The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizing power of the cationic species, `K^(+), Ca^(2+), Mg^(2+), Ba^(2+)`?

Options

A. `Ca^(2+) lt Mg^(2+) lt Be^(2+) lt K^(+)`
B. `Mg^(2+) lt Be^(2+) lt K^(+) lt Ca^(2+)`
C. `Be^(2+) lt K^(+) lt Ca^(2+) lt Mg^(2+)`
D. `K^(+) lt Ca^(2+) lt Mg^(2+) lt Be^(2+)`

Explanation

To determine the increasing order of the polarizing power of the cationic species \( K^+, Ca^{2+}, Mg^{2+}, Ba^{2+} \), we need to consider two main factors: the charge of the cation and the size of the cation.

### Step-by-Step Solution:

1. **Understanding Polarizing Power**:
- Polarizing power refers to the ability of a cation to distort the electron cloud of an anion.
- It is influenced by the charge of the cation and its size.

2. **Charge Consideration**:
- The polarizing power is directly proportional to the charge of the cation.
- Cations with a higher charge will generally have a higher polarizing power.

3. **Size Consideration**:
- The polarizing power is inversely proportional to the size of the cation.
- Smaller cations will have a greater polarizing power compared to larger cations, provided the charge is the same.

4. **Analyzing the Given Cations**:
- The cations in question are \( K^+ \) (charge +1), \( Ca^{2+} \) (charge +2), \( Mg^{2+} \) (charge +2), and \( Ba^{2+} \) (charge +2).
- Since \( K^+ \) has a +1 charge, it will have lower polarizing power compared to the +2 charged cations.

5. **Comparing the +2 Cations**:
- Among \( Ca^{2+}, Mg^{2+}, \) and \( Ba^{2+} \):
- **Size Order**: As we move down the group in the periodic table, the size of the cations increases. Thus, \( Mg^{2+} \) < \( Ca^{2+} \) < \( Ba^{2+} \).
- Therefore, \( Mg^{2+} \) will have the highest polarizing power among the +2 cations, followed by \( Ca^{2+} \), and then \( Ba^{2+} \).

6. **Final Order of Polarizing Power**:
- Combining the observations:
- \( Mg^{2+} \) > \( Ca^{2+} \) > \( Ba^{2+} \) > \( K^+ \)
- Thus, the increasing order of polarizing power is:
\[ K^+ < Ba^{2+} < Ca^{2+} < Mg^{2+} \]

### Conclusion:
The correct sequence representing the increasing order of the polarizing power of the cationic species is:
\[ K^+ < Ba^{2+} < Ca^{2+} < Mg^{2+} \]