Question

A crystalline solid is made of X, Y and Z elements. Atoms of X form f.c.c. packing Y occupy octahedral voids. while atoms of Z occupy tetrahedral voids. What will be the simplest formula of the solid if atoms along any one body diagonal are removed?

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

Answer 1

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

If one body diagonal is removed.

I) For $Y$, body centred octahedral void is removed

$Z_Y=\frac{1}{4}\times 12=3$

II) For $Z$, Two tetrahedral voids will be removed.

$Z_Z=8-2=6$

III) For, $X$, two body corner atom will be removed

$Z_X=6\times \frac{1}{8}+6\times \frac{1}{2}=3.75$

Formula, $X_{3.75}{Y}_3{Z}_8\Rightarrow X_5{Y}_4{Z}_8$