Classification of Elements and Periodicity in Properties

1. From Dobereiner to the Modern Periodic Law

• Dobereiner's triads (1817): in a triad, the middle element's atomic mass ≈ mean of the outer two (Li, Na, K: (7+39)/2 = 23). Worked only for a few sets and failed for F, Cl, Br.
• Newlands' law of octaves (1865): arranged by increasing atomic mass, every 8th element repeated properties. Worked only up to Ca (Z = 20); broke down once transition metals appeared.
• Lothar Meyer's atomic volume curve (1869): atomic volume (mass/density) plotted against atomic mass is periodic. Alkali metals sit at the crests (largest volume); transition metals sit in the troughs (most compact, densest).
• Mendeleev's periodic law (1869): properties are a periodic function of atomic mass. Merits: left gaps that correctly predicted eka-aluminium (Ga) and eka-silicon (Ge); corrected Be's valency from 3 to 2. Demerits: anomalous pairs where a heavier element was placed before a lighter one purely to keep similar properties together (Ar before K, Te before I, Co before Ni), no separate position for isotopes, and no single consistent slot for hydrogen.
• Moseley's experiment (1913): √ν = a(Z−b) for characteristic X-ray frequency ν, proving atomic number (not mass) is the fundamental property. This gives the Modern Periodic Law: properties are a periodic function of atomic number (Z), and periodicity itself arises because valence-shell configurations repeat at regular intervals (e.g. every alkali metal is ns¹).

2. Periods, Blocks and Group-Number Rules

• Period number = highest principal quantum number (n) in the valence shell. Period 3 has only 8 elements (not 18) because 4s fills before 3d (Aufbau), so the period ends after 3s and 3p are full.
• Block = the subshell receiving the last (differentiating) electron. Group number: s-block = number of valence s-electrons; p-block = 10 + (valence s + p electrons); d-block = (n−1)d electrons + valence ns electrons; f-block is always Group 3 (IIIB).
• Worked pattern 1 (Copernicium, Z = 112): configuration [Rn] 5f¹⁴ 6d¹⁰ 7s². Highest n = 7 ⇒ Period 7. Last electron enters 6d ⇒ d-block. Group = 10 (d) + 2 (s) = Group 12.
• Exceptions in configuration: Cr (Z=24) and Cu (Z=29) are 3d⁵4s¹ and 3d¹⁰4s¹ (extra stability of half-filled/fully-filled d); Pd (Z=46) is 4d¹⁰5s⁰ (empty 5s); He is 1s² (s-block by configuration) but placed in Group 18 for its noble-gas chemistry.

3. Diagonal Relationship and Special Categories

• Representative (normal) elements: all s- and p-block elements (Groups 1, 2, 13–17), excluding noble gases. Typical elements: the Period 3 set Na–Cl, whose behaviour best represents their group's general chemistry (better than the Period 2 member). Metalloids: B, Si, Ge, As, Sb, Te — border metals and non-metals, with amphoteric oxides.
• Diagonal relationship: Li–Mg, Be–Al and B–Si (2nd period element with the 3rd period element one group to its right) show close chemical similarity, because moving right (size falls) and moving down (size rises) roughly cancel diagonally, keeping ionic radius, electronegativity and ionic potential (φ = charge/radius²) nearly equal (Li⁺ = 0.76 Å, Mg²⁺ = 0.72 Å).
• Li & Mg: both form nitrides directly (Li₃N, Mg₃N₂), insoluble fluorides/carbonates/phosphates, and their carbonates decompose on heating. Be & Al: both give amphoteric oxides/hydroxides, go passive in conc. HNO₃, form covalent electron-deficient polymeric chlorides (BeCl₂, AlCl₃), and neither colours a Bunsen flame.

4. Atomic Radius, Ionic Radius and Isoelectronic Series

• Three radius definitions: covalent radius (half the internuclear distance in a homonuclear covalent bond) < metallic/crystal radius < van der Waals radius (half the distance between non-bonded neighbouring atoms, always 40–80% bigger than covalent radius).
• Stevenson–Schomaker (heteronuclear bond length): d_A–B = r_A + r_B − 0.09Δχ (Å), or −9.0Δχ in pm, where Δχ = |χ_A−χ_B|. Porterfield's version uses −7.0(Δχ)² (pm).
• Worked pattern 2: C–C = 1.54 Å, X–X = 1.00 Å, χ_C = 2.0, χ_X = 3.0. r_C = 0.77, r_X = 0.50, Δχ = 1.0. d_C–X = 0.77 + 0.50 − 0.09(1.0) = 1.18 Å.
• Why noble gases look "largest" in their period: their tabulated radius is a van der Waals radius (no covalent bond to measure), while every other element in that period is measured as a covalent radius — not a genuine anomaly in metallic/covalent size.
• 3d series radius dip-then-flat-then-rise: falls Sc→Cr, stays nearly flat Cr→Cu (d-electron shielding balances rising Z), rises slightly at Zn (inter-electronic repulsion in the filled 3d¹⁰).
• Lanthanide contraction: poor shielding by the 14 inner 4f electrons steadily shrinks the lanthanides from Ce to Lu, making the 2nd and 3rd transition series (4d vs 5d) almost the same size (Zr ≈ Hf = 1.60 Å, Nb ≈ Ta = 1.46 Å) despite the extra shell.
• Ions: cation always smaller than its parent atom (higher Z_eff per electron, often a whole shell removed: Na 1.86 Å → Na⁺ 1.02 Å); anion always larger (added inter-electronic repulsion: Cl 0.99 Å → Cl⁻ 1.84 Å).
• Isoelectronic series: same electron count, radius falls as Z rises: N³⁻(1.71) > O²⁻(1.40) > F⁻(1.36) > Na⁺(1.02) > Mg²⁺(0.72) > Al³⁺(0.53 Å).

