Question

Which of the following is incorrect about ${\text{NaCl}}$ structure?
A) Nearest neighbours of ${\text{N}}{{\text{a}}^ + }$ ion is six ${\text{C}}{{\text{l}}^ - }$ ion.
B) ${\text{N}}{{\text{a}}^ + }$ ions make FCC lattice.
C) ${\text{C}}{{\text{l}}^ - }$ ions are packed in a cubic close packed arrangement.
D) There are eight next nearest neighbours of ${\text{N}}{{\text{a}}^ + }$ ion.

Answer 1

Hint: We know that the smallest repeating unit of a crystal lattice is known as a unit cell. In a face centered unit cell, atoms are present at the centre of all the six faces of the cube and at all the eight corners of the cube.

 Complete step by step answer:
We know that ${\text{NaCl}}$ has a cubic unit cell. Thus, the ${\text{N}}{{\text{a}}^ + }$ and ${\text{C}}{{\text{l}}^ - }$ ions are closely packed.
The formula of ${\text{NaCl}}$ shows that the ${\text{N}}{{\text{a}}^ + }$ and ${\text{C}}{{\text{l}}^ - }$ ions are present in the ${\text{1:1}}$ ratio.
${\text{N}}{{\text{a}}^ + }$ ions occupy octahedral voids in the crystal lattice of ${\text{NaCl}}$. This is because the size of ${\text{N}}{{\text{a}}^ + }$ ions is smaller than that of ${\text{C}}{{\text{l}}^ - }$ ions. The ${\text{C}}{{\text{l}}^ - }$ ions are located at the corners and the centre of each face of the unit cell.
We know that the lattice of ${\text{NaCl}}$ is face centered cubic (FCC). The coordination number of FCC is twelve and it contains four atoms per unit cell.
Each ${\text{N}}{{\text{a}}^ + }$ ion is surrounded by six ${\text{C}}{{\text{l}}^ - }$ ions and each ${\text{C}}{{\text{l}}^ - }$ ion is surrounded by six ${\text{N}}{{\text{a}}^ + }$ ions. Thus, the coordination number of each ion is six.
The structure of unit cell of ${\text{NaCl}}$ is as follows:

The white sphere represent ${\text{C}}{{\text{l}}^ - }$ ions and the red spheres represent ${\text{N}}{{\text{a}}^ + }$ ions.
Thus, the statement ‘there are eight next nearest neighbours of ${\text{N}}{{\text{a}}^ + }$ ion’ is incorrect.
So,Option D is correct.
Note:The sodium chloride structure is a face centered cubic structure. There are four atoms per unit cell of a face centered cubic lattice. Six chloride ions surround one sodium ion and six sodium ions surround one chloride ion. The packing efficiency of the FCC lattice is $74\% $.