The paramagnetic lanthanoid ion among the following is

Options

A. Ce^(4+)`
B. `Yb^(2+)`
C. `Lu^(3+)`
D. `Sm^(2+)`

Answer

To determine which lanthanoid ion is paramagnetic among the given options, we need to analyze the electronic configurations of each ion and check for unpaired electrons.

### Step-by-Step Solution:

1. **Identify the Lanthanoid Ions**: The given lanthanoid ions are:
- Ce⁴⁺ (Cerium)
- Yb²⁺ (Ytterbium)
- Lu³⁺ (Lutetium)
- Sm²⁺ (Samarium)

2. **Determine the Atomic Numbers and Electronic Configurations**:
- **Cerium (Ce)**: Atomic number 58
- Electronic configuration: [Xe] 4f¹ 5d¹ 6s²
- For Ce⁴⁺: Remove 4 electrons → [Xe] 4f⁰ 5d⁰ 6s⁰ (Diamagnetic)

- **Ytterbium (Yb)**: Atomic number 70
- Electronic configuration: [Xe] 4f¹⁴ 6s²
- For Yb²⁺: Remove 2 electrons → [Xe] 4f¹⁴ 6s⁰ (Diamagnetic)

- **Lutetium (Lu)**: Atomic number 71
- Electronic configuration: [Xe] 4f¹⁴ 5d¹ 6s²
- For Lu³⁺: Remove 3 electrons → [Xe] 4f¹⁴ 5d⁰ 6s⁰ (Diamagnetic)

- **Samarium (Sm)**: Atomic number 62
- Electronic configuration: [Xe] 4f⁶ 6s²
- For Sm²⁺: Remove 2 electrons → [Xe] 4f⁶ 6s⁰ (Paramagnetic)

3. **Analyze the Electronic Configurations**:
- **Ce⁴⁺**: All orbitals are filled → Diamagnetic
- **Yb²⁺**: All orbitals are filled → Diamagnetic
- **Lu³⁺**: All orbitals are filled → Diamagnetic
- **Sm²⁺**: 4f subshell is partially filled (4f⁶) → Paramagnetic

4. **Conclusion**: Among the given lanthanoid ions, only **Sm²⁺** has unpaired electrons, making it paramagnetic.

### Final Answer:
The paramagnetic lanthanoid ion among the following is **Sm²⁺**.

---