An element with density 2.8 g/cm³ forms a fcc unit cell with edge length 4 × 10⁻⁸ cm. Calculate the molar mass of the element?

For fcc unit cell, the number of atoms per unit cell, Z = 4.
Density, d = ZM/NAa³
Here, M = molar mass
NA = 6.022 × 10²³ /mol = Avogadro's number
a = 4 × 10⁻⁸ cm = edge length
Density d = 2.8 g/cm³
Density d = ZM/NAa³
2.8 = (4 × M) / (6.022 × 10²³ × (4 × 10⁻⁸)³)
2.8 = 4M / (6.022 × 10²³ × 64 × 10⁻²⁴)
2.8 = 4M / (385.408 × 10⁻¹)
2.8 = 4M / 38.5408
M = (2.8 × 38.5408) / 4
M = 27 g/mol
Hence, the molar mass of the element is 27 g/mol.