For a face centred cubic structure,
No. of X atoms = 8 × \(\frac{1}{8}\) = 1
No. of Y atoms 6 × \(\frac{1}{2}\) = 3
Formula of the compound = XY₃

Atoms are present in the corners of cube = A and atom present at body centre = B.
We know that a cubic unit cell has 8 corners. Therefore contribution of each atom A at the corner = \(\frac{1}{8}\).
Since number of atoms per unit cell is 8, therefore total contribution = 8 &therefore \(\frac{1}{8}\). We also know that atoms in the body centre, therefore number of atoms of B per unit cell = 1. Thus formula of the compound is AB.

A body-centred cubic system consists of all eight corners plus one atom at the centre of cube.

Number of tetrahedral voids(V_T) in a crystal is twice the number of atoms (n) in a crystal i.e.,V_T= 2n
So, number of tetrahedral voids per atom is given by V_T/ n= 2

Among the three options KCl, NaCl and MgCl₂, the size of anion is same. So larger the cation, larger will be the cation/anion ratio i.e., KCl will have larger cation/anion ratio among the three. So,we left with two options KCl and CaF₂. Among these two CaF₂ will have maximum value of cation/anion ratio because decrease in ionic radii of anion from Cl^- to F^- does not overcome the effect of decrease in ionic radii of cation from K⁺ to Ca²⁺.

When polar crystal is subjected to a mechanical stress,electricity is produced – a case of piezoelectricity.Reversely, if electric field is applied, mechanical stress is developed. Piezoelectric crystal acts as a mechanical electrical transductor.

All the given statements are correct about F-centres.