Question

The crystalline structure of $NaCl$ is

Answer 1

Hint: For face centred structure, number of atoms per unit cell is equal to four, for cubic cells it is equal to two, for body centred its equal to two and for hexagonal close packing it is six. $NaCl$ contains four atoms per unit cell.

Complete step-by-step answer:This question belongs to the concept of solid state. Let us see what crystalline structure actually means.
Crystalline structure means how atoms, molecules and ions are arranged in an orderly manner of a crystalline material.
Now let us see all the types of crystalline structure based on symmetry:
1. Cubic
2. Tetragonal
3. Hexagonal
4. Rhombohedral
5. Orthorhombic
6. Monoclinic
7. Triclinic
Now let us see types of arrangement of unit cell:
1. Simple cubic
2. Face centred cubic
3. Body centred cubic
4. Hexagonal close packing
Also let us see number of atoms per unit cell:
1. Simple cubic - $1$
2. Face centred cubic - $4$
3. Body centred cubic - $2$
4. Hexagonal close packing - $6$

Here, we have to find the crystalline structure of $NaCl$ compound therefore, in case of $NaCl$ the number of ions present in one unit cell of $NaCl$ lattice is $8$
Now let us see how,
There are $8$ $C{l^ - }$ ions at the corner contributing one-eighth to the unit cell each and $6$ $C{l^ - }$ at the face centre contributing one half to the unit cell.
Therefore, total $ = \dfrac{1}{8} + 6 \times \dfrac{1}{2} = 4$
Now from $N{a^ + }$ there are $4$ octahedral voids occupied
So, we can conclude that it has $4$ atoms per unit cell.
Hence $NaCl$ is face centred cubic.

So option B is the correct answer.

Note: Remember the number of atoms per unit for every arrangement. Contribution of an atom from the corner is one-eighth of the whole atom. Out of the four $Na$ atoms in a unit cell, one comes from the eight corners and the rest three from the six faces.