question_answer

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 are diagonally removed then 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) \[XY{{Z}_{2}}\]

Correct Answer: A

Solution :

[a] Number of X-atoms in unit cell = 4 (ccp) Number of Y-atoms=4 Number of Z-atoms=8 If atoms along one body diagonal are removed then 2X, 1Y and 2Z atoms will be absent. Effective number of atoms may be calculated as \[X=4-\left( 2\times \frac{1}{8} \right)=\frac{15}{4}\] \[Y=4-1=3\] \[z=8-2=6\] Simplest ratio Simplest formula \[={{X}_{5}}{{Y}_{4}}{{Z}_{8}}\]