Can you get this USNCO question?

Atomic structure and periodicityNational 2019

In which list are the ions ranked in order of increasing ionic radius?

17% of national qualifiers got this right

Explanation

draft

Ionic radius depends on both electron configuration (isoelectronic comparisons) and position in the group (period).

$\ce{K+}$ and $\ce{Ca^2+}$ are isoelectronic (both have the $\ce{Ar}$ core, 18 electrons). Since $\ce{Ca^2+}$ has more protons (20) pulling on the same electron shell than $\ce{K+}$ (19 protons), $\ce{Ca^2+}$ is smaller: $\ce{Ca^2+} < \ce{K+}$ .
Similarly, $\ce{Rb+}$ and $\ce{Sr^2+}$ are isoelectronic (both have the $\ce{Kr}$ core, 36 electrons). $\ce{Sr^2+}$ has more protons (38) than $\