Question

A mineral having the formula $A{B}_2$ crystallises in the cubic close-packed lattice with $A$ atoms occupying the lattice point. The ratio of co-ordination numbers of $A$ and $B$ is:

• A. $2:1$
• B. $3:1$
• C. $4:1$
• D. $5:1$

Answer 1

The correct option is A $2:1$

Explanation: In a cube, there are 8 vertices, 6 faces and 12 edges.

In a CCP lattice, the atoms are present on all the vertices and face centers.

Lattice points in CCP are all 8 vertices and 6 face centers.

In a crystal, A atoms occupy all corner sites and center of each face in a cube. B atoms are located in a way that they surround 4 A- atoms. They occupy all tetrahederal sites and hence have a coordination number 4.

Number of tetrahederal sites in CCP-lattice = 4

For every A-atom, 2 tetrahederal sites are available and B-atoms are present on all tetrahederal sites. Stoichiometry ratio becomes 1 : 2 which satisfies the compound.

Now, each B-atom surrounds 4 A-atoms and each A-atom surrounds 8 B-atoms. Hence, the coordination ratio of the compound becomes 8 : 4 i.e. 2 : 1

Hence, the correct option is $\text{A}$