Question

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

Answer 1

Formula calculation of compound:

• In a face-centered cubic lattice, atom (A) occupies the corner positions.
• There are 8 corner positions and each position contributes one eighth to the unit cell.
• Hence, the total number of (A) atoms per unit cell:- $8\times (1/8)=1$
• Atom (B) occupied the face center position.
• There are six face center positions, but one atom of (B) is missing from one of the face-centered points.
• Thus, there are 5 face center positions that are occupied with (B).
• Each such position contributes one-half to the unit cell.
• Hence, the total number of (B) atoms per unit cell:- $5\times (1/2)=2.5$

Hence, the formula of the compound is ${\mathrm{A}}_2{\mathrm{B}}_5$.