The density of mercury is 13.6 g/mL. Calculate volume of mercury atom assuming that each atom is occupying a cube of edge length equal to the diameter of mercury atom is x×10^–23. Find the x.

d = 13.6g/mL
Atomic mass of Hg = 200 = M
1 g atomic weight of Hg = 200 g = weight
of 6.023×10²³ atoms
Number of atoms present in 1 g of Hg
$=\frac{6.023\times {10}^{23}}{200}=3.0115\times {10}^{21}$
Volume of 1 atom of Hg or unit cell
$\frac{1\mathrm{g}\text{ of }\mathrm{Hg}}{\text{ Number of atoms }\times \text{ density }}=2.44\times {10}^{-23}{\mathrm{cm}}^3$