Question

A crystalline solid is made of $X,Y$ and $Z$. Atoms of $X$ are present in $ccp$ lattice; $Y$ occupies all the octahedral voids and $Z$ occupies all the tetrahedral voids. If all atoms along with body diagonal are removed, then the formula of solid will be :

(1) $X_5{Y}_4{Z}_8$ (2) $X_8{Y}_4{Z}_5$
(3) $X_{2}Y{Z}_2$ (4) $XY{Z}_2$

Answer 1

Solution:- (A) $X_5{Y}_4{Z}_8$

Along a body diagonal, one octahedral void (at the body centre), 2 tetrahedral voids (one almost between each corner and the body centre) and 2 corner atoms are present.

Therefore, when all particle along one body diagonal are removed, $2X$ atoms from corner are removed, $1Y$ atom removed & $2Z$ atoms will be removed.

Therefore, the formula of the solid will be-

$X_{(\frac{6}{8}+3)}{Y}_{(\frac{12}{4}+0)}{Z}_{(8-2)}\Rightarrow X_{\frac{15}{4}}{Y}_3{Z}_6\Rightarrow X_5{Y}_4{Z}_8$

Hence the formula of solid will be $X_5{Y}_4{Z}_8$.