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: Identify the series involved.
The ions \[ \mathrm{La^{3+},\ Ce^{3+},\ Pm^{3+},\ Yb^{3+}} \] belong to the lanthanoid series.
These elements show a regular trend in ionic size across the series.

Step 2: Recall the concept of lanthanoid contraction.
Across the lanthanoid series, from left to right, the ionic radii of \( \mathrm{Ln^{3+}} \) ions gradually decrease.
This decrease is called lanthanoid contraction.

Step 3: Explain why the contraction occurs.
As atomic number increases, more protons are added to the nucleus.
Although electrons are also added, they enter the \( 4f \)-subshell, which shields nuclear charge very poorly.
As a result, effective nuclear charge increases and the ionic size decreases.

Step 4: Arrange the given ions according to their positions in the series.
Among the given ions: \[ \mathrm{La^{3+}} \] comes first, then \[ \mathrm{Ce^{3+}}, \] then \[ \mathrm{Pm^{3+}}, \] and finally \[ \mathrm{Yb^{3+}} \] comes much later in the series.

Step 5: Use lanthanoid contraction to compare sizes.
Since ionic radii decrease from left to right in the lanthanoid series: \[ \mathrm{La^{3+}} \] will be the largest, and \[ \mathrm{Yb^{3+}} \] will be the smallest.
Thus, the decreasing order is: \[ \mathrm{La^{3+} > Ce^{3+} > Pm^{3+} > Yb^{3+}} \]

Step 6: Convert into increasing order to match options.
The options are written in increasing order.
So the correct increasing order is: \[ \mathrm{Yb^{3+} < Pm^{3+} < Ce^{3+} < La^{3+}} \]

Step 7: Final conclusion.
Hence, the correct order of ionic radii is \[ \boxed{\mathrm{Yb^{3+} < Pm^{3+} < Ce^{3+} < La^{3+}}} \] Therefore, the correct option is \[ \boxed{(4)} \]