Question

A compound alloy of gold and copper crystallises in a cubic lattice in which the gold atoms occupy the lattice points at the corners of a cube and the copper atoms occupy the centres of each of the cube faces. What is the formula of this alloy compound?

• A. $AuC{u}_3$
• B. $A{u}_{3}Cu$
• C. $A{u}_{2}C{u}_3$
• D. $AuCu$

Answer 1

The correct option is A $AuC{u}_3$

$Au$ atoms are at 8 corners of the cube. Atom at corners are shared by eight eight unit cell
Thus,
$\text{Number of}Au\text{atoms in a unit cell}=\frac{1}{8}\times 8=1$
$Cu$ atoms are at the face-centres of 6 faces in a cube.
Each atom in face centre is shared by two unit cells.
Thus,
$\text{Number of}Cu\text{atoms in a unit cell}=\frac{1}{2}\times 6=3$
Therefore, the empirical formula of the unit call is $AuC{u}_3$.