A solid is made of two elements X and Z. The atoms Z are in CCP arrangement while the atoms X occupy all the tetrahedral sites. What is the formula of the compound?

Tetrahedral sites are twice as compared to octahedral sites, then the ratio of X and Z is 2 : 1. Hence formula of the compound ${\mathrm{X}}_2\mathrm{Z}$

                                                                                                               OR

Z-ccp arrangement

Z  (Coordination number) for ccp  = 4 = Number of Z atoms

Number of tetrahedral holes = $2\times \mathrm{Z}\left(\mathrm{C}.\mathrm{N}\right)$

                                                            = $2\times 4 = 8$

Since X occupies  tetrahedral holes,

therefore Number of atoms of X = 8 

$$\begin{gathered} \mathrm{Z} : \mathrm{X} = 4 : 8 \\ = 1 : 2 \\ \Rightarrow {\mathrm{X}}_2\mathrm{Z} \end{gathered}$$