Correct order of ionic Radii is :-

Options

A. `Yb^(+3) lt Pm ^(+3) lt La^(+3) lt Ce^(+3)`
B. `Ce^(+3) lt Yb^(+3) lt Pm^(+3) lt La^(+3)`
C. `Yb^(+3) lt Pm^(+3) lt Ce^(+3) lt La^(+3)`
D. `Pm^(+3) lt La^(+3) lt Ce^(+3) lt Yb^(+3)`

Answer

To determine the correct order of ionic radii for the elements in the lanthanoid series, we need to consider the trend of ionic sizes as we move across the series. Here’s a step-by-step solution:

### Step 1: Identify the Elements
The elements given in the question are:
- Ytterbium (Yb)
- Promethium (Pm)
- Cerium (Ce)
- Lanthanum (La)

### Step 2: Understand the Lanthanoid Series
The lanthanoid series consists of 15 elements from Lanthanum (La, Z=57) to Lutetium (Lu, Z=71). The series includes:
- La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu

### Step 3: Recognize the Trend in Ionic Radii
As we move from left to right across the lanthanoid series, the ionic radii decrease. This is primarily due to the phenomenon known as "lanthanoid contraction," where the increase in nuclear charge is not effectively shielded by the f-electrons, leading to a stronger attraction between the nucleus and the electrons, and thus a smaller ionic radius.

### Step 4: Determine the Ionic Radii in +3 Oxidation State
For the +3 oxidation state of the elements:
- Lanthanum (La³⁺) has the largest ionic radius.
- Cerium (Ce³⁺) is smaller than La³⁺.
- Promethium (Pm³⁺) is smaller than Ce³⁺.
- Ytterbium (Yb³⁺) has the smallest ionic radius among these.

### Step 5: Write the Correct Order
Based on the above analysis, the correct order of ionic radii from largest to smallest is:
1. La³⁺ (Lanthanum)
2. Ce³⁺ (Cerium)
3. Pm³⁺ (Promethium)
4. Yb³⁺ (Ytterbium)

Thus, the correct order of ionic radii is:
**La³⁺ > Ce³⁺ > Pm³⁺ > Yb³⁺**