Which of the following lantanide ion is paramagnetic ?

Options

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

Explanation

To determine which lanthanide ion is paramagnetic from the given options (Ce^4+, Yb^2+, Lu^3+, and Eu^2+), we need to analyze the electronic configurations of each ion and identify the presence of unpaired electrons.

### Step-by-Step Solution:

1. **Identify the Electronic Configuration of Each Element:**
- **Cerium (Ce)**: The electronic configuration is [Xe] 4f^1 5d^1 6s^2.
- **Ytterbium (Yb)**: The electronic configuration is [Xe] 4f^14 6s^2.
- **Lutetium (Lu)**: The electronic configuration is [Xe] 4f^14 5d^1 6s^2.
- **Europium (Eu)**: The electronic configuration is [Xe] 4f^7 6s^2.

2. **Adjust for the Given Ion Charges:**
- **Ce^4+**: To find the configuration, we remove 4 electrons (2 from 6s and 2 from 5d and 4f). The configuration becomes [Xe].
- **Yb^2+**: Remove 2 electrons from the 6s orbital. The configuration remains [Xe] 4f^14.
- **Lu^3+**: Remove 3 electrons (2 from 6s and 1 from 5d). The configuration becomes [Xe] 4f^14.
- **Eu^2+**: Remove 2 electrons from the 6s orbital. The configuration becomes [Xe] 4f^7.

3. **Determine the Number of Unpaired Electrons:**
- **Ce^4+**: [Xe] has no unpaired electrons (all are paired).
- **Yb^2+**: [Xe] 4f^14 has no unpaired electrons (all are paired).
- **Lu^3+**: [Xe] 4f^14 has no unpaired electrons (all are paired).
- **Eu^2+**: [Xe] 4f^7 has 7 unpaired electrons (1 unpaired electron in each of the 7 f-orbital slots).

4. **Conclusion:**
- Since Eu^2+ has unpaired electrons, it is paramagnetic. The other ions (Ce^4+, Yb^2+, and Lu^3+) are diamagnetic because they have all paired electrons.

### Final Answer:
The lanthanide ion that is paramagnetic is **Eu^2+**.