Which of the following lantanide ion is paramagnetic ?

Options

A. `La^(3+)`
B. `Ce^(4+)`
C. `Gd^(3+)`
D. `Lu^(3+)`

Answer

To determine which of the following lanthanide ions is paramagnetic, we need to analyze the electronic configurations of the given lanthanide ions and check for unpaired electrons. Paramagnetic substances have unpaired electrons, while diamagnetic substances have all electrons paired.

### Step-by-Step Solution:

1. **Identify the Lanthanide Ions**: The lanthanide series consists of elements with atomic numbers from 57 (Lanthanum) to 71 (Lutetium). The ions we will consider are La³⁺, Ce⁴⁺, Gd³⁺, and Lu³⁺.

2. **Write the General Electronic Configuration**: The general electronic configuration for lanthanides is:
\[ [Xe] 4f^{1-14} 5d^{0-1} 6s^2 \]
Here, [Xe] represents the electron configuration of xenon.

3. **Analyze Each Ion**:
- **La³⁺ (Lanthanum 3+)**:
- Atomic number: 57
- Electronic configuration: \([Xe] 5d^1 6s^2\)
- For La³⁺, we remove 3 electrons (1 from 5d and 2 from 6s):
\[ \text{La}^{3+} = [Xe] 4f^0 \]
- All electrons are paired → **Diamagnetic**.

- **Ce⁴⁺ (Cerium 4+)**:
- Atomic number: 58
- Electronic configuration: \([Xe] 4f^2 5d^0 6s^2\)
- For Ce⁴⁺, we remove 4 electrons (2 from 4f and 2 from 6s):
\[ \text{Ce}^{4+} = [Xe] 4f^0 \]
- All electrons are paired → **Diamagnetic**.

- **Gd³⁺ (Gadolinium 3+)**:
- Atomic number: 64
- Electronic configuration: \([Xe] 4f^7 5d^1 6s^2\)
- For Gd³⁺, we remove 3 electrons (1 from 5d and 2 from 6s):
\[ \text{Gd}^{3+} = [Xe] 4f^7 \]
- The 4f subshell has 7 electrons, which means there are unpaired electrons → **Paramagnetic**.

- **Lu³⁺ (Lutetium 3+)**:
- Atomic number: 71
- Electronic configuration: \([Xe] 4f^{14} 5d^1 6s^2\)
- For Lu³⁺, we remove 3 electrons (1 from 5d and 2 from 6s):
\[ \text{Lu}^{3+} = [Xe] 4f^{14} \]
- All electrons are paired → **Diamagnetic**.

4. **Conclusion**: The only lanthanide ion that is paramagnetic is **Gd³⁺**.

### Final Answer:
**Gd³⁺ (Gadolinium 3+) is the paramagnetic lanthanide ion.**