Question

A compound alloy of gold and copper crystallises in a cubic lattice in which gold atoms occupy corners of cubic unit cell and copper atoms occupy the centre of faces of cube. What is formula of alloy compound?

Answer 1

Gold occupies corner of the unit cell. There are 8 corners and contribution of each corner is $\frac{1}{8}$. Therefore total gold atom is $8\times \frac{1}{8}=1$.

Copper occupies faces of cube. There are 6 faces and contribution of each face is $\frac{1}{2}.$ Total atoms are $6\times \frac{1}{2}=3$.

THerefore, formula is $AuC{u}_3$.