Modern Periodic Law (Moseley, 1913): Properties of elements are periodic functions of atomic number, not atomic mass.

Table structure: 7 periods × 18 groups. s-block (Groups 1–2), p-block (Groups 13–18), d-block (Groups 3–12), f-block (lanthanoids + actinoids).

Block configuration: s: $ns^{1-2}$; p: ns^2$np^{1-6}$$$; d: (n-1)d^{1-10}$$ns^{0-2}$$$; f: $$(n-2)f^{1-14}$$$.

Atomic radius trend: Decreases L→R across period (rising Zeff at constant n); increases top→bottom in group (new shell added).

Ionic radius: Cations smaller than parent atom; anions larger. For isoelectronic species: radius ∝ 1/Z.

Isoelectronic 10$e^{-}$ benchmark: $N^{3-}$ (146) > $O^{2-}$ (140) > $F^{-}$ (133) > $Na^{+}$ (98) > $Mg^{2+}$ (66) > $Al^{3+}$ (51) pm.

IE general trend: Increases across period; decreases down group. Driven by Zeff and atomic size.

IE Exception 1 — Be > B: Be (899 kJ/mol) loses from filled 2$s^{2}$; B (800 kJ/mol) loses from 2$p^{1}$. Filled subshell is extra stable.

IE Exception 2 — N > O: N (1402 kJ/mol) has half-filled 2$p^{3}$ (extra stability). O (1314 kJ/mol) has 2$p^{4}$ with one paired electron — repulsion lowers removal energy.

EGE general trend: More negative across period; less negative down group.

EGE Exception — Cl > F: EGE(Cl) = −349 kJ/mol vs EGE(F) = −328 kJ/mol. F's compact 2p orbital causes electron–electron repulsion, reducing energy released on electron addition.

Electronegativity: F = 4.0 (highest, Pauling scale); increases across period; decreases down group.

Diagonal relationships: Li–Mg, Be–Al, B–Si. Caused by similar charge-to-size (polarizing power) ratios.

Anomalous first element: H, Li, Be, B … behave differently from their group due to no d-orbitals, small size, and high electronegativity.

Noble gases: Positive EGE; Group 18; He placed here (not Group 2) because it is chemically inert.