Modern Periodic Law (Moseley, 1913): Properties of elements are periodic functions of atomic number — not atomic mass. The table has 7 periods, 18 groups, and 4 blocks (s, p, d, f).

Isoelectronic radius rule: For species with the same electron count, radius decreases as proton number rises. Benchmark: $\text{N}^{3-} > \text{O}^{2-} > \text{F}^{-} > \text{Na}^{+} > \text{Mg}^{2+} > \text{Al}^{3+}$

IE exceptions (Period 2): IE(Be) = 899 > IE(B) = 800 kJ/mol [filled 2$s^{2}$ stability]; IE(N) = 1402 > IE(O) = 1314 kJ/mol [half-filled 2$p^{3}$ stability]. Both break the general "IE increases L→R" rule.

EGE anomaly: EGE(Cl) = −349 kJ/mol is more negative than EGE(F) = −328 kJ/mol. Fluorine's compact 2p orbital causes electron–electron repulsion when an extra electron is added, reducing energy released. EN and EGE are NOT the same.

Diagonal relationships: Li–Mg, Be–Al, B–Si share properties due to similar polarizing power (charge/size ratio). Key: Be and Al both have amphoteric oxides; both dissolve in NaOH; both form covalent chlorides hydrolyzed by water.