Question

Crystal structure of $NaCl$ :
A. Face centered cubic
B. Body centered cubic
C. Hexagonal
D. Tetrahedral

Answer 1

The structure of $NaCl$ is formed by sodium ion and chloride ion. The repeating units of sodium and chloride ion make the unit cell of the cubic crystal.

Complete step by step answer: $NaCl$ is also called rock salt. It is an inorganic salt which consists of sodium cation and chloride anion. So it is an ionic compound and found as white crystals. Both the cation and the anion present in $NaCl$ is in the ratio of $1:1$ .
$NaCl$ is obtained mainly from seawater. The molecular mass of $NaCl$ is $58.4{\text{ }}g/mol$. The $1:1$ stoichiometric ratio of $Na:Cl$ leads to the formation of the face centered cubic unit cell. Specifically the lattice consists of repeating FCC unit cells.
The sodium ions are smaller in size compared to the chloride ions. As $N{a^ + }$ and $C{l^ - }$ are in one to one ratio in a compound, the coordination numbers of sodium and chlorine are equal.
The unit cell contains four types of site in the lattice namely unique central position, face site, edge sites and corner site. A corner site is shared by $7$ other unit cells so one corner is $\dfrac{1}{8}$ of an ion. A face site is shared by one other unit cell and an edge site is shared by $3$ other unit cells.
The number of atoms per unit cell is calculated from the occurrence of the ions in the positions. $NaCl$ is a face centered cubic unit cell which consists of four $N{a^ + }$ cations and four $C{l^ - }$ anions. This calculation is shown below which involves the multiplication of the number of ions per unit cell and the contribution to other unit cells based on their position.
For $N{a^ + }$ ion: $1$ in center + $12$ in edge $\times$ $\dfrac{1}{4}$ = $4$ sodium ions total per unit cell
For $C{l^ - }$ ion: $6$ in face $\times$ $\dfrac{1}{2}$ + $8$ in corner $\times$ $\dfrac{1}{8}$ = $4$ chloride ions total per unit cell
Thus each ion in the crystal structure of the lattice has six other kinds of ions as the nearest neighbors and twelve of the same kind of ions as the second nearest neighbors. Hence option A is the correct answer.
Body centered cubic has only two atoms per unit cell as eight in the corners and one at the centre so $NaCl$ do not have a body centered cubic structure. Hexagonal and tetrahedral are the sites or the voids or empty space of the crystal lattice. Thus these are incorrect options.
Thus option A is the correct answer.

Note:
Several compounds of alkali metal ions of $Na,{\text{ }}Li,{\text{ }}K{\text{ }}and{\text{ }}Rb$ possess similar structure of $NaCl$. The halides of $Cs,{\text{ }}Ag$ or the oxides of $Ba,{\text{ }}Co$ are ionic compounds and have similar structures.