An element with molar mass 27 g/mol forms a cubic unit cell with edge length 4.05 × 10⁻⁸ cm. If its density is 2.7 g/cm³, what is the nature of the cubic unit cell?

Given:Molar mass of the given element, M = 27 g/mol = 0.027 kg/mol
Edge length, a = 4.05 × 10⁻⁸ cm = 4.05 × 10⁻¹⁰ m
Density, d = 2.7 g/cm³ = 2.7 × 10³ kg/m³
We know that
d = Z × M / (a³ × NA)
Where, Z is the number of atoms in the unit cell and NA is the Avogadro number.
Thus,
Z = d × a³ × NA / M
Z = 2.7 × 10³ × (4.05 × 10⁻¹⁰)³ × 6.022 × 10²³ / 0.027
(NA = 6.022 × 10²³)
Z = 4 or Z ≈ 4 (fcc)
Since, the number of atoms in the unit cell is 4, the given cubic unit cell has face-centred cubic (fcc) or cubic-close packed (ccp) structure.