The density of mercury is 13.6 g/mL. Calculate approximately the diameter of an atom of mercury in $

Question

The density of mercury is 13.6 g/mL. Calculate approximately the diameter of an atom of mercury in $\AA$, assuming that each atom is occupying a cube of edge length equal to the diameter of the mercury atom. (Atomic mass of Hg = 200)

Professor PC Thomas Classes · Answer

Mass of 1 Hg atom = $200 / 6.022	imes10^{23} = 3.32 	imes 10^{-22}$ g. Volume occupied by 1 atom = Mass/Density = $3.32 	imes 10^{-22} / 13.6 = 2.44 	imes 10^{-23}$ mL. Since volume is a cube of edge $d$, $d^3 = 2.44 	imes 10^{-23} cm^3 \implies d \approx 2.91 	imes 10^{-8}$ cm = 2.91 $\AA$.