State and explain Soddy and Fajans' radioactive displacement law with examples.

1. 1 · State the law. When a radioactive nucleus emits radiation, its atomic number and mass number change in a fixed way, so the daughter is displaced in the periodic table.
2. 2 · Alpha decay. A decreases by 4 and Z by 2: ₉₂U²³⁸ → ₉₀Th²³⁴ + ₂He⁴.
3. 3 · Beta decay. A is unchanged and Z increases by 1: ₉₀Th²³⁴ → ₉₁Pa²³⁴ + ₋₁e⁰.
4. 4 · Gamma decay. No change in A or Z; the excited nucleus only gives out energy.
5. 5 · Real-life link. Carbon-14 → nitrogen-14 by beta decay is used to date ancient charcoal and bones.
6. 6 · Close. In every equation, A and Z must balance on both sides.

Scoring tip: Balance A (top numbers) and Z (bottom numbers) on both sides: an unbalanced equation loses the mark.