Answer:-

Given: Edge length (a) = 405 pm = 4.05 × 10^-8 cm
Molar mass = 27 g mol^-1, Density (ρ) = 2.7 g/cm³ 

To find: Nature of cubic unit cell

Formula: Density (ρ) = M X n/(a³ x NA)

Calculation: From the formula,

Density, ρ = M x n/(a³ NA)`

∴ 2.7 g cm^-3 = (27 gmol^-1 x n/((4.05 x 10^-8)³ cm³  x  6.022  x  10²³ atom mol^-1)

∴ n = (2.7 g cm^-3 x (4.05 x 10³-8) cm³ x 6.022 x 10²³ atom mol^-1)/(27 g mol^-1)`

= 4.00

∴ Number of atoms in unit cell = 4

Since unit cell contains 4 atoms, it has face-centred cubic (fcc) or ccp structure.

The nature of the given cubic unit cell is face-centred cubic (fcc) or ccp unit cell.