Atomic Structure and Periodic Table

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your ECAT exam.

The atom consists of a dense nucleus (protons + neutrons) surrounded by electrons in defined energy levels. Understanding atomic structure is essential because it explains chemical behaviour, periodic trends, and the basis of bonding.

Key Definitions:

• Atomic number (Z) = number of protons = identity of the element
• Mass number (A) = protons + neutrons
• Isotopes = atoms of the same element (same Z) with different A (different neutrons), e.g., ¹²C and ¹³C
• Moles and molar mass: 1 mole = 6.022 × 10²³ particles; molar mass of carbon-12 = 12 g/mol

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

• n (principal): 1, 2, 3… — shell, determines energy and average distance from nucleus
• l (azimuthal): 0 to (n−1) — subshell: s (0), p (1), d (2), f (3)
• m_l (magnetic): −l to +l — orbital orientation
• m_s (spin): +½ or −½ — electron spin

Aufbau Principle: Electrons fill orbitals in order of increasing n + l value (Boron rule). When n + l is equal, the orbital with lower n fills first. The order: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p.

⚡ ECAT exam tips:

• Hund’s rule of maximum multiplicity: electrons fill degenerate orbitals singly first, with parallel spins — this maximises total spin and minimises electron repulsion
• The Madelung rule (n + l rule) predicts the filling order accurately
• Shielding constant (Z_eff = Z − σ): valence electrons in same group experience decreasing Z_eff down the group, making outer electrons easier to remove (ionisation energy decreases)
• de Broglie wavelength: λ = h/(mv); only significant for very small masses

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🟡 Standard — Regular Study (2d–2mo)

For ECAT students who want genuine understanding of atomic structure.

Bohr’s Model and Its Limitations

Bohr proposed that electrons orbit the nucleus in discrete energy levels with quantised angular momentum: mvr = nh/(2π). This successfully explained the hydrogen spectrum:

$$E_n = -\frac{13.6 \text{ eV}}{n^2}$$

The Rydberg formula for hydrogen spectral lines:

$$\frac{1}{\lambda} = R_H \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$$

where R_H = 1.097 × 10⁷ m⁻¹. For the Balmer series (visible spectrum), n₁ = 2. Transitions to n₁ = 1 (Lyman series) are in the UV; to n₁ = 3 (Paschen) are in the infrared.

However, Bohr’s model failed for multi-electron atoms and could not explain fine structure. It was superseded by the wave-mechanical (quantum) model.

Wave-Particle Duality and the Heisenberg Uncertainty Principle

Electrons exhibit both particle and wave properties. The Heisenberg Uncertainty Principle states:

$$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$$

This means we cannot simultaneously know the exact position and momentum of an electron. The orbital concept replaces the Bohr orbit — an orbital is a probability distribution (ψ²) describing where an electron is likely to be found, not a fixed path.

Electron Configurations and the Periodic Table

The periodic table is arranged by increasing atomic number, reflecting electron configuration. The s-block (Groups 1–2, plus He) fills ns¹⁻². The p-block (Groups 13–18) fills np¹⁻⁶. The d-block (transition metals, Groups 3–12) fills (n−1)d¹⁻¹⁰ns⁰⁻². The f-block (lanthanides and actinides) fills (n−2)f¹⁻¹⁴ns².

Important periodic trends for ECAT:

Property	Trend across period (left to right)	Trend down group
Atomic radius	Decreases (Z_eff increases)	Increases (n increases)
Ionisation energy	Generally increases	Decreases (Z_eff decreases)
Electron affinity	Generally increases	Decreases
Electronegativity	Increases	Decreases
Metallic character	Decreases	Increases

⚡ Common student mistakes:

1. Confusing shells and subshells — n=2 has subshells 2s and 2p (three orbitals each)
2. Forgetting that 4s fills before 3d because of the Madelung rule, but 3d is lower in energy once filled
3. Mixing up electron affinity (energy released when adding an electron) with ionisation energy
4. Not knowing that ionisation energy drops from N to O in period 2 (due to electron–electron repulsion in the 2p⁴ configuration of oxygen)

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for ECAT mastery with historical and conceptual depth.

