Question

A solid crystal is composed of X, Y and Z atoms. Z atoms (radius 200 pm) form cubic closed packed structure where as X (radius 50 pm) and Y (radius 100 pm) occupy respective voids. Assume all the voids are occupied.
If all the atoms along one body diagonal are removed, then the formula of the compound becomes:

• A. $X_8{Y}_4{Z}_5$
• B. $X_8{Y}_4{Z}_4$
• C. $X_8{Y}_4{Z}_8$
• D. $X_8{Y}_6{Z}_7$

Answer 1

The correct option is A $X_8{Y}_4{Z}_5$

For CCP, Z = 4, X = 8, Y = 4
On removing atoms along one body diagonal
2z - contributing to 1/4th of an atom, 2x atoms, 1y atom is removed.
$\therefore Formula\to X_6{Y}_3{Z}_{3.75}$
$\left(or\right)X_8{Y}_4{Z}_5$