given by:

That is, μ = √(n(n + 2)) BM, where n is the number of unpaired electrons.

Ques. Calculate the magnetic moment of these species

(i) Cr 

Solution: 

No. of unpaired electrons in chromium (observed configuration [Ar] 4s¹ 3d⁵) = 6.

μ = √[n(n + 2)] BM

μ = √[6(6 + 2)] BM

μ = √[6 × 8] BM

μ = √48 BM

μ ≈ 6.93 BM.

Note: Species with unpaired electrons absorb visible wavelengths corresponding to electronic transitions and therefore frequently show colours. Paired-electron (diamagnetic) species are generally colourless in the same way when transitions in the visible region are absent.