### Related Formula R = R_0 A^1/3$R = R_0 A^{1/3}$ V = frac43pi R^3$V = \frac{4}{3}\pi R^3$ ### Core Logic Since radius R$R$ is proportional to A^1/3$A^{1/3}$, the volume V$V$ (which depends on R^3$R^3$) will be directly proportional to the mass number A$A$. ### Step 1: Show Proportionality V = frac43pi (R_0 A^1/3)^3 = frac43pi R_0^3 A$V = \frac{4}{3}\pi (R_0 A^{1/3})^3 = \frac{4}{3}\pi R_0^3 A$ This proves that V propto A$V \propto A$. ### Step 2: Calculate Ratio fracV_2V_1 = fracA_2A_1$\frac{V_2}{V_1} = \frac{A_2}{A_1}$ Given that A_2 = 4A_1$A_2 = 4A_1$: fracV_2V_1 = frac4A_1A_1 = 4$\frac{V_2}{V_1} = \frac{4A_1}{A_1} = 4$ ### Pattern Recognition Nuclear density is constant for all nuclei. Therefore, Mass propto$\propto$ Volume. Since Mass number (A$A$) represents mass, Volume is strictly linearly proportional to Mass number. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Nuclei