The correct order of stability of `Al^(+) , Al^(+2) , Al^(+3)` is :

Options

A. `Al^(+3) gt Al^(+2) gt Al^(+)`
B. `Al^(+2) gt Al^(+3) gt Al^(+)`
C. `Al^(+2) lt Al^(+) gt Al^(3+)`
D. `Al^(+3) gt Al^(+) gt Al^(+2)`

Answer

To determine the correct order of stability of the aluminum cations \( \text{Al}^+, \text{Al}^{+2}, \text{Al}^{+3} \), we will analyze the electronic configurations of each cation and their stability based on the principles of electron configuration and stability associated with filled and half-filled orbitals.

### Step-by-Step Solution:

1. **Identify the Electronic Configuration of Aluminum:**
- Aluminum (Al) has an atomic number of 13. Its ground state electronic configuration is:
\[ \text{Al}: 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^1 \]

2. **Determine the Electronic Configuration of Each Cation:**
- **For \( \text{Al}^+ \):**
- Losing one electron (from the 3p orbital):
\[ \text{Al}^+: 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \]
- **For \( \text{Al}^{+2} \):**
- Losing two electrons (one from the 3s and one from the 3p orbital):
\[ \text{Al}^{+2}: 1s^2 \, 2s^2 \, 2p^6 \, 3s^1 \]
- **For \( \text{Al}^{+3} \):**
- Losing three electrons (two from the 3s and one from the 3p orbital):
\[ \text{Al}^{+3}: 1s^2 \, 2s^2 \, 2p^6 \]
- This configuration is the same as that of the noble gas Neon (Ne).

3. **Assess Stability Based on Electron Configuration:**
- **Stability of \( \text{Al}^{+3} \):**
- The \( \text{Al}^{+3} \) cation has achieved a noble gas configuration, which is highly stable.
- **Stability of \( \text{Al}^+ \) and \( \text{Al}^{+2} \):**
- \( \text{Al}^+ \) has a fully filled 3s orbital, which is more stable than \( \text{Al}^{+2} \) that has a half-filled 3s orbital.
- Thus, \( \text{Al}^+ \) is more stable than \( \text{Al}^{+2} \).

4. **Order of Stability:**
- Based on the analysis, the order of stability from most stable to least stable is:
\[ \text{Al}^{+3} > \text{Al}^+ > \text{Al}^{+2} \]

### Final Answer:
The correct order of stability of \( \text{Al}^+, \text{Al}^{+2}, \text{Al}^{+3} \) is:
\[ \text{Al}^{+3} > \text{Al}^+ > \text{Al}^{+2} \]