Which of the following cations posses neither noble gas nor pseudo noble gas configurations?
(i) `Bi^(3+)` (ii) `Pb^(2+)`
(iii) `Sn^(2+)` (iv) `Tl^(+)`

Options

A. (ii), (iii)
B. (i), (iv)
C. (i), (ii), (iii)
D. (i), (ii), (iii), (iv)

Explanation

To determine which of the given cations (`Bi^(3+)`, `Pb^(2+)`, `Sn^(2+)`, `Tl^(+)`) possess neither noble gas nor pseudo noble gas configurations, we need to analyze the electronic configurations of each cation.

### Step 1: Identify the electronic configurations of the neutral atoms

1. **Bismuth (Bi)**: Atomic number = 83
- Electronic configuration: `[Xe] 4f^14 5d^10 6s^2 6p^3`

2. **Lead (Pb)**: Atomic number = 82
- Electronic configuration: `[Xe] 4f^14 5d^10 6s^2 6p^2`

3. **Tin (Sn)**: Atomic number = 50
- Electronic configuration: `Kr 4d^10 5s^2 5p^2`

4. **Thallium (Tl)**: Atomic number = 81
- Electronic configuration: `[Xe] 4f^14 5d^10 6s^2 6p^1`

### Step 2: Determine the electronic configurations of the cations

1. **Bismuth (Bi^(3+))**:
- Remove 3 electrons from the outermost shell:
- Configuration: `Bi^(3+)`: `[Xe] 4f^14 5d^10 6s^2 6p^0` (removing 3 electrons from 6s and 6p)

2. **Lead (Pb^(2+))**:
- Remove 2 electrons from the outermost shell:
- Configuration: `Pb^(2+)`: `[Xe] 4f^14 5d^10 6s^2 6p^0` (removing 2 electrons from 6p)

3. **Tin (Sn^(2+))**:
- Remove 2 electrons from the outermost shell:
- Configuration: `Sn^(2+)`: `[Kr] 4d^10 5s^2 5p^0` (removing 2 electrons from 5p)

4. **Thallium (Tl^(+))**:
- Remove 1 electron from the outermost shell:
- Configuration: `Tl^(+)`: `[Xe] 4f^14 5d^10 6s^2 6p^0` (removing 1 electron from 6p)

### Step 3: Analyze the configurations

- **Noble gas configuration**: A cation has a noble gas configuration if its electronic configuration matches that of a noble gas (e.g., `Ne`, `Ar`, `Kr`, `Xe`).
- **Pseudo noble gas configuration**: A cation has a pseudo noble gas configuration if it has a full outer shell (s and p) plus a filled d subshell.

Now we check each cation:

1. **Bi^(3+)**: `[Xe] 4f^14 5d^10 6s^2 6p^0` - Matches noble gas configuration (Xe).
2. **Pb^(2+)**: `[Xe] 4f^14 5d^10 6s^2 6p^0` - Matches noble gas configuration (Xe).
3. **Sn^(2+)**: `[Kr] 4d^10 5s^2 5p^0` - Matches pseudo noble gas configuration (filled d subshell).
4. **Tl^(+)**: `[Xe] 4f^14 5d^10 6s^2 6p^0` - Matches noble gas configuration (Xe).

### Conclusion

None of the cations `Bi^(3+)`, `Pb^(2+)`, `Sn^(2+)`, and `Tl^(+)` possess neither noble gas nor pseudo noble gas configurations.

### Final Answer
All of the given cations possess either noble gas or pseudo noble gas configurations.