An unknown nucleus has a nuclear density of 2.29 × 10¹⁷ ~kg/m³$2.29 \times 10^{17} \mathrm{~kg/m}^3$ and mass of 19.926 × 10⁻²⁷ ~kg$19.926 \times 10^{-27} \mathrm{~kg}$. Its mass number A$A$ is approximately: (Take R₀ = 1.2 × 10⁻¹⁵ ~m, 4π = 12.56$R_0 = 1.2 \times 10^{-15} \mathrm{~m}, 4\pi = 12.56$)

Related Formula

r = r₀ A1/3$r = r_0 A^{1/3}$

Core Logic

Evaluate statements A and B (Volume of nucleus): The radius of a nucleus is given by r = r₀ A1/3$r = r_0 A^{1/3}$. The volume is V = (4)/(3)π r³ = (4)/(3)π (r₀ A1/3)³ = (4)/(3)π r₀³ A$V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (r_0 A^{1/3})^3 = \frac{4}{3}\pi r_0^3 A$. Thus, Volume is directly proportional to mass number A$A$ (V ∝ A$V \propto A$), not A1/3$A^{1/3}$. Statement A is False. Statement B is True.

Evaluate statements C and D (Mass Defect): Mass defect (Δ m$\Delta m$) is strictly defined as the difference between the sum of the masses of the individual unbound nucleons (protons and neutrons) and the actual mass of the bound nucleus. Statement C incorrectly defines it as the difference between an atom and its nucleus (which is just electron mass and binding energy). Statement D correctly defines it based on the nucleus and its constituents. Statement C is False. Statement D is True.

Step 1: Final Conclusion

B and D are true, while A and C are false.

Pattern Recognition

Radius ∝ A1/3$\propto A^{1/3}$. Volume ∝ A$\propto A$. Density is constant (independent of A$A$). Mass defect is strictly nucleon mass sum minus nucleus mass.

Chapter Mix

Class 12 Physics: Nuclei