Arrange the following species in increasing order of polarizing power ? `Ag^(+),TI^(+)Na^(+)`.

Options

A. `TI^(+) gt Ag^(+)gt Na^(+)`
B. `TI^(+) gt Na^(+) gt Ag^(+)`
C. `Ag^(+) gt Na ^(+) gt TI^(+)`
D. `Na^(+)gt TI^(+)gt Ag^(+)`.

Answer

To arrange the species \( \text{Ag}^+, \text{Ti}^+, \text{Na}^+ \) in increasing order of polarizing power, we need to consider the factors that affect polarizing power.

### Step-by-Step Solution:

1. **Understanding Polarizing Power**:
- Polarizing power of a cation is the ability of the cation to distort the electron cloud of an anion. It is influenced by the charge and size of the cation.
- The polarizing power is inversely proportional to the size of the cation. Smaller cations with higher charges have greater polarizing power.

2. **Comparing the Cations**:
- **Sodium ion (\( \text{Na}^+ \))**: Sodium has a larger ionic radius compared to silver and titanium. Thus, it has the least polarizing power.
- **Silver ion (\( \text{Ag}^+ \))**: Silver has a smaller ionic radius than sodium and has a pseudo-noble gas configuration, which contributes to its relatively higher polarizing power compared to sodium.
- **Titanium ion (\( \text{Ti}^+ \))**: Titanium has a smaller ionic radius than both sodium and silver, and it is also a transition metal, which generally leads to higher polarizing power due to its charge density.

3. **Arranging in Order**:
- Based on the above analysis, we can arrange the cations in order of increasing polarizing power:
- \( \text{Na}^+ \) (least polarizing power)
- \( \text{Ag}^+ \)
- \( \text{Ti}^+ \) (most polarizing power)

4. **Final Order**:
- Therefore, the increasing order of polarizing power is:
\[ \text{Na}^+ < \text{Ag}^+ < \text{Ti}^+ \]