JEE Main & Advanced Chemistry The Solid State / ठोस प्रावस्था Ionic radii and Radius ratio

(1) Ionic radii : X-ray diffraction or electron diffraction techniques provides the necessary information regarding unit cell. From the dimensions of the unit cell, it is possible to calculate ionic radii.           

Let, cube of edge length 'a' having cations and anions say \[NaCl\] structure.           

Then, \[{{r}_{c}}+{{r}_{a}}=a/2\]                 

where \[{{r}_{c}}\] and \[{{r}_{a}}\] are radius of cation and anion.

Radius of  \[C{{l}^{-}}\] \[=\sqrt{\frac{{{(a/2)}^{2}}+{{(a/2)}^{2}}}{2}}=\frac{a}{4}\]

For bcc  lattice say \[CsCl.\] \[{{r}_{c}}+{{r}_{a}}=\frac{\sqrt{3}a}{2}\]

(2) Radius ratio : Ionic compounds occur in crystalline forms. Ionic compounds are made of cations and anions. These ions are arranged in three dimensional array to form an aggregate of the type (A+B?)n . Since, the Coulombic forces are non-directional, hence the structures of such crystals are mainly governed by the ratio of the radius of cation \[({{r}_{+}})\] to that of anion \[({{r}_{-}}).\] The ratio \[{{r}_{+}}\] to \[{{r}_{-}}\] \[({{r}_{+}}/{{r}_{-}})\] is called as radius ratio.

 \[\text{Radius}\ \text{ ratio }=\text{ }\frac{{{r}_{+}}}{{{r}_{-}}}\]                      

Limiting Radius ratios and Structure