Pauli Exclusion Principle and Electronic Structure

No two electrons in an atom can have all four quantum numbers identical. This means each orbital (defined by n, l, m_l) can hold at most two electrons, with opposite spins (m_s = +½ and m_s = −½). This single principle explains why electron shells fill as they do and why atoms have discrete spectral lines.

Quantum Mechanical Derivation of the Hydrogen Atom

Solving the Schrödinger equation for hydrogen gives exact energy levels identical to Bohr’s formula. The wavefunctions (orbitals) for hydrogen are products of radial and angular functions. For the 1s orbital:

$$\psi_{1s} = \frac{1}{\sqrt{\pi a_0^3}} e^{-r/a_0}$$

where a₀ = 0.529 Å (Bohr radius). The radial probability distribution for 1s peaks at r = a₀, confirming the Bohr radius as the most probable distance.

Shielding and Effective Nuclear Charge (Z_eff)

Electrons in inner shells shield outer electrons from the full nuclear charge. Slater’s rules give approximate Z_eff values. For a 2p electron in nitrogen (Z=7): Slater gives Z_eff ≈ 7 − 2.45 = 4.55. This explains why atomic radius decreases across a period — each added proton increases Z more than shielding increases.

Atomic Radii Across the Periodic Table

Covalent atomic radii (measured as half the bond distance in homonuclear diatomic molecules) show clear trends. Atomic radius of Na ≈ 186 pm, Mg ≈ 160 pm, Al ≈ 143 pm, Si ≈ 117 pm, P ≈ 110 pm, S ≈ 104 pm, Cl ≈ 99 pm, Ar ≈ 71 pm (estimated). Van der Waals radii are larger than covalent radii — noble gases don’t form covalent bonds as a rule.

Ionisation Energy — Detailed Trends

First ionisation energy (I₁) in kJ/mol for period 2 elements: Li 520, Be 900, B 801, C 1086, N 1402, O 1314, F 1681, Ne 2081. Notable drops at Be→B (p-electron easier to remove than s²), N→O (pair repulsion in 2p⁴), and Ne (noble gas, full shell). Second ionisation energies (I₂) show a dramatic jump when removing an electron from a stable noble gas configuration.

Electron Affinity and Electronegativity

Electron affinity (EA) is the energy released when a neutral atom gains an electron. Chlorine has the highest EA among common elements (−349 kJ/mol), not fluorine (−328 kJ/mol), because fluorine’s small size causes strong electron–electron repulsion in the 2p subshell. Electronegativity (Pauling scale) measures an atom’s ability to attract bonding electrons and increases across a period and decreases down a group. Fluorine (EN = 3.98) is the most electronegative element; caesium (EN = 0.79) is the least among metals.

The s-Block and p-Block Elements — Key Characteristics

Alkali metals (Group 1, ns¹): low I₁, low EN, large atomic radius, form +1 ions, highly reactive (especially with water: 2Na + 2H₂O → 2NaOH + H₂↑). Alkaline earth metals (Group 2, ns²): I₂ is much higher than I₁, form +2 ions, react with acids but not water (except Mg with steam).

Group 13 (ns²np¹): B is a metalloid; Al is a metal with amphoteric oxide; Ga, In, Tl are metals. They show the +3 oxidation state (ns²np¹ → loses all three outer electrons) but also +1 (especially for heavier elements due to the inert pair effect).

Group 14 (ns²np²): C forms covalent compounds, Si and Ge are metalloids, Sn and Pb are metals. The stability of +2 oxidation state increases down the group (Pb²⁺ > Pb⁴⁺), while for C and Si, +4 is dominant.

Group 17 (ns²np⁵): highly reactive non-metals, form −1 ions with s-block metals, have very high EN and electron affinity. HF is a weak acid; HCl, HBr, HI are strong acids (acid strength increases down the group: HF << HCl < HBr < HI due to decreasing H–X bond strength).

Group 18 (ns²np⁶): noble gases — full valence shells, extremely high I₁, no tendency to gain electrons, historically considered inert until Xe compounds (XeF₂, XeF₄, XeF₆) were discovered in 1962.

ECAT Previous Year Patterns:

• Electronic configurations and quantum numbers: frequently tested
• Periodic trends (atomic radius, IE, EA, EN): every year in some form
• Bohr model and spectral lines: calculation-based questions
• Aufbau principle, Hund’s rule, Pauli: conceptual questions

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