Answer :
Explanation:
The nucleus of an atom can be modeled as several protons and neutrons closely packed together.
Mass of the particle, [tex]m=1.67\times 10^{-27}\ kg[/tex]
Radius of the particle, [tex]R=10^{-15}\ m[/tex]
(a) The density of the nucleus of an atom is given by mass per unit area of the particle. Mathematically, it is given by :
[tex]d=\dfrac{m}{V}[/tex], V is the volume of the particle
[tex]d=\dfrac{m}{(4/3)\pi r^3}[/tex]
[tex]d=\dfrac{1.67\times 10^{-27}}{(4/3)\pi (10^{-15})^3}[/tex]
[tex]d=3.98\times 10^{17}\ kg/m^3[/tex]
So, the density of the nucleus of an atom is [tex]3.98\times 10^{17}\ kg/m^3[/tex].
(b) Density of iron, [tex]d'=7874\ kg/m^3[/tex]
Taking ratio of the density of nucleus of an atom and the density of iron as :
[tex]\dfrac{d}{d'}=\dfrac{3.98\times 10^{17}}{7874}[/tex]
[tex]\dfrac{d}{d'}=5.05\times 10^{13}[/tex]
[tex]d=5.05\times 10^{13}\ d'[/tex]
So, the density of the nucleus of an atom is [tex]5.05\times 10^{13}[/tex] times greater than the density of iron. Hence, this is the required solution.