(a) Using what you know about the diameters of atoms from Section 1.3, estimate the length of one side of a cube made up of \(1 \mathrm{~mol}\) of closely packed carbon atoms. (b) The mass density of graphite (a form of carbon) is \(2.2 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\). By how much does the length you calculated in part \(a\) change when you do your calculation with this mass density value? Remember that \(1 \mathrm{~mol}\) is the number of atoms in \(12 \times 10^{-3} \mathrm{~kg}\) of carbon.

Data From Section 1.3:

Atoms are spherical and have a diameter of about \(10^{-10} \mathrm{~m}\). Atomic nuclei are also spherical, with a diameter of about \(10^{-15} \mathrm{~m}\), making atoms mostly empty space.