Given below are two statements: (A): The density of the copper (⁶⁴Cu₂₉) nucleus is greater than that of the carbon (¹²C₆) nucleus. (R): The nucleus of mass number A has a radius proportional to A¹/³.
❓ Question Given below are two statements: Assertion (A): The density of the copper ( 64 Cu 29 ^{64}\text{Cu}_{29} ) nucleus is greater than that of the carbon ( 12 C 6 ^{12}\text{C}_6 ) nucleus. Reason (R): The nucleus of mass number A A has a radius proportional to A 1 / 3 A^{1/3} . 🖼️ Question Image ✍️ Short Solution We need to check (1) whether A is true, (2) whether R is true, and (3) whether R explains A. 🔹 Step 1 — Is the Reason (R) true? Empirically and from the liquid-drop model , the nuclear radius is given by R = r 0 A 1 / 3 , where r 0 ≈ 1.2 fm r_0\approx 1.2\text{ fm} So R is true . 🔹 Step 2 — Use R to examine the Assertion (A) Density of a nucleus ρ \rho ≈ mass / volume. Mass ∝ A \propto A ( number of nucleons ). Volume V ∝ R 3 ∝ ( A 1 / 3 ) 3 ∝ A Thus ρ = mass volume ∝ A A = constant . Therefore, to first approximation nuclear density is independent of A A — nuclei have roughly the s...