Crystal has face centred cubic structure, having atomic weight `6.023y g mol^-1`. If the minimum distance between two atoms is `y^(1//3)` nm and the observed density is `20 kg m^-3` find type of defect in crystal lattice.

Explanation

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 `xx` (radius of cation + radius of anion)
Therefore, the edge length (a) of the unit cell of AB crystal = `2xxY^(1//3)nm=2Y^(1//3)xx10^(-9)m`.
We know, `rho=(ZxxM)/(Nxxa^(3))`
Given: `M=6.022Yg*mol^(-1)=6.022xx10^(-3)Ykg*mol^(-1)`
`therefore" "rho=(4xx6.022xx10^(-3)Y)/(6.022xx10^(23)xx(2Y^(1//3)xx10^(-9))^(3))=5.0kg*m^(-3)`
(1) Density of the crystal = `5.0kg*m^(-3)`
(2) The observed density `(=20kg*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.