Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6\times10^{-27}$ kg and radius of nucleus is $1.5\times10^{-15}~\mathrm{A^{1/3}}$ m. The approximate ratio of the nuclear density and water density is $n\times10^{13}$. The value of $n$ is __________.

Radius $=1.5 \times 10^{-15} A^{1 / 3}$ <br/><br/> $\text { Volume }=\frac{4 \pi}{3} r^{3}$ <br/><br/> Mass of nucleus $=\left(1.6 \times 10^{-27}\right) \mathrm{A} \mathrm{kg}$ <br/><br/> $$ \text { Density of nucleus }=\frac{1.6 \times 10^{-27} \times A}{\frac{4}{3} \times \pi \times\left(1.5 \times 10^{-15} A^{\frac{1}{3}}\right)^{3}} $$ <br/><br/> $$ \begin{aligned} & =\frac{1.6 \times 3 \times 8 \times 10^{18}}{4 \pi \times 27} \\\\ & =\frac{32}{9 \pi} \times 10^{17} \end{aligned} $$ <br/><br/> Density of water $=1000 \mathrm{~kg} / \mathrm{m}^{3}$ <br/><br/> $\frac{\text { Density of nucleus }}{\text { Density of water }}=\frac{\frac{32}{9 \pi} \times 10^{17}}{1000}$ <br/><br/> $=\frac{320}{9 \pi} \times 10^{13}$ <br/><br/> $=11.32 \times 10^{13}$ <br/><br/> value of $n=11$