An ax ceramic compound has the rock salt crystal structure. if the radii of the a and x ions are 0.137 nm and 0.241 nm, respectively, and the respective atomic weights are 22.7 g/mol and 91.4 g/mol, what is the density of this material? 0.571 g/cm3

P = n'∑Ac + ∑AA/VcNA

= n' (∑Ac + ∑AA) / 9³NA

=n' (∑Ac + ∑AA) / (2 (rA + rX)) ³ NA

n' = number of atoms per unit cell

= 4 (assumption)

rA = 0.137 * 10⁻⁷ cm

rX = 0.241 * 10⁻⁷ cm

NA = Avagadros number

= 6.022 * 10²³

∑Ac = Atomic weight of all cations

∑AA = Atomic weight of all anions

p = n' (∑Ac + ∑∑AA) / (2 (rA + rx)) ³NA

= 4 (22.7 + 91.4 / (2 (0.137 * 10⁻⁷ + 0.241 * 10⁻⁷)) ³ 6.022 * 10²³

= 1.75 gm/cc