Question

The correct order of ionic radii of Ce, La, Pm and Yb in \( +3 \) oxidation state is

• A. \( \mathrm{La^{3+} < Pm^{3+} < Ce^{3+} < Yb^{3+}} \)
• B. \( \mathrm{La^{3+} < Ce^{3+} < Pm^{3+} < Yb^{3+}} \)
• C. \( \mathrm{Yb^{3+} < Ce^{3+} < Pm^{3+} < La^{3+}} \)
• D. \( \mathrm{Yb^{3+} < Pm^{3+} < Ce^{3+} < La^{3+}} \)
• E. \( \mathrm{La^{3+} > Pm^{3+} > Ce^{3+} > Yb^{3+}} \)

Hint:

For \( \mathrm{Ln^{3+}} \) ions, size decreases steadily across the lanthanoid series due to lanthanoid contraction. Left-side lanthanoids are larger, right-side lanthanoids are smaller.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question is about the trend of ionic radii in the lanthanide series. The key concept here is the "lanthanide contraction".
Step 2: Key Formula or Approach:
Lanthanide Contraction: As we move across the lanthanide series from left to right (from Lanthanum to Lutetium), the atomic and ionic radii of the elements in the same oxidation state (e.g., +3) show a steady decrease. This is because, with each step, a proton is added to the nucleus and an electron is added to the 4f subshell. The 4f electrons have very poor shielding effect. Consequently, the effective nuclear charge experienced by the outermost electrons increases, pulling the electron cloud closer to the nucleus and causing the radius to decrease.
Step 3: Detailed Explanation:
The elements given are Lanthanum (La), Cerium (Ce), Promethium (Pm), and Ytterbium (Yb). Their atomic numbers are:
- La (Z=57)
- Ce (Z=58)
- Pm (Z=61)
- Yb (Z=70)
These elements are all part of the lanthanide series (or La is the precursor). The order of increasing atomic number is La<Ce<Pm<Yb.
According to the lanthanide contraction, the ionic radius for the M\(^{3+}\) ions should decrease as the atomic number increases.
Therefore, the order of decreasing ionic radii should be:
\[ \text{La}^{3+}>\text{Ce}^{3+}>\text{Pm}^{3+}>\text{Yb}^{3+} \] This means the order of increasing ionic radii will be the reverse:
\[ \text{Yb}^{3+}<\text{Pm}^{3+}<\text{Ce}^{3+}<\text{La}^{3+} \] Let's check the options:
(A) Incorrect order.
(B) Incorrect order.
(C) Incorrect order of Ce and Pm.
(D) \( \text{Yb}^{3+}<\text{Pm}^{3+}<\text{Ce}^{3+}<\text{La}^{3+} \). This matches our derived order.
(E) Incorrect inequality signs for the stated order.
Step 4: Final Answer:
The correct order of increasing ionic radii is \( \text{Yb}^{3+}<\text{Pm}^{3+}<\text{Ce}^{3+}<\text{La}^{3+} \). This corresponds to option (D).