In which of the following 'd' subshells are degenerate

Options

A. `Cu_((aq))^(2+)`
B. `Fe_((aq))^(2+)`
C. `Fe_((aq))^(3+)`
D. `Cu_((aq))^(1+)`

Answer

To determine which of the given 'd' subshells are degenerate, we need to analyze the electronic configurations of the ions provided in the question: Cu²⁺, Fe²⁺, Fe³⁺, and Cu¹⁺.

### Step-by-step Solution:

1. **Identify the Electronic Configurations**:
- **Cu²⁺**: The atomic number of copper (Cu) is 29. The electronic configuration of neutral Cu is:
\[ \text{Cu: } 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^1 \]
For Cu²⁺, we remove two electrons (one from 4s and one from 3d):
\[ \text{Cu}^{2+}: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^9 \]

- **Fe²⁺**: The atomic number of iron (Fe) is 26. The electronic configuration of neutral Fe is:
\[ \text{Fe: } 1s^2 2s^2 2p^6 3s^2 3p^6 3d^6 4s^2 \]
For Fe²⁺, we remove two electrons (from 4s):
\[ \text{Fe}^{2+}: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^6 \]

- **Fe³⁺**: For Fe³⁺, we remove one more electron from 3d:
\[ \text{Fe}^{3+}: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 \]

- **Cu¹⁺**: For Cu¹⁺, we remove one electron from 4s:
\[ \text{Cu}^{1+}: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} \]

2. **Analyze the 'd' Subshells**:
- **Cu²⁺ (3d⁹)**: Not degenerate (one vacancy).
- **Fe²⁺ (3d⁶)**: Not degenerate (four vacancies).
- **Fe³⁺ (3d⁵)**: Not degenerate (five vacancies).
- **Cu¹⁺ (3d¹⁰)**: Degenerate (completely filled).

3. **Conclusion**:
The only 'd' subshell that is degenerate is in **Cu¹⁺**, where the 3d subshell is completely filled (3d¹⁰).

### Final Answer:
The 'd' subshell that is degenerate is in **Cu¹⁺**.