Question

In a face-centred cubic lattice, atom A occupies the corner position and atom B occupies the face -centred positions. If one atom of B is missing from one of the face - centred points, the formula of the compound is

• A. $A_2{B}_5$
• B. $A_{2}B$
• C. $A{B}_2$
• D. $A_2{B}_2$

Answer 1

The correct option is A

$A_2{B}_5$

fcc Lattice, A $\to$ corner positions
B $\to$ Face- centres
$\Rightarrow$ One atom of B is missing from one of the face centres.
$A\Rightarrow \frac{1}{2}\times \theta =1B\Rightarrow \frac{1}{2}\times 5=\frac{5}{2}\Rightarrow A_1{B}_{\frac{5}{2}}\Rightarrow A_2{B}_5$