Electron Structure and Periodic Properties

Understanding electron structure begins with light. The electromagnetic spectrum spans from low-energy radio waves to high-energy gamma rays. The energy of a photon is E = hν, where h is Planck’s constant (6.626 × 10^-34 J·s) and ν is frequency. Higher frequency means higher energy.

The Bohr model explained the hydrogen emission spectrum by proposing that electrons occupy specific energy levels (orbits). Electrons can jump between levels by absorbing or emitting photons of precise energy: ΔE = E_final − E_initial. This model correctly predicted hydrogen’s spectral lines but failed for multi-electron atoms.

Modern quantum mechanics replaced Bohr’s circular orbits with orbitals — probability regions where electrons are most likely found. The wave-particle duality of electrons (demonstrated by diffraction experiments) means electrons behave as both particles and waves, which is why their positions are described probabilistically.

Each electron in an atom is described by four quantum numbers:

• n (principal) — energy level: 1, 2, 3, ... Higher n means higher energy and larger orbital.
• l (angular momentum) — sublevel shape: 0 to (n−1). Values 0, 1, 2, 3 correspond to s, p, d, f.
• m_l (magnetic) — orbital orientation: −l to +l. For l=1 (p), m_l = −1, 0, +1 (three p orbitals).
• m_s (spin) — electron spin: +½ or −½.

The Pauli exclusion principle states that no two electrons in the same atom can have the same set of all four quantum numbers. This means each orbital holds at most 2 electrons (with opposite spins).

An electron configuration lists the sublevels occupied by an atom’s electrons in order of energy. Three rules govern the filling order:

• Aufbau principle — fill lowest-energy orbitals first: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, ...
• Pauli exclusion principle — maximum 2 electrons per orbital (opposite spins).
• Hund’s rule — within a sublevel, place one electron in each orbital before pairing any.

Example: Nitrogen (Z=7): 1s² 2s² 2p³. The three 2p electrons occupy three separate orbitals (one each), all with parallel spins.

An orbital diagram uses boxes (or lines) for orbitals and arrows (↑↓) for electrons, visually showing Hund’s rule. A noble gas abbreviation replaces the inner-shell configuration with the preceding noble gas symbol in brackets: Na = [Ne] 3s¹.

Valence electrons are the electrons in the outermost energy level (highest n value). They determine an element’s chemical behavior and bonding.

• For main-group elements, the number of valence electrons equals the group number (using the 1–8 numbering): Group 1 has 1, Group 2 has 2, ..., Group 17 has 7, Group 18 has 8 (except He, which has 2).
• For transition metals, both the ns and (n−1)d electrons participate in chemistry.

The periodic table is organized by electron configuration: s-block (Groups 1–2), p-block (Groups 13–18), d-block (transition metals), and f-block (lanthanides/actinides). The period number equals the highest principal quantum number of the valence electrons. This direct connection between position and configuration makes the periodic table a powerful predictive tool.

A few elements have electron configurations that deviate from the standard filling order because a half-filled or fully filled d sublevel provides extra stability:

• Chromium (Z=24): Expected [Ar] 4s² 3d⁴, actual [Ar] 4s¹ 3d⁵ (half-filled d).
• Copper (Z=29): Expected [Ar] 4s² 3d⁹, actual [Ar] 4s¹ 3d¹⁰ (fully filled d).
• Similar exceptions occur with Mo, Ag, Au, and other transition metals.

When transition metals form cations, electrons are removed from the ns orbital before the (n−1)d orbital (even though ns filled first). For example, Fe²⁺ = [Ar] 3d⁶ (not [Ar] 4s² 3d⁴, which is the neutral atom minus two 4s electrons).

Atomic and ionic radii follow predictable patterns driven by nuclear charge and electron shielding:

Atomic radius:

• Across a period (left to right): radius decreases. Increasing nuclear charge (more protons) pulls electrons closer, but shielding stays roughly the same (same shell).
• Down a group (top to bottom): radius increases. Each new period adds a shell, increasing the distance of the outermost electrons from the nucleus.

Ionic radius:

• Cations are smaller than their parent atoms (electrons removed, nuclear charge now exceeds electron count).
• Anions are larger than their parent atoms (electrons added, increased electron-electron repulsion expands the cloud).

Isoelectronic species (same electron count) decrease in size as nuclear charge increases: O^2- > F^- > Na⁺ > Mg²⁺ > Al³⁺ (all have 10 electrons, but Al³⁺ has 13 protons pulling them in).

Three energy-related properties also follow periodic patterns:

Ionization energy (IE) — the energy required to remove the highest-energy electron from a gaseous atom:

• Increases across a period (harder to remove electrons as nuclear charge grows).
• Decreases down a group (valence electrons are farther from the nucleus and better shielded).

Electronegativity (EN) — the tendency of an atom in a bond to attract shared electrons toward itself:

• Increases across a period and decreases down a group (same reasoning as IE).
• Fluorine has the highest electronegativity; francium the lowest.

Electron affinity (EA) — the energy change when a gaseous atom gains an electron:

• Generally becomes more negative (more exothermic) across a period, and less negative down a group.
• Halogens have the most negative EA values (they strongly attract an extra electron to complete their octet).

Use this sequence when students get stuck:

1. Locate the element (period/group/block) first; this anchors expected valence behavior.
2. Write configuration systematically (Aufbau order), then verify Pauli and Hund.
3. For ions, remove electrons from highest principal quantum number first (for transition metals, remove 4s before 3d).
4. Apply trend logic as effective nuclear charge vs. shielding, not memorized arrows alone.

High-frequency errors: treating Cr/Cu exceptions as random, removing d electrons before 4s in cations, and overgeneralizing periodic trends without noting known exceptions. A reliable final check is to compare your conclusion with neighboring elements in the same period and group for consistency.