Solid State

AB has a rock salt (NaCl) structure. This type of crystal structure possesses fcc unit cell and contains four formula units per unit cell, i.e., Z = 4.

In case of a rock salt structure, the edge-length (a) of the unit cell = 2 $\times$ (radius of cation + radius of anion)

Therefore, the edge-length (a) of the unit cell of AB crystal = 2 $\times$ Y^1/3 nm = 2Y^1/3 $\times$ 10^$-$9 m.

We know, $\rho = {{Z \times M} \over {N \times {a^3}}}$

Given : M = 6.022 Y g mol^$-$1 = 6.022 $\times$ 10^$-$3 Y kg mol^$-$1

$\therefore$ $\rho = {{4 \times 6.022 \times {{10}^{ - 3}}Y} \over {6.022 \times {{10}^{23}} \times {{(2{Y^{1/3}} \times {{10}^{ - 9}})}^3}}} = 5.0$ kg m^$-$3

(1) Density of the crystal = 5.0 kg m^$-$3

(2) The observed density (= 20 kg m^$-$3) is higher than that of the calculated density. This indicates that the crystal structure of AB is likely to have non-stoichiometric defect in the form of metal excess or metal deficiency defect or to have impurity defect in the form of substitutional impurity defect or interstitial impurity defect.