Question

A compound is formed by two elements X and Y. Atoms of the element Y (as anions) make ccp and those of the element X (as cations) occupy all the octahedral voids. What is the formula of the compound?

Answer 1

Hint : The three dimensional structure of a strong crystalline material is set up through the periodic patterning of the atoms that make up the crystal. The most efficient conformation of the atomic sphere inside a unit cell is known as the closest packing formation.

Complete Step By Step Answer:
The atoms Z are in CCP arrangement while the atoms X possess all the tetrahedral locales. The quantity of tetrahedral sites is double the number of atoms present in arrangement.
A solid is made up of two elements X and Z. The atoms in $Z:CCP$ arrangement the atoms in $X:$ all the octahedral sites to find the formula of the compound: In the arrangement;
Since, atoms of Y form CCP (cubic close packing) which is analogous to FCC (face centered cubic). So, effective number of atoms of Y in lattice $=4$ ,
Number of octahedral voids $=$ Number of atoms forming CCP $=4$ ,
So, the effective number of atoms of X in the lattice, Therefore, there are eight spheres at right corners. And one sphere is present at the center of each face. It will occupy the tetrahedral sites. Tetrahedral sites are twice the number of octahedral sites.
$X:Y=4:4\Rightarrow X:Y=1:1$
Thus, the formula of the compound is XY.

Note :
The arrangement of the atoms in a crystalline solid affects atomic coordination numbers, interatomic separations, and the sorts and strengths of bonding that happen inside the solid. A comprehension of atomic packing in a unit cell and crystal lattice cross section can offer knowledge to the physical, chemical, electrical, and mechanical properties of a given crystalline material.