Question

In crystalline solids anions B are arranged in cubic close packing. Cations A are equally distributed between octahedral and tetrahedral voids. If all the octahedral voids are occupied, the formula:

Answer 1

Hint : Cubic close packing means the atoms are as close as they can get and are packed together. A cubic close packed structure is a face centred cubic basically packed together having the same size of anions and cations so that they are equal.

Complete Step By Step Answer:
Cubic close packing can also be seen as the face centred cubic.
The crystalline solids can be divided into three types of cubic lattices: -
Simple cubic structure which has about fifty percent packing density
Face centred cubic is the one having somewhat seventy four percent packing
Body centred cubic is the one which has sixty-eight packaging
It is given that crystalline soli B anions are arranged in the cubic close packing that is face centred cubic. Face centred cubic has a total of four anions in its per unit cell.
Now face centred cubic has octahedral voids and tetrahedral voids, the octahedral voids are always half the number of tetrahedral voids.
Its iOS given that the number of cations in octahedral voids are same as that in tetrahedral voids therefore if there are $x$ number of cations then there are $x$ number of cations in the tetrahedral voids.
The number of octahedral voids per unit cell are four and from above relation there are four more in tetrahedral voids as well.
Now the ratio of the number of cations and anions per unit cell are $\dfrac{{cation}}{{anion}}$
$= \dfrac{{4 + 4}}{4}$
$= \dfrac{8}{4}$
$= \dfrac{2}{1}$
By the above relation we can say that the formula for the compound is ${A_2}B$ , where A is the cation and B is the anion.
${A_2}B$ is the formula for the compound.

Note :
The layers of close-packed spheres are arranged such that the spheres of every third layer overlay one another gives face-centered cubic packing. Try packing six spheres together in the shape of an equilateral triangle and place another sphere on top to create a triangular pyramid. Now what you need to do is to create another such grouping of seven spheres and place the two pyramids together facing in opposite directions.