TS EAMCET · Chemistry · d and f Block Elements

The correct order of ionic radii of trivalent ions \(\mathrm{Y}^{3+}\), \(\mathrm{La}^{3+}, \mathrm{Eu}^{3+}\), and \(\mathrm{Lu}^{3+}\) is \[ (\mathrm{Y}=39, \mathrm{La}=57, \mathrm{Eu}=63, \mathrm{Lu}=71) \]

A \(\mathrm{Lu}^{3+} < \mathrm{Eu}^{3+} < \mathrm{La}^{3+} < \mathrm{Y}^{3+}\)
B \(\mathrm{La}^{3+} < \mathrm{Eu}^{3+} < \mathrm{Lu}^{3+} < \mathrm{Y}^{3+}\)
C \(\mathrm{Y}^{3+} < \mathrm{Lu}^{3+} < \mathrm{Eu}^{3+} < \mathrm{La}^{3+}\)
D \(\mathrm{Y}^{3+} < \mathrm{La}^{3+} < \mathrm{Eu}^{3+} < \mathrm{Lu}^{3+}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\mathrm{Y}^{3+} < \mathrm{Lu}^{3+} < \mathrm{Eu}^{3+} < \mathrm{La}^{3+}\)

Step-by-step Solution

Detailed explanation

La, Eu, Lu are the lanthanide elements and their trivalent cations are very stable. The ionic radii decreases along the period as the atomic weight lanthanide contraction increase. However, the change is in ionic radii is very small amount.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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