The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizing order of the polarizing power of the cationic species, K+, Ca++, Mg2+, Be2+?

The correct option is K⁺ < Ca²⁺ < Mg²⁺ < Be²⁺.

Concept and Logic:
According to Fajan's rules, the polarizing power of a cation (its ability to distort the electron cloud of an anion) depends on its charge-to-size ratio, also known as ionic potential.

A higher positive charge and a smaller ionic radius result in a higher charge density, which leads to greater polarizing power. The relationship can be represented as:

$$\text{Polarizing Power}\propto \frac{\text{Charge of cation}}{\text{Size of cation}}$$

Let us analyze the given cationic species based on their charge and size:

1. Comparison of Charge:
Among the given ions, K⁺ has a charge of +1, while Ca²⁺, Mg²⁺, and Be²⁺ all have a charge of +2.
Since polarizing power is directly proportional to charge, the monovalent cation K⁺ has a much lower polarizing power than the divalent cations.

2. Comparison of Size for Divalent Cations:
Be²⁺, Mg²⁺, and Ca²⁺ are all alkaline earth metal cations belonging to Group 2 of the periodic table.
Down a group in the periodic table, the number of electron shells increases, which increases the ionic size:
Be²⁺ < Mg²⁺ < Ca²⁺

Since polarizing power is inversely proportional to ionic size, the smaller the cation, the greater its polarizing power. Therefore, the polarizing power of these divalent cations increases in the opposite order of their size:
Ca²⁺ < Mg²⁺ < Be²⁺

Conclusion:
Combining the charge and size trends, K⁺ (lowest charge and largest size) has the lowest polarizing power, and Be²⁺ (highest charge-to-size ratio) has the highest.
Thus, the increasing order of polarizing power is:
K⁺ < Ca²⁺ < Mg²⁺ < Be²⁺