 Solution

For a graphene honeycomb with C-C bond length $b$, a primitive cell has two atoms and area $3\sqrt{3}{b}^2/2$. Its areal atomic density isFor the nanotube atom-count estimate, treat each shell as a graphene cylinder. The atoms per axial length areUsing the fringe spacing as an internal ruler gives representative estimates $n\simeq 16$, $r_{\mathrm{in}}\simeq 2.2\mathrm{nm}$ and $r_{\mathrm{out}}\simeq 7.45\mathrm{nm}$, consistent with $15$ radial spacings of $0.35\mathrm{nm}$. ThenThe meaningful estimate is of order $2\times 10^4$ atoms per nm, not an exact count. It assumes nearly complete cylindrical shells, uses projected dimensions in a reasonably straight segment, and neglects defects, corrugation and extra external carbon. Image uncertainty in wall count and diameter changes the estimate by tens of percent; no external scale bar is available in this figure.