Answer
Density of nucleus = 3 $\times 10^{15}$ g/cm$^{3}$
Density of atom = 0.4 g/cm$^{3}$
Work Step by Step
Mass of proton = $1.673 \times 10^{-24}$ g
Radius of nucleus = $ 10^{-13}/2=5\times 10^{-14}$ cm
Volume of nucleus = $\frac{4}{3}\times3.14\times( 5\times 10^{-14})^{3}$ = 5 $\times 10^{-40}$ cm$^{3}$
Density of nucleus = $\frac{1.673\times 10^{-24}}{5\times 10^{-40}}$ = 3 $\times 10^{15}$ g/cm$^{3}$
Mass of atom = $1.673 \times 10^{-24}+9\times 10^{-28}$ g
Radius of atom = $ 10^{-8}$cm
Volume of atom = $\frac{4}{3}\times3.14\times(1\times10^{-8})^{3}$ = 4 $\times 10^{-24}$
cm$^{3}$
Density of atom = $\frac{1.673 \times 10^{-24}+9\times 10^{-28}}{4\times 10^{-24}}$ = 0.4 g/cm$^{3}$
