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Ionic Radius


Ions are formed when the neutral atoms lose or gain electrons. A positive ion or cation is formed by the loss of one or more electrons by the neutral atom whereas a negative ion or anion is formed by the gain of one or more electrons by the atom. The term ionic radii refers to the size of the ions in the ionic crystals. The ionic radius of an ion may vary from crystal to crystal because of change in surrounding ions.

The equilibrium distance between the nuclei of the two adjacent ions can be determined by X-ray analysis of ionic crystals. Assuming ions to be spheres, the internuclear distance can be taken as the sum of the ionic radii of the adjacent ions (Fig. 6.6). Knowing the ionic radius of one of the ions, the ionic radius of other can be calculated.

     Fig. 6.6.  lllustration of ionic radius

The radius of cation is smaller than that of the parent atom. 

Fig. 6.7. Relative sizes of Na atom and Na+ion

Cation is formed by the loss of one or more electron from the gaseous atom. Now, in the cation the nuclear charge remains the same as that in the parent atom but the number of electrons becomes less. As a result of this, the nuclear hold on the remaining electrons increases because of the increase in the effective nuclear charge per electron. This causes a decrease in the size.

In many cases the formation of cation also involves the removal of the valence shell completely. For example, formation of Na+ ion from Na atom involves the removal of third shell completely. This also result in the decrease in the size of the ion.

The comparative sizes of certain atoms and their corresponding cations are given in Table 6.7. 

Table 6.7. Atomic and Ionic Radii of Some Elements 

The radius of anion is larger than that of parent atom. Anion is formed by the gain of one or more electrons by the gaseous atom. In the anion, the nuclear charge is the same as that in the parent atom but the number of electrons has increased. Since same nuclear charge now acts on increased number of electrons, the effective nuclear charge per electron decreases in the anion. The electron cloud is held less tightly by the nucleus. This causes increase in the size. The relative sizes of chlorine atom and chloride ion have been shown in Fig. 6.8.

Fig. 6.8. Relative sizes of Cl atom and Cl- ion.

The comparative sizes of some atoms and their corresponding anions are given in Table 6.8. 

Table 6.8. Atomic and Ionic Radii of Some Elements 


 The ions having same number of electrons but different magnitude of nuclear charge are called iso-electronic ions. In fact, these are the ions of different elements having same electronic arrangement. For example, each one of sulphide (S2-), chloride (Cl-) and potassium (K+) ion has eighteen electrons but they have different nuclear charge, +16, +17 and + 19 respectively.

Variation of size among iso-electronic ions. Within the series of iso-electronic ions, as the nuclear charge increases, the attractive force between the electrons and nucleus also increases. This results in the decrease of ionic radius. In other words, size of the iso-electronic ions decreases with the increase in the magnitude of nuclear charge. For example, N3-, ()2-, F”, Na+, Mg 2+, Al3+ are iso-electronic and have 10 electrons each. The sizes of these ions are in the order:

Mg2+ having the highest nuclear charge (12 units) bas the smallest size whereas N3- ion having the smallest nuclear charge (7 units) has the largest size. Variation of size among these ions has been shown in Table 6.9. 

Table 6.9. Variation of Size Among Iso-electronic Ions



`Example 6.3 The following species are isoelectronic with the noble gas neon. Arrange them in order of increasing size: Na+, r-, Q2-, Mg2+, Al3+.

Solution . In Na+, p-, 02-, Mg2+, AJ3+, the nuclear charges are 11, 9, 8, 12 and 13 respectively. Among isoelectronic species, greater the nuclear charge smaller is the size. Therefore, the sizes of the above ionic species are in the order:

Al3+ < Mg2+ < Na+ < F- < O2-.


Example 6.4. Select from each group the species which has the smallest radius stating appropriate reason.

(i) O,O-, O2-   (ii) K+, srl+ , Ar

(iii) Si, P, CI

Solution. (i) The species 0 has the smallest radius because the radius of anion is always larger than the radius of the atom from which it is formed. o- and o:z- are anions of oxygen.

(ii) K+ has the smallest radius. In K+ and AI the outermost shell is third whereas in sc2+ it is fourth. Out of K+ and AI, K+ has smaller size because it has greater nuclear charge.

(iii) Cl has the smallest radius. Si, P and Cl belong to same period. In a period atomic radius decreases with increase in atomic number due to increase in effective nuclear charge.


Example 6.5. Name a species that will be isoelectronic with each of the following atoms or ions:

(i) Ne (ii) Cl- (iii) Ca2+ (iv) Rb

Solution. (i) Sodium ion, Na+

(ii) Potassium ion, K+

(iii) Sulphide ion, S2- (iv) sr+


Example 6.6. Out of Na+ and Na which has smaller size and why?

Solution. Na+ has smaller size than Na. Na+ is formed by removal of one electron from Na. Therefore, Na+ has one electron less than Na. However, Na and Na+ have same nuclear charge. Therefore, electrons in Na+ are more tightly held than in Na. Moreover, removal of one electron from Na leads to complete removal of the third shell so that in Na+, the outermost shell is second. Hence, Na+ has smaller size than Na.


Example 6.7. Give examples of three cations and three anions which are isoelectronic with argon.

Solution       Cations: K+, Ca2+, Sc3+

Anions: CI-,