Q.Justify the given statement with suitable examples— "the Properties of the elements are a periodic function of their atomic numbers".

Concept: Periodic Law – when elements are arranged by increasing atomic number, their physical and chemical properties recur at regular intervals.

The modern periodic table organizes elements by atomic number $Z$ (number of protons), which determines electronic configuration. Elements in the same group share the same valence-shell structure, so their properties repeat periodically.

Examples demonstrating periodicity:

1. Valency: Group 1 elements (Li, Na, K; $Z = 3, 11, 19$) all have one valence electron ($ns^1$) and show valency 1. Group 17 elements (F, Cl, Br; $Z = 9, 17, 35$) have seven valence electrons ($ns^2 np^5$) and valency 1 (by gaining one electron).

2. Atomic radius: Decreases across a period (Li $>$ Be $>$ B $>$ C) due to increasing nuclear charge, then jumps at the next period (Na $>$ C), repeating the trend. …

The modern periodic law replaced Mendeleev's original formulation (based on atomic mass) because atomic number—the number of protons in the nucleus—is the fundamental identity of an element. As atomic number increases, electrons fill orbitals in a predictable sequence: $1s, 2s, 2p, 3s, 3p, 4s, 3d, \ldots$ This filling pattern creates families of elements with similar valence-shell configurations, and since chemical behavior is governed by valence electrons, properties repeat in cycles.

A periodic function is one that repeats its values at regular intervals. Mathematically, $f(x + T) = f(x)$ for some period $T$. In the periodic table, properties don't repeat with a single fixed period—the intervals are 2, 8, 8, 18, 18, 32—but the recurrence is systematic and tied to the completion of electron shells.

Evidence from Physical Properties

1. Atomic radius

Atomic size decreases across a period (left to right) as nuclear charge increases while electrons enter the same shell, pulling them closer. It increases down a group as new shells are added.

• Period 2: Li (152 pm) → Be (112 pm) → B (88 pm) → C (77 pm) → N (70 pm) → O (66 pm) → F (64 pm)
• Group 1: Li (152 pm) → Na (186 pm) → K (227 pm) → Rb (248 pm)

The pattern of decrease-then-jump repeats with each new period.

2. Ionization energy

The energy required to remove the outermost electron shows clear periodicity. It generally increases across a period (harder to remove electrons as nuclear charge rises) and decreases down a group (outer electrons are farther from the nucleus).

Noble gases consistently show peaks in ionization energy because their filled-shell configurations are exceptionally stable. Alkali metals (Li, Na, K, Rb) consistently show valleys because their single $ns^1$ electron is easily removed.

3. Electronegativity

The tendency to attract bonding electrons follows the same periodic trend: increases across a period, decreases down a group.

• Period 3: Na (0.93) → Mg (1.31) → Al (1.61) → Si (1.90) → P (2.19) → S (2.58) → Cl (3.16)

Fluorine, at the top right of the periodic table, is the most electronegative element; this position recurs conceptually with each halogen being the most electronegative in its period.

Evidence from Chemical Properties

4. Valency

Valency with respect to oxygen increases from 1 to 4 across the first half of a period, then often decreases (or shows variable valency).

• Period 2: Li₂O (valency 1) → BeO (2) → B₂O₃ (3) → CO₂ (4) → N₂O₅ (5) → OF₂ (oxygen now central)
• Period 3: Na₂O (1) → MgO (2) → Al₂O₃ (3) → SiO₂ (4) → P₂O₅ (5) → SO₃ (6) → Cl₂O₇ (7)

The pattern of increasing oxidation states repeats each period.

5. Oxide character

Oxides transition from basic (metallic elements) to amphoteric to acidic (non-metallic elements) across a period. This trend recurs in every period.

• Period 3: Na₂O (strongly basic) → MgO (basic) → Al₂O₃ (amphoteric) → SiO₂ (weakly acidic) → P₄O₁₀ (acidic) → SO₃ (strongly acidic) → Cl₂O₇ (very strongly acidic)

6. Hydride character

Across a period, hydrides change from ionic/saline (react with water to give H₂) to covalent (stable or acidic). …