Question

In a solid having rock salt structure, if all the atoms touching one body diagonal plane are removed (except body centre), then the formula of the left unit cell is:

• A. $A_{3.5}{B}_{2.5}$
• B. $A_7{B}_3$
• C. $A_5{B}_3$
• D. $A_3{B}_5$

Answer 1

Answer: (A)

$A_{3.5}{B}_{2.5}$

In rocksalt $\left(NaCl\right)$ structure, $C{l}^{-}$ ions forms fcc and $N{a}^{+}$ ions are present on the edge centre and body center.

Let, in the given compound $AB$, $A$ forms fcc and $B$ is present on the edge center and body center.

The effective number of atoms of $A=4$

The effective number of atoms of $B=4$

Now, if all atoms touching one body diagonals plane are removed except body center then, $4$ atoms are removed from the corner and $2$ atoms are removed from face centers and $2$ are removed from edge centers.

So, Effective number of atoms of $B$ left $=4-\frac{2}{2}-\frac{2}{4}=2.5$

Effective number of atoms of $A$ left $=4-\frac{4}{8}=3.5$

So, the formula of unit cell is $A_{3.5}{B}_{2.5}$