Answer
$5.9\times10^{-12} \%$
Work Step by Step
1. Calculate the volume of a carbon-12 nucleus.
$V_n=\frac{4}{3}\pi r^3=\frac{4}{3}\pi(2.7\times10^{-15}m)^3= 8.2\times 10^{-44}\ m^{-3}$
2. Calculate the volume of a carbon-12 atom.
$V_{atom}=\frac{4}{3}\pi r^3=\frac{4}{3}\pi(70\times10^{-3}m)^3= 1.4\times 10^{-30}\ m^{-3}$
3. Compute the percentage of the carbon atom's volume that is occupied by the nucleus.
$\frac{8.2\times10^{-44}}{1.4\times10^{-30}}\times100\%=5.9\times10^{-12}\%$
