Stability of trivalent and mono valent cation of group 13 (Boron family) will be in order :

Options

A. `Ga^(3+) gt ln^(3+) gt Tl^(3+)`
B. `Tl^(3+) gt ln^(3+) gt Ga^(3+)`
C. `Tl^(+) gt In^(+) gt Ga^(+)`
D. `ln^(3+) gt Ti^(3+) gt Ga^(3+)`

Answer

To determine the stability of the trivalent and monovalent cations of Group 13 (the Boron family), we need to analyze the oxidation states and the factors affecting their stability.

### Step-by-Step Solution:

1. **Identify the Group 13 Elements**:
The elements in Group 13 include Boron (B), Aluminum (Al), Gallium (Ga), Indium (In), and Thallium (Tl). However, we will focus on Gallium, Indium, and Thallium for this question.

2. **Oxidation States**:
The common oxidation states for these elements are +1 (monovalent) and +3 (trivalent). The +3 state arises from the loss of three electrons, while the +1 state arises from the loss of one electron.

3. **Electronic Configuration**:
The outer electronic configuration for these elements can be represented as ns²np¹. For Gallium, Indium, and Thallium, the outermost electrons are involved in bonding.

4. **Stability of +3 Oxidation State**:
The stability of the +3 oxidation state decreases down the group. This decrease in stability is primarily due to the **inert pair effect**, which refers to the reluctance of the s electrons to participate in bonding as we move down the group.

5. **Inert Pair Effect**:
As we go down the group, the presence of d and f orbitals in heavier elements (like Indium and Thallium) leads to poor shielding of the s electrons. Consequently, these s electrons are less likely to be involved in bonding, making the +3 oxidation state less stable.

6. **Order of Stability for +3 Oxidation State**:
Based on the above reasoning, the stability order for the +3 oxidation state is:
- Ga³⁺ > In³⁺ > Tl³⁺

7. **Stability of +1 Oxidation State**:
Conversely, the stability of the +1 oxidation state increases down the group. This is because the +1 state involves the loss of only one electron, which is more favorable as the inert pair effect becomes more pronounced.

8. **Order of Stability for +1 Oxidation State**:
For the +1 oxidation state, the stability order is:
- Tl¹⁺ > In¹⁺ > Ga¹⁺

9. **Final Conclusion**:
Therefore, the correct answers for the stability orders are:
- For +3 oxidation state: Ga³⁺ > In³⁺ > Tl³⁺ (Option A)
- For +1 oxidation state: Tl¹⁺ > In¹⁺ > Ga¹⁺ (Option C)