Stability of monovalent and trivalent cations of `Ga,In, Tl` lie in following sequence :

Options

A. `Ga^(3+) lt In^(3+) gt Tl^(3+)`
B. `Ga^(3+) gt In^(3+) gt Tl^(3+)`
C. `Tl^(oplus) gt In^(oplus) gt Ga^(oplus)`
D. `Ga^(oplus) lt In^(oplus) gt Tl^(oplus)`

Explanation

To determine the stability of monovalent (M^+) and trivalent (M^3+) cations of Gallium (Ga), Indium (In), and Thallium (Tl), we need to analyze the trends in the stability of these cations as we move down Group 13 of the periodic table.

### Step-by-Step Solution:

1. **Understanding the Group 13 Elements**:
- The elements in Group 13 include Boron (B), Aluminum (Al), Gallium (Ga), Indium (In), and Thallium (Tl).
- We are specifically interested in Ga, In, and Tl.

2. **Oxidation States**:
- Group 13 elements can exhibit +1 and +3 oxidation states.
- The +3 oxidation state is typically more stable for lighter elements (like Ga and In), while the +1 oxidation state becomes more stable for heavier elements (like Tl).

3. **Inert Pair Effect**:
- The inert pair effect refers to the tendency of the two electrons in the outermost s orbital to remain non-bonding (inert) as we move down the group.
- This effect becomes more pronounced for heavier elements, leading to a preference for the +1 oxidation state in Thallium (Tl).

4. **Stability of Trivalent Cations (M^3+)**:
- As we go down the group from Ga to Tl, the stability of the +3 oxidation state decreases.
- The order of stability for the +3 cations is:
- Ga^3+ > In^3+ > Tl^3+
- This means Ga^3+ is the most stable, followed by In^3+, and Tl^3+ is the least stable.

5. **Stability of Monovalent Cations (M^+)**:
- Conversely, the stability of the +1 oxidation state increases down the group.
- The order of stability for the +1 cations is:
- Tl^+ > In^+ > Ga^+
- This indicates that Tl^+ is the most stable, followed by In^+, and Ga^+ is the least stable.

6. **Final Sequence**:
- Therefore, the stability of the cations can be summarized as follows:
- For M^3+: Ga^3+ > In^3+ > Tl^3+
- For M^+: Tl^+ > In^+ > Ga^+

### Conclusion:
The stability of monovalent and trivalent cations of Ga, In, and Tl lies in the following sequences:
- For trivalent cations: Ga^3+ > In^3+ > Tl^3+
- For monovalent cations: Tl^+ > In^+ > Ga^+