Question

An alloy of $Cu,Ag$ and $Au$ is found to have copper constituting fcc lattice. If silver atoms occupy the edge-centers and gold is present at body-center, the alloy has the formula _______.

• A. $C{u}_{4}A{g}_{2}Au$
• B. $C{u}_{4}A{g}_{4}Au$
• C. $C{u}_{4}A{g}_{3}Au$
• D. $CuAgAu$

Answer 1

The correct option is C $C{u}_{4}A{g}_{3}Au$

In fcc arrangement, $Cu$ atoms occupy the corners and face-centers.

$\therefore$ Number of $Cu$ atoms $=8\times \frac{1}{8}+6\times \frac{1}{2}=4$

Number of silver atoms $=$ Number of edge-centres $\times \frac{1}{4}$
$=12\times \frac{1}{4}=3$

Number of gold atoms $=1$ (at body-centre)

$\therefore$ Formula of alloy $=C{u}_{4}A{g}_{3}Au$.