Question

A mineral having formula $A{B}_2$ crystallises in the cubic close-packed lattice, with the $A$ atoms occupying the lattice points. Hence coordination number of $A$ and $B$ atoms are:

• A. $4,8$
• B. $4,4$
• C. $8,8$
• D. $8,4$

Answer 1

The correct option is A $4,8$

There are two types of closed -packed lattices-

Hexagonal closed packed lattice and Cubic close-packed lattice.

Only FCC lattice forms the cubic closed packed lattice.

So, $A$ forms the FCC lattice $\Rightarrow Z_{eff}=4$

$B$ occupies the tetrahedral voids $\Rightarrow Z_{eff}=8$

Therefore, one atom of $A$ is surrounded by $8$ atoms of $B$ and $B$ will be surrounded by $4$ atoms of $A$.

Coordination number of $A=8$

Coordination number of $B=4$

Therefore, the formula of the compound will be $A_4{B}_8$ Or $A{B}_2$

Hence, the correct option is A.