Question

How many of the following lanthanides ion are paramagnetic and have ionic size smaller than $\text{Eu}^{3+}$?

$\text{Ce}^{3+}$, $\text{Pr}^{3+}$, $\text{Pm}^{3+}$, $\text{Yb}^{3+}$, $\text{Lu}^{3+}$, $\text{Ho}^{3+}$, $\text{Gd}^{3+}$, $\text{Dy}^{3+}$

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (B)

4

Answer 2

Paramagnetism in lanthanide ions arises from unpaired electrons in the 4f orbitals. Lanthanide contraction leads to a decrease in ionic size across the series.

The electronic configurations and number of unpaired electrons for the given ions are:

• $\text{Ce}^{3+}$: $[Xe] 4f^1$ (1 unpaired electron) - Paramagnetic
• $\text{Pr}^{3+}$: $[Xe] 4f^3$ (3 unpaired electrons) - Paramagnetic
• $\text{Pm}^{3+}$: $[Xe] 4f^5$ (5 unpaired electrons) - Paramagnetic
• $\text{Eu}^{3+}$: $[Xe] 4f^6$ (6 unpaired electrons) - Paramagnetic
• $\text{Gd}^{3+}$: $[Xe] 4f^7$ (7 unpaired electrons) - Paramagnetic
• $\text{Dy}^{3+}$: $[Xe] 4f^9$ (5 unpaired electrons) - Paramagnetic
• $\text{Ho}^{3+}$: $[Xe] 4f^{10}$ (4 unpaired electrons) - Paramagnetic
• $\text{Yb}^{3+}$: $[Xe] 4f^{13}$ (1 unpaired electron) - Paramagnetic
• $\text{Lu}^{3+}$: $[Xe] 4f^{14}$ (0 unpaired electrons) - Diamagnetic

All ions except $\text{Lu}^{3+}$ are paramagnetic.

Ionic size decreases with increasing atomic number due to lanthanide contraction. $\text{Eu}$ has an atomic number of 63. Ions with atomic numbers greater than 63 will have smaller ionic sizes than $\text{Eu}^{3+}$.

• Ions with atomic numbers less than 63: $\text{Ce}$ (58), $\text{Pr}$ (59), $\text{Pm}$ (61) - larger than $\text{Eu}^{3+}$.
• Ions with atomic numbers greater than 63: $\text{Gd}$ (64), $\text{Dy}$ (66), $\text{Ho}$ (67), $\text{Yb}$ (70), $\text{Lu}$ (71) - smaller than $\text{Eu}^{3+}$.

We need ions that are both paramagnetic and smaller than $\text{Eu}^{3+}$.

• Paramagnetic ions with atomic numbers greater than 63 are:
  • $\text{Gd}^{3+}$ (Z=64)
  • $\text{Dy}^{3+}$ (Z=66)
  • $\text{Ho}^{3+}$ (Z=67)
  • $\text{Yb}^{3+}$ (Z=70)

Therefore, there are 4 such ions.