Question

Which of the following ions are diamagnetic?

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

Hint:

Lanthanide ions with completely empty or completely filled 4f orbitals are diamagnetic. Check oxidation states and resulting electron configurations!

Answer 1

The Correct Option is C

Diamagnetism is exhibited by species with all electrons paired (i.e., no unpaired electrons).

Let’s analyze electron configurations: 

• \( \mathrm{La} \): Atomic number 57. Configuration: [Xe] 5d\(^{1}\)6s\(^{2}\) 
  \( \Rightarrow \mathrm{La^{3+}} \): Loses 3 electrons → [Xe] (no unpaired electrons) → Diamagnetic
• \( \mathrm{Ce} \): Atomic number 58. Configuration: [Xe] 4f\(^{1}\)5d\(^{1}\)6s\(^{2}\) 
  \( \Rightarrow \mathrm{Ce^{4+}} \): Loses 4 electrons → [Xe] (no unpaired electrons) → Diamagnetic
• \( \mathrm{Ce^{2+}} \): Configuration after losing 2 electrons = [Xe] 4f\(^{2}\) → 2 unpaired electrons → Paramagnetic
• \( \mathrm{Lu^{3+}} \): Atomic number 71. Configuration: [Xe] 4f\(^{14}\)5d\(^{1}\)6s\(^{2}\), loses 3e⁻ → [Xe] 4f\(^{14}\) (completely filled) → Diamagnetic
• \( \mathrm{Yb^{3+}} \): Atomic number 70 → [Xe] 4f\(^{13}\), loses 3e⁻ → 4f\(^{13}\) → one unpaired → Paramagnetic
• \( \mathrm{Lu^{2+}} \): Configuration = [Xe] 4f\(^{14}\)5d\(^{1}\) (one unpaired d-electron) → Paramagnetic
• \( \mathrm{Yb^{2+}} \): Configuration = [Xe] 4f\(^{14}\) (completely filled f-shell) → Diamagnetic

Conclusion: Only \( \mathrm{La^{3+}} \) and \( \mathrm{Ce^{4+}} \) are both diamagnetic.