Chemistry: Atomic Structure and Bonding

Chemistry: Atomic Structure and Bonding

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Atomic Structure and Bonding unifies two halves of chemistry: the atom itself (a nucleus of protons and neutrons surrounded by electrons in quantised orbitals) and the forces that hold atoms together (ionic, covalent, metallic). The atom is specified by atomic number Z (protons) and mass number A (protons + neutrons); atoms with the same Z but different A are isotopes.

Electrons fill orbitals in the order governed by the Aufbau principle, Pauli exclusion principle (max 2 electrons, opposite spins, per orbital), and Hund’s rule (degenerate orbitals singly occupied before pairing). Each orbital is described by four quantum numbers (n, ℓ, mℓ, ms).

Bond type is decided by electronegativity difference (ΔEN): < 0.4 nonpolar covalent, 0.4–1.7 polar covalent, > 1.7 ionic. Must-remember formula: E = hν, and the Rydberg relation 1/λ = R(1/n₁² − 1/n₂²) for hydrogen-line spectra.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Atomic Sub-structure

A neutral atom has Z protons in the nucleus, A − Z neutrons, and Z electrons in a cloud of orbitals. Protons carry +1, electrons −1, neutrons 0; the nucleus concentrates >99.9% of the atom’s mass in ~10⁻¹⁵ m, while the electron cloud extends to ~10⁻¹⁰ m. Atomic radius therefore refers to the orbital boundary, not a hard surface.

Quantum Description of Electrons

The Bohr model treated electrons as orbiting the nucleus in fixed, quantised levels (angular momentum mvr = nh/2π) and successfully explained hydrogen’s line spectrum via E = hν and photon emission when an electron drops from n₂ to n₁:

1/λ = R(1/n₁² − 1/n₂²), where R ≈ 1.097 × 10⁷ m⁻¹.

The modern quantum-mechanical model replaces orbits with orbitals — probability regions described by wavefunctions. The principal quantum number n (1, 2, 3, …) sets the shell and energy; ℓ (0 → n−1) sets subshell shape — s, p, d, f; mℓ (−ℓ … +ℓ) sets orbital orientation within a subshell; ms = ±½ sets spin. One orbital holds a maximum of two electrons of opposite spin (Pauli).

Electron Configuration Rules

• Aufbau: fill lowest-energy subshells first, following the (n+ℓ) rule — 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p …
• Pauli: at most 2 e⁻ per orbital, paired spins.
• Hund: within a subshell, place electrons singly in degenerate orbitals with parallel spins before pairing — minimises repulsion.

Bonding Models

Ionic bonds form when ΔEN > 1.7 — one atom transfers an electron to another, producing a cation + anion held electrostatically (e.g., Na → Na⁺ + e⁻; Cl + e⁻ → Cl⁻). Lattice energy scales as q₁q₂/r.

Covalent bonds share electron pairs. Equal sharing gives a nonpolar bond (H₂, Cl₂); unequal sharing gives a polar covalent bond with partial charges δ⁺ and δ⁻ (HCl, H₂O). A coordinate (dative) bond is a covalent bond in which one atom supplies both electrons (e.g., NH₃ → BCl₃).

Metallic bonding is a lattice of cations immersed in a delocalised “sea” of valence electrons, explaining conductivity, malleability, and lustre.

Lewis Structures, VSEPR, and Hybridization

Lewis structures place valence electrons as dots; most main-group atoms follow the octet rule (H seeks 2, Be and B often fall short, period-3+ atoms like S and P can expand the octet). VSEPR then predicts geometry from electron-pair repulsion — the table below summarises the common cases.

Steric #	Lone pairs	Geometry	Bond angle
2	0	Linear	180°
3	0	Trigonal planar	120°
4	0	Tetrahedral	109.5°
3	1	Trigonal pyramidal	~107°
2	2	Bent	~104.5°

Observed angles are explained by hybridization: mixing s and p (and sometimes d) orbitals gives sp (180°), sp² (120°), sp³ (109.5°), sp³d (90°/120°), and sp³d² (90°) sets.

Bond Properties

Bond energy is the energy to break one mole of a specific bond (kJ mol⁻¹); higher values mean stronger bonds. Bond length is the equilibrium internuclear distance, inversely related to bond order. For HAT-UG, memorise the order: single < double < triple, and C≡N > C=O > C–C in bond energy.

