KCET · Chemistry · Aldehydes and Ketones

The correct arrangement for the ions in the increasing order of their radii is

A \( \mathrm{Ca}^{2+}, \mathrm{K}^{+}, \mathrm{S}^{2-} \)
B \( \mathrm{Ol}^{-}, \mathrm{F}^{-}, \mathrm{S}^{2-} \)
C \( \mathrm{Na}^{+}, \mathrm{Cl}^{-}, \mathrm{Ca}^{2+} \)
D \( N a^{+}, A l^{3+}, B e^{2+} \)

Verified Solution

Answer & Solution

Correct Answer

(A) \( \mathrm{Ca}^{2+}, \mathrm{K}^{+}, \mathrm{S}^{2-} \)

Step-by-step Solution

Detailed explanation

The number of electrons and the group number of the given species are given below:
\(\begin{array}{|l|l|l|l|l|}
\hline Ions & At. No & Group & Period & No. of e^{-} s \\
\hline S^{2-} & 16 & 16 & 3 & 18 \\
\hline K^{+} & 13 & 1 & 4 & 18 \\
\hline C a^{2+} & 20 & 2 & 4 & 18 \\
\hline
\end{array}\)
There ions are isoelectronic, therefore \( S^{2-} \) have greater size due to higher effective nuclear charge \( \left(Z_{\text {eff }}\right) \) followed by
\( \mathrm{K}^{+} \)then \( \mathrm{Ca}^{2+} \) Hence, the correct order of decreasing ionic radii is \( \mathrm{Ca}^{2+} < \mathrm{K}^{+} < \mathrm{S}^{2-} \)

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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