Question

Radius ratio \[ = \dfrac{{{r_{cs}}^ + }}{{{r_{cl}}^ - }} = \dfrac{{1.69{A^0}}}{{1.81{A^0}}} = 0.9337\]
Hence co-ordination of $C{s^ + }$ ion is

Answer 1

Hint: Radius Ratio refers to as the ratio of cation to the anion. The equation for finding radius ratio is, Radius ratio $\rho = \dfrac{{{r_A}^ + }}{{{r_B}^ - }}$. This rule helps in the determination of arrangement of ions in various types of crystal structures, it is also possible to predict the coordination number of any compound with the help of radius ratio. It also helps to determine the stability of an ionic crystal structure. The radius ratio in between 0.225 to 0.414 will be able to fit into tetrahedral voids in the crystal lattice thereby preferring tetrahedral coordination and coordination number of 4 and between 0.414 to 0.732, it will prefer octahedral coordination and coordination number 6, and between 0.732 – 1.000, it will prefer cubic coordination and coordination number 8.

Complete step by step answer:
Given in the question are,
Radius of cation, $C{s^ + } = 1.69{A^0}$
Radius of anion. $C{l^ - } = 1.81{A^0}$
Radius, ratio, $\rho = \dfrac{{{r_A}^ + }}{{{r_B}^ - }}$
 \[\dfrac{{{r_{cs}}^ + }}{{{r_{cl}}^ - }} = \dfrac{{1.69{A^0}}}{{1.81{A^0}}} = 0.9337\]

Therefore, it lies in the range of 0.732 – 1.000
The type of void is cubic.

Hence co-ordination of $C{s^ + }$ ion = 8.

Note: Radius ratio rule plays a very important role in the determination of a stable structure in an ionic crystal and it also helps in the determination of the arrangement of the ions in the crystal structure. The radius-ratio rule affects the stability and arrangement of a structure. Ionic radius is used to predict the crystal structures which include the lengths of the axes, lattice parameters, etc. However, this prediction is possible only when the values of the radius of the ions are taken from the same origin or same reference ion. This is very important for achieving the correct relative sizes.