Question

The pair(s) of diamagnetic ions is (are):

• A. \( \text{La}^{3+}, \, \text{Ce}^{4+} \)
• B. \( \text{Yb}^{2+}, \, \text{Lu}^{3+} \)
• C. \( \text{La}^{2+}, \, \text{Ce}^{3+} \)
• D. \( \text{Yb}^{3+}, \, \text{Lu}^{2+} \)

Hint:

To determine if an ion is paramagnetic or diamagnetic, calculate its electron configuration and count unpaired electrons. Diamagnetism requires all electrons to be paired.

Answer 1

The Correct Option is A, B

Step 1: Understand magnetic behavior 
- An ion is diamagnetic if it has no unpaired electrons.
- It is paramagnetic if one or more unpaired electrons are present. 
Step 2: Electron configurations and unpaired electrons

• \( \text{La}^{3+} \): Atomic number 57. Electronic configuration: \([ \text{Xe} ]\, 4f^0 \, 5d^0 \, 6s^0\) → 0 unpaired electrons → Diamagnetic.
• \( \text{Ce}^{4+} \): Atomic number 58. Configuration: \([ \text{Xe} ]\, 4f^0 \, 5d^0 \, 6s^0\) → 0 unpaired electrons → Diamagnetic.
• \( \text{Yb}^{2+} \): Atomic number 70. Configuration: \([ \text{Xe} ]\, 4f^{14} \, 5d^0 \, 6s^0\) → 0 unpaired electrons → Diamagnetic.
• \( \text{Lu}^{3+} \): Atomic number 71. Configuration: \([ \text{Xe} ]\, 4f^{14} \, 5d^0 \, 6s^0\) → 0 unpaired electrons → Diamagnetic.
• \( \text{La}^{2+} \): Has configuration \([ \text{Xe} ]\, 4f^0 \, 5d^1 \, 6s^0\) → 1 unpaired electron → Paramagnetic.
• \( \text{Ce}^{3+} \): Configuration: \([ \text{Xe} ]\, 4f^1 \, 5d^0 \, 6s^0\) → 1 unpaired electron → Paramagnetic.
• \( \text{Yb}^{3+} \): Configuration: \([ \text{Xe} ]\, 4f^{13} \, 5d^0 \, 6s^0\) → 1 unpaired electron → Paramagnetic.
• \( \text{Lu}^{2+} \): Configuration: \([ \text{Xe} ]\, 4f^{14} \, 5d^1 \, 6s^0\) → 1 unpaired electron → Paramagnetic.

Conclusion:

• (A) \( \text{La}^{3+} \), \( \text{Ce}^{4+} \): Both diamagnetic → Correct.
• (B) \( \text{Yb}^{2+} \), \( \text{Lu}^{3+} \): Both diamagnetic → Correct.
• (C), (D): Include paramagnetic ions → Incorrect.

Final Answer: \( \boxed{\text{A, B}} \)