Question

Sol. [Key Concept: Nuclear density is constant → A from mass] Given

$$\begin{matrix} & \rho = 2.29 \times 10^{17}\text{ }kg/m^{3},\text{~}\text{mass}\text{~}m = 19.926 \times 10^{- 27}\text{ }kg \\ & R_{0} = 1.2 \times 10^{- 15}\text{ }m\text{~}\text{and}\text{~}R = R_{0}A^{\frac{1}{3}} \\ & \text{~}\text{Now use volume}\text{~} = \frac{\text{~}\text{Mass}\text{~}}{\text{~}\text{Density}\text{~}} \\ & \ \Rightarrow \ \frac{4}{3}\pi R^{3} = \frac{M}{\rho} \\ & \ \Rightarrow \ \frac{4}{3}\pi\left\lbrack R_{0}(A)^{1/3} \right\rbrack^{3} = \frac{M}{\rho} \\ & \ \Rightarrow \ \frac{4}{3}\pi R_{0}^{3}A = \frac{M}{\rho} \\ & \ \Rightarrow A = \frac{M}{\rho} \times \frac{3}{4\pi \times R_{0}^{3}} = \frac{19.926 \times 10^{- 27} \times 3}{2.29 \times 10^{17} \times 12.56 \times \left( 1.2 \times 10^{- 15} \right)^{3}} \approx 12 \end{matrix}$$