The calculated and observed magnetic moments (in B.M.) of aqua complex of a lanthanide ion are 0 and – 3.5 respectively. The lanthanide ion is -

CONCEPT:

Magnetic Moments of Lanthanide Ions

• Magnetic moments of lanthanide ions arise from both spin and orbital contributions due to their unpaired 4f electrons.
• Magnetic moments can be calculated theoretically using the formula: \(\mu_{\text{calc}} = \sqrt{n(n + 2)}\)
  where n is the number of unpaired electrons.
• Observed magnetic moments can differ due to factors such as ligand field effects and temperature.

EXPLANATION:

• The calculated magnetic moment of 0 indicates a fully paired electronic configuration.
• The observed magnetic moment of -3.5 B.M. suggests interaction effects or contributions not captured by simple calculations.
• Among the lanthanide ions listed, the specific case where the calculated moment is 0 and the observed moment is significantly different (negative in this case due to complex factors) is characteristic of Europium ( \(\text{Eu}^{3+}\)).
  • Europium in its \( \text{Eu}^{3+}\) state has a 4f⁶ electronic configuration, typically leading to a lower observed moment due to crystal field and spin-orbit coupling effects.
  • The observed magnetic moment for Eu³⁺ is due to the populated excited state.

The correct answer is: 3) Eu³⁺