Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) The density of the copper (binom6429mathrmCu)$(\binom{64}{29}\mathrm{Cu})$ nucleus is greater than that of the carbon (binom126mathrmC)$(\binom{12}{6}\mathrm{C})$ nucleus. [cite: 20] Reason (R): The nucleus of mass number A has a radius proportional to mathrmA^1/3$\mathrm{A}^{1/3}$. [cite: 21] In the light of the above statements, choose the most appropriate answer from the options given below: [cite: 22]

### Related Formula R = R_0 A^1/3$R = R_0 A^{1/3}$ [cite: 667] rho = fractextMasstextVolume = fracm_n Afrac43pi R^3$$\rho = \frac{\text{Mass}}{\text{Volume}} = \frac{m_n A}{\frac{4}{3}\pi R^3}$$ [cite: 664] ### Core Logic Substituting the expression for radius R$R$ into the density equation: [cite: 664] rho = fracm_n Afrac43pi (R_0 A^1/3)^3 = fracm_n Afrac43pi R_0^3 A = fracm_nfrac43pi R_0^3$$\rho = \frac{m_n A}{\frac{4}{3}\pi (R_0 A^{1/3})^3} = \frac{m_n A}{\frac{4}{3}\pi R_0^3 A} = \frac{m_n}{\frac{4}{3}\pi R_0^3}$$ [cite: 664] As observed, the mass number A$A$ cancels out perfectly, implying that the density of all nuclei is roughly identical and constant regardless of their mass numbers[cite: 664, 666]. Thus, the nuclear density of copper is equal to that of carbon, meaning Assertion (A) is incorrect[cite: 20, 663]. Reason (R) is correct since R propto A^1/3$R \propto A^{1/3}$ is a foundational empirical law of nuclear physics[cite: 21, 668]. ### Pattern Recognition Nuclear mass scales with A$A$, while volume scales with R^3 propto (A^1/3)^3 = A$R^3 \propto (A^{1/3})^3 = A$[cite: 664]. Therefore, textDensity propto fracAA = textconstant$\text{Density} \propto \frac{A}{A} = \text{constant}$[cite: 664, 666]. Always look out for options asserting varying nuclear densities across heavy vs light elements—it is a common trap. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Nuclei