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 one body diagonal are removed then the simplest formula of solid will be:

• A. $X_5{Y}_4{Z}_8$
• B. $X_8{Y}_4{Z}_5$
• C. $X_{2}Y{Z}_2$
• D. $XY{Z}_2$

Answer 1

The correct option is A $X_5{Y}_4{Z}_8$

X-atoms forms ccp lattic.
Number of X-atoms in unit cell (on eight corners and 6 face centres)= 4
Number of Y-atoms (in 4 octahedral voids) = 4
Number of Z-atoms ( in 8 tetrahedral voids) = 8
Removal of atoms along one body diagonal removes 2X atoms on 2 corners, 1Y atom at the body centre and 2Z atoms on the 2 tetrahderal voids. Effective number of atoms may be calculated as
$X=4-(2\times \frac{1}{8})=\frac{15}{4}$
$Y=4-1=3$
$Z=8-2=6$
Ratio of atoms
$=X:Y:Z=\frac{15}{4}:3:6=5:4:8$
So the formula of the compound is$X_5{Y}_4{Z}_8$