Question

A solid is made of two elements \[X\] and \[Y\]. The atoms \[Z\] are in \[CCP\] arrangement while the atoms \[X\] occupy all the tetrahedral sites. What is the formula of the compound?
A. \[XZ\]
B. \[X{{Z}_{2}}\]
C. \[{{X}_{2}}Z\]
D. \[{{X}_{2}}{{Z}_{3}}\]

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 atomic sphere inside a unit cell is known as the closest packing formation

Complete step by step solution:
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 \[CCP\] arrangement.
A solid is made up of two elements \[X\] and \[Z\].
The atoms in \[Z\]: \[CCP\] arrangement
The atoms in \[X\]: all the tetrahedral sites
To find the formula of the compound:
In the \[CCP\] arrangement,
Number of formula units per unit cell: \[=4\left( 1+3 \right)\]
Therefore, there are eight spheres at right corners. And one sphere is present at the center of each face.
\[Z=4\]
\[X\], it will occupy the tetrahedral sites.
Tetrahedral sites are twice the number of octahedral sites
Hence, \[X=8\]
The easiest whole number ratio between them gives
\[Z:X=4:8=1:2\]
Hence the formula created is \[Z{{X}_{2}}\]

Therefore, the correct option is (C), \[Z{{X}_{2}}\].

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.