AP EAMCET · Chemistry · Structure of Atom

The ions \(\mathrm{S}^{2-}, \mathrm{Cl}^{-}, \mathrm{K}^{+}, \mathrm{Ca}^{2+}\) are isoelectronic. Their ionic radii show

A a decrease from \(\mathrm{S}^{2-}\) to \(\mathrm{Cl}^{-}\)and then increase from \(\mathrm{K}^{+}\)to \(\mathrm{Ca}^{2+}\)
B an increase from \(\mathrm{S}^{2-}\) to \(\mathrm{Cl}^{-}\)and then decrease from \(\mathrm{K}^{+}\)to \(\mathrm{Ca}^{2+}\)
C a significant decrease from \(\mathrm{S}^{2-}\) to \(\mathrm{Ca}^{2+}\)
D a significant increase from \(\mathrm{S}^{2-}\) to \(\mathrm{Ca}^{2+}\)

Verified Solution

Answer & Solution

Correct Answer

(C) a significant decrease from \(\mathrm{S}^{2-}\) to \(\mathrm{Ca}^{2+}\)

Step-by-step Solution

Detailed explanation

For isoelectronic species, the ionic radii decrease with increase in nuclear charge. So, the cation with greater + ve charge i.e. \(\mathrm{Ca}^{2+}\) will have smaller radius and the anion with greater - ve charge i.e. \(\mathrm{S}^{2-}\) will have a larger radius. \(\because\)…

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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