Question

In the sodium chloride structure, each $N{a}^{+}$ ion is surrounded by six $C{l}^{-}$ions as nearest neighbours and ................ $N{a}^{+}$ ions as next nearest neighbours. Fill in the blank.

• A. $12$
• B. $10$
• C. $6$
• D. $8$

Answer 1

The correct option is A $12$

In the rock salt structure, $C{l}^{-}$ ions occupies the fcc lattice points. However all the $N{a}^{+}$ ions are occupied at octahedral positions, i.e. edge centers and body centres.
Each $N{a}^{+}$ ions are surrounded by 6 $C{l}^{-}$ ions. The distance between $N{a}^{+}$ and $C{l}^{-}$ as nearest neighbours is half of the edge length, $\frac{a}{2}$.
where $a$ is the edge length of the cube.
As shown in the diagram the $N{a}^{+}$ ions are situated at edge centrs and body center of the cube.
The distance between the two $N{a}^{+}$ ions, one positioned at edge center and another at body center is $\frac{a}{\sqrt{2}}$ which can be easily calculated by Pythagoras Theorem.
Similarly the distance between the two $N{a}^{+}$ ions, both positioned at edge centers is $\frac{a}{\sqrt{2}}$.
Hence, the total no. of $N{a}^{+}$ ions as the next nearest neighbours to $N{a}^{+}$ is $12$.
Option A is the correct answer.