Question: The radii of \[N{{a}^{+}}\]is 95 pm and that of \[C{{l}^{-}}\]is 181 pm. Hence, the coordination num...

Question

The radii of $N{{a}^{+}}$ is 95 pm and that of $C{{l}^{-}}$ is 181 pm. Hence, the coordination number of $N{{a}^{+}}$ will be:
(A) 4
(B) 6
(C) 8
(D) Unpredictable

Answer 1

Solution

Hint: To answer this question, we should know NaCl is a crystal structure with a face centered cubic. We should first find the radius ratio and then we will compare the value.

Step by step answer:
We should first explain NaCl unit cell structure that is face centred cubic. As we know that the smallest repeating unit of the crystal lattice is the unit cell, the building block of NaCl crystal. We should note that in an FCC unit cell, it contains atoms at all the corners of the crystal lattice and at the centre of all the faces of the cube. The atom present at the face-centre is shared between 2 adjacent unit cells and only half of each atom belongs to an individual cell. In FCC unit cell atoms are present in all the corners of the crystal lattice Also; we should note that there is an atom present at the centre of every face of the cube.
Now, we will calculate the edge length of unit cell:
Give that radius of ion of sodium ( $N{{a}^{+}}$ ) is= 95 pm
Chlorine $\left( C{{l}^{-}} \right)$ ion radius is= 181 pm
We should know that radius ratio is the ratio of size of cation and anion. We have to find the radius ratio, the formula is as follows:
$Radius\,ratio:\,\dfrac{Radius\,of\,cation}{Radius\,of\,anion}$
$Radius\,ratio:\,\dfrac{95\,pm}{181\,pm}=0.524$ pm
We will compare this radius ratio value with the table given below:

Radius Ratio	Coordination Number	Coordination
1.0	12	Cubic close packed(CCP)Hexagonal closed packed(HCP)
1.0-0.732	8	Cubic
0.732-0.414	6	Octahedral
0.414-0.225	4	Tetragonal
0.225-0.155	3	Triangular
<0.155	2	Linear

So, when we compare the calculated radius ratio of 0.524 pm with the above table, we can say that the coordination number of $N{{a}^{+}}$ is 6. Hence, the correct option is B.
Note: We should know that there are three types of unit cell. They are:

Simple Cubic Unit Cell
Body-centred Cubic Unit Cell
Face centered cubic unit cell
We should know that in a simple cubic cell, the atoms are present only at the corners. Every atom at the corner is shared among 8 adjacent unit cells. There are 4 unit cells in the same layer and 4 in the upper (or lower) layer.
In the body centred cubic cell, we should know that in BCC atoms are present at each corner of the cube and an atom at the centre of the structure.