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 understand the concept of polarizing power and the factors that affect it.

### Step-by-Step Solution:

1. **Define Polarizing Power**:
Polarizing power refers to the ability of a cation to distort the electron cloud of an anion. The greater the polarizing power, the more the cation can polarize the anion.

2. **Factors Affecting Polarizing Power**:
- **Charge of the Cation**: Higher charge increases polarizing power.
- **Size of the Cation**: Smaller cations have higher charge density, which increases polarizing power.
- **Electronic Configuration**: Cations with pseudo noble gas configurations can have higher polarizing power.

3. **Analyze Each Cation**:
- **\( \text{Ag}^+ \)**: Silver has an atomic number of 47. When it loses one electron to form \( \text{Ag}^+ \), it has a pseudo noble gas configuration (46 electrons). This gives it a relatively high polarizing power.
- **\( \text{Na}^+ \)**: Sodium has an atomic number of 11. When it loses one electron, it has 10 electrons, resembling the noble gas configuration of neon. It is also relatively small in size.
- **\( \text{Ti}^+ \)**: Titanium has an atomic number of 22. When it loses electrons to form \( \text{Ti}^+ \), it is larger than both \( \text{Ag}^+ \) and \( \text{Na}^+ \) and has a lower charge density compared to \( \text{Ag}^+ \).

4. **Compare the Polarizing Powers**:
- **Highest Polarizing Power**: \( \text{Ag}^+ \) due to its pseudo noble gas configuration and relatively small size.
- **Middle Polarizing Power**: \( \text{Na}^+ \) due to its small size and noble gas configuration.
- **Lowest Polarizing Power**: \( \text{Ti}^+ \) due to its larger size and lower charge density.

5. **Final Order**:
Arranging them in increasing order of polarizing power, we get:
\[ \text{Ti}^+ < \text{Na}^+ < \text{Ag}^+ \]

### Conclusion:
The increasing order of polarizing power for the species \( \text{Ag}^+, \text{Ti}^+, \text{Na}^+ \) is:
\[ \text{Ti}^+ < \text{Na}^+ < \text{Ag}^+ \]