The correct order of ionic radii `Y^(3+)` , `La^(3+)` , `Eu^(3+)` and `Lu^(3+)` is `(AT. No : Y = 39, La = 57, Eu = 63, Lu = 71)`

Options

A. `Lu^(3+) lt Eu^(3+) lt La^(3+) lt Y^(3+)`
B. `La^(3+) lt Eu^(3+) lt Lu^(3+) lt Y^(3+)`
C. `Y^(3+) lt La^(3+) lt Eu^(3+) lt Lu^(3+)`
D. `Y^(3+) lt Lu^(3+) lt Eu^(3+) lt La^(3+)`

Explanation

To determine the correct order of ionic radii for the ions \( Y^{3+} \), \( La^{3+} \), \( Eu^{3+} \), and \( Lu^{3+} \), we need to consider the trends in ionic radii among these elements, particularly focusing on the effects of lanthanide contraction.

### Step-by-Step Solution:

1. **Identify the Elements and Their Ionic Forms**:
- We have the following ions: \( Y^{3+} \) (Yttrium), \( La^{3+} \) (Lanthanum), \( Eu^{3+} \) (Europium), and \( Lu^{3+} \) (Lutetium).
- Their atomic numbers are:
- Yttrium (Y) = 39
- Lanthanum (La) = 57
- Europium (Eu) = 63
- Lutetium (Lu) = 71

2. **Understand the Concept of Ionic Radii**:
- Ionic radius generally decreases across a period and increases down a group in the periodic table.
- However, for lanthanides, there is a phenomenon known as **lanthanide contraction**, where the ionic radii decrease with increasing atomic number due to the poor shielding effect of the f-electrons.

3. **Analyze the Ionic Sizes**:
- \( Y^{3+} \) is not a lanthanide but is in the same group as Lanthanum. It has a larger ionic radius compared to \( La^{3+} \) because it has fewer f-electrons and does not experience lanthanide contraction.
- \( La^{3+} \) has a larger ionic radius than the later lanthanides due to the lack of significant lanthanide contraction affecting it.
- \( Eu^{3+} \) and \( Lu^{3+} \) are both lanthanides, and due to lanthanide contraction, \( Lu^{3+} \) will have a smaller ionic radius than \( Eu^{3+} \).

4. **Establish the Order**:
- Based on the above analysis, the order of ionic radii from largest to smallest is:
- \( La^{3+} > Eu^{3+} > Lu^{3+} > Y^{3+} \)

5. **Final Arrangement**:
- Rearranging the ionic sizes, we get:
- \( Y^{3+} < Lu^{3+} < Eu^{3+} < La^{3+} \)

### Conclusion:
Thus, the correct order of ionic radii is:
\[ Y^{3+} < Lu^{3+} < Eu^{3+} < La^{3+} \]