5. Ionization Energy

• Definition: M(g) + IE₁ → M⁺(g) + e⁻; successive IEs always increase, IE₁ < IE₂ < IE₃, since each further electron is removed from an increasingly positive ion.
• Governing factors: IE ∝ 1/(atomic size); IE ∝ Z_eff; penetration power order s > p > d > f (so a full ns² or half-filled np³ boosts IE beyond the smooth trend).
• Period 2 anomaly: expected Li < Be < B < C < N < O < F < Ne becomes Li < B < Be < C < O < N < F < Ne. Be > B because Be's filled 2s² resists ionization more than B's lone 2p¹. N > O because N's half-filled 2p³ is extra stable, while O's 2p⁴ already has one paired (repelled) electron that ionizes more easily.
• Period 3 anomaly: Na < Al < Mg < Si < S < P < Cl < Ar, by the same two rules (Mg > Al from filled 3s²; P > S from half-filled 3p³).
• Group 13 irregularity: B > Tl > Ga > Al > In. Ga sits above Al because of poor d-orbital shielding (scandide-like contraction after the 3d row); Tl sits above Ga because of poor f-orbital shielding (lanthanide contraction after the 4f row).
• Second ionization energy pattern: IE₂ reflects the stability of M⁺'s configuration. Na's IE₂ is enormous (breaks into the stable, filled 2p⁶ core of Na⁺) — far larger than Mg's IE₂ (removes a normal 3s electron from an already-stable Mg⁺).

6. Electron Gain Enthalpy and Electronegativity

• Definition: X(g) + e⁻ → X⁻(g), Δ_egH ≈ −E_a (electron affinity). First EGA is usually negative (exothermic); second EGA is ALWAYS positive (O⁻ + e⁻ → O²⁻, Δ_egH₂ = +744 kJ/mol) because the incoming electron is repelled by the existing negative charge.
• Cl > F, S > O anomaly: the compact n = 2 shell in F and O suffers severe inter-electronic repulsion when accepting one more electron, so the magnitude of Δ_egH is actually SMALLER (less negative) for F and O than for the larger n = 3 elements below them: Cl > F > Br > I, and S > Se > Te > Po > O. Oxygen has the least negative EGA in Group 16.
• Noble gases and Group 2: near-zero or positive Δ_egH (stable filled configuration, no room to accommodate an extra electron favourably).
• Electronegativity (χ): tendency to attract shared bonding electrons. Pauling's scale uses bond-energy differences; Mulliken's scale χ_M = ½(IE + EA) in eV, converted to Pauling by χ_P = χ_M/2.8.
• % ionic character (Hannay–Smith): 16Δχ + 3.5(Δχ)², where Δχ = χ_A − χ_B.
• Electronegativity rises with: % s-character in hybridization (sp > sp² > sp³) and with higher oxidation state (Fe³⁺ > Fe²⁺).

7. Oxides, Inert Pair Effect and Chemical Periodicity

• Oxide classes: basic (electropositive metal oxides, form hydroxides; basic character rises down a group: Na₂O, K₂O, CaO), acidic (non-metal oxides, form oxyacids; acidity rises across a period: CO₂, SO₃, Cl₂O₇), amphoteric (metalloids/select metals: BeO, Al₂O₃, ZnO, SnO, PbO), neutral (CO, NO, N₂O, H₂O).
• Period 3 oxide strip: Na₂O (strongly basic) > MgO (basic) > Al₂O₃ (amphoteric) > SiO₂ (weakly acidic) > P₄O₁₀ (acidic) > SO₃ (acidic) > Cl₂O₇ (strongly acidic).

• Inert pair effect: the ns² pair in heavier p-block elements (n ≥ 4, Groups 13–15) resists bonding due to poor shielding by intervening d/f electrons, so the LOWER oxidation state becomes progressively more stable going down the group: Group 13, Tl⁺ most stable; Group 14, Pb²⁺ most stable; Group 15, Bi³⁺ most stable.
• Consequences: Pb⁴⁺ and Bi⁵⁺ are strong oxidizers (readily fall back to the stable lower state); PbI₄ and BiI₅ don't exist (I⁻'s reducing power destroys the higher oxidation state) — though TlI₃ exists, unusually, as Tl⁺(I₃)⁻ rather than as Tl³⁺(I⁻)₃.

8. How JEE Frames Questions

• Assertion-reason / two-statement MCQs: the dominant format. One statement states a plain trend, the other states an exception (Be > B, N > O, Cl > F, Ga vs Al, etc.) — both need to be checked independently before combining.
• Ranking questions: 3–5 elements ranked by radius, IE, EGA or metallic character — always re-derive using the group/period position and the exception rules, never guess from memory of a similar-looking list.
• Statement-matching (List I / List II): matches a property (highest EN, largest size, metalloid behaviour, most negative EGA) to element pairs; work each property from first principles.
• Formula numericals: bond length (Stevenson–Schomaker/Porterfield), % ionic character, group-number-from-configuration, or an energy calculation combining IE₁ and IE₂.

9. Quick Sheet and Checklist

Before the exam, check you can:

• Assign period, block and group number from an electron configuration, including the +10 p-block offset.
• Reproduce both Period 2 and Period 3 IE anomalies and explain WHY (filled s² / half-filled p³) rather than just memorising the order.
• Rank an isoelectronic series by radius and identify a diagonal-relationship pair correctly.
• State the Cl>F / S>O electron-gain-enthalpy anomaly and why the second EGA is always positive.
• Use the inert-pair effect to predict which oxidation state is more stable/more oxidizing for Tl, Pb, Bi and their lighter group-mates.
• Classify a Period 3 oxide as basic, amphoteric or acidic and rank the whole row.