Question

Assume that protons and neutrons have equal masses. Mass of a mucleon is $1.6 \times 10^{-27} kg$ and radius of nucleus is $1.5 \times 10^{-15} A ^{1 / 3} m$. The approximate ratio of the nuclear density and water density is $n \times 10^{13}$. The value of $n$ is ___

Answer 1

$ \text { density of nuclei }=\frac{\text { mass of nuclei }}{\text { volume of nuclei }} $
$ \rho=\frac{1.6 \times 10^{-27} A }{\frac{4}{3} \pi\left(1.5 \times 10^{-15}\right)^3 A }$
$=\frac{1.6 \times 10^{-27}}{14.14 \times 10^{-45}}=0.113 \times 10^{18}$
$\rho_{ w }=10^3$
$ \text { Hence } \frac{\rho}{\rho_{ w }}=11.31 \times 10^{13} $