Intermolecular Forces

Covalent bonds hold atoms inside a molecule; intermolecular forces hold molecules to each other and dictate boiling point, solubility, and state.

• London dispersion — present in all molecules; grows with electron count and surface area.
• Dipole–dipole — between polar molecules.
• Hydrogen bonding — H bonded to F, O, or N interacting with a lone pair on F, O, or N of a neighbour (H₂O, HF, NH₃, DNA base pairs).

Exam-Specific Notes

HAT-UG weights Subject Knowledge at ~4% in the overall score, so one or two questions on atomic structure and bonding are likely. The typical format is a single-best MCQ mixing a definition (e.g., “Which quantum number defines orbital shape?”), a calculation (Rydberg wavelength, mole–mass conversion), or a VSEPR/geometry prediction. Common traps include confusing mass number with atomic number, applying the octet rule to BeCl₂ or BF₃ (exceptions), and misidentifying Hund’s rule as a statement about spin pairing.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge Cases and Quantisation

The Bohr model fails beyond hydrogen because it ignores electron–electron repulsion. The Heisenberg uncertainty principle (Δx·Δp ≥ h/4π) is the deeper reason for the orbital picture: an electron’s position and momentum cannot both be defined precisely, so we work with probability densities |ψ|² rather than orbits. In multi-electron atoms, shielding by inner electrons lowers the effective nuclear charge Z_eff, so orbital energies depend on both n and ℓ — which is why 4s fills before 3d.

Wave–Particle Duality and Photons

Light carries quantised energy E = hν and momentum p = h/λ. The de Broglie wavelength λ = h/mv assigns wave properties to matter. Photoelectron emission demonstrates that binding energy = hν − KE. The Rydberg formula links directly to Bohr’s quantisation: E_n = −13.6 eV / n², and the photon energy for a transition is ΔE = 13.6 eV (1/n₁² − 1/n₂²).

Advanced Bonding Considerations

Resonance delocalises electrons across several Lewis structures (e.g., ozone, benzene, carbonate); the real molecule is a weighted hybrid with bond lengths intermediate between single and double. Formal charge (FC = valence − lone-pair − ½ bonding) helps choose the best Lewis structure: lowest FC magnitudes and negative FC on the most electronegative atom. Expanded octets appear in period-3+ elements (PCl₅, SF₆) using empty d orbitals, though MO theory reframes this without invoking d-orbital participation.

For ionic compounds, lattice energy (Born–Landé) depends on ion charge and size; this explains why MgO (Mg²⁺, O²⁻) melts far higher than NaCl (Na⁺, Cl⁻). Covalent character creeps into ionic bonds via Fajans’ rules: small cation + large charge + polarising power distort the anion’s electron cloud.

Worked Example — Mole Calculation

Question: How many molecules are in 4.20 g of CO₂? M(CO₂) = 12.01 + 2(16.00) = 44.01 g mol⁻¹. n = m/M = 4.20 / 44.01 = 0.0954 mol. N = n · N_A = 0.0954 × 6.022 × 10²³ = 5.75 × 10²² molecules.

Common Mistakes

• Treating electronegativity as a measurable atomic property rather than a Pauling-derived scale.
• Confusing Hund’s rule (degenerate occupancy) with Pauli (paired spins in one orbital).
• Predicting geometry from the central atom’s bonds only and ignoring lone pairs (NH₃ is pyramidal, not trigonal planar).
• Forgetting that hydrogen bonding requires F, O, or N — not just any polar X–H bond.
• Equating molecular formula with empirical formula (H₂O₂ vs HO; C₆H₆ vs CH).

Connections to Adjacent Topics

Atomic structure underpins periodic trends (periodicity in radius, IE, EA, EN), spectroscopy (UV-vis, IR, NMR), and acid–base behaviour. Bonding concepts feed directly into reaction mechanisms (curly arrows track electron pairs), organic functional groups, and solid-state chemistry (giant covalent, ionic, metallic, molecular).

Practice Prompts

1. Predict the geometry, hybridisation, and polarity of SF₄.
2. An element has two isotopes of mass 69.0 u (60.1%) and 71.0 u (39.9%). Calculate its relative atomic mass and identify the element.

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