Question

An element with molar mass 27 g mol⁻¹ forms a cubic unit cell with edge length 4.05 ✕ 10⁻⁸ cm. If its density is 2.7 g cm⁻³, what is the nature of the cubic unit cell?

Answer 1

Molar mass of the given element, M = 27 g mol⁻¹ = 0.027 kg mol⁻¹

Edge length, a = 4.05 × 10⁻⁸ cm = 4.05 × 10⁻¹⁰ m

Density, d = 2.7 g cm⁻³ = 2.7 × 10³ kg m⁻³

Applying the relation,

`d=(ZxxM)/(a^3xxN_A)`

Where, Z is the number of atoms in the unit cell and N_A is the Avogadro number.

Thus,

`Z=(`

   `=(2.7xx10^3xx(4.05xx10^(-10^3))xx6.022xx10^23)/0.027`

    = 4

Since the number of atoms in the unit cell is four, the given cubic unit cell has a face-centred cubic (fcc) or cubic-closed packed (ccp) structure.