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

Answer: 11

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