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

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.