An ionic solid of tetrahedral structure has a cation of radius 1.06A Find the radius of the anion if ionic radius ratio is 0.32
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Answer:
Radius Ratio Rule is not much of a big topic in the chapter “The Solid State”. However, it plays a very important role in the determination of a stable structure in an ionic crystal. It also helps in the determination of the arrangement of the ions in the crystal structure. Let us study this radius-ratio rule in detail and how it affects the stability and arrangement of a structure.
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Ionic Model & Ionic Radius
The electrostatic interaction between charged spheres is responsible for the formation of bonding in an ionic model. The determination of the sizes of the ionic radius is possible by the internuclear separation of the separate contributions of the anion from cation.
The radius of one ion is calculated on the basis of a standard ion (by assuming the value of one ion). The standard ion is oxide ion which helps in the determination of the other ions. This is because an oxide ion occurs in combination with many different elements. Moreover, an oxide ion is comparatively unpolarizable. Therefore, the significant change in the size is negligible on the basis of the counterion present.
Ionic radius is helpful in the prediction of crystal structures including lengths of the axes, lattice parameters, etc. However, this prediction is possible provided the values of the radius of the ions are taken from the same origin or same reference ion. This is important for achieving the correct relative sizes.
It is essential to understand that ionic radius differs on the basis of coordination number. The increase in coordination number results in the ions moving further away from the central ion to fit more ions. Therefore, increase in coordination number will increase the interionic separation and decrease the short ranged repulsion. This, in turn, will allow the electrons present on the central ion to expand thereby increasing the size of the central ion.
Therefore, we can conclude that ionic radius will increase with an increase in coordination number. The sizes of ions help in the prediction of the structure which will form during the combination of ions. The prediction is of the ions in the structure is done by Radius Ratio or Radius Ration rule. How? Let us understand!