Atomic Structure and Periodicity: What BCS Candidates Must Master
Core concepts
Begin with the quantum-mechanical picture: principal, azimuthal, magnetic and spin quantum numbers, the rules governing them (n ≥ 1, l = 0 to n−1, m = −l to +l, m_s = ±½), and the building-up sequence that produces electron configurations. Know the Aufbau principle, Hund's rule and the Pauli exclusion principle as separate statements, because questions often test which rule a given configuration violates. Be fluent in writing configurations for cations (remove electrons from the highest-n shell first, e.g. Fe → Fe²⁺ loses 4s before 3d) and in recognising anomalous cases such as Cr ([Ar]3d⁵4s¹) and Cu ([Ar]3d¹⁰4s¹). Periodicity follows from these configurations: atomic radius falls across a period and rises down a group; ionisation energy generally rises across a period but dips at group 13→14 and group 15→16 because of subshell and pairing effects; electron affinity and electronegativity trends follow similar logic.
Traps to watch
- Confusing first and second ionisation energies; the second IE of an alkali metal is enormous.
- Forgetting that noble gases have no electronegativity scale value in the Pauling system.
- Mixing up isoelectronic series: among N³⁻, O²⁻, F⁻, Na⁺, Mg²⁺, the smallest radius belongs to Mg²⁺ (highest nuclear charge per electron).
- Assuming radius always decreases across a period without noting that transition-metal radii plateau.
Worked example
Rank Mg²⁺, F⁻, O²⁻ and Na⁺ in order of increasing ionic radius. All are isoelectronic with 10 electrons. The larger the nuclear charge, the stronger the pull, so radius decreases as Z rises: Mg²⁺ (Z = 12) < Na⁺ (11) < F⁻ (9) < O²⁻ (8). Rule of thumb: for isoelectronic species, more protons means a smaller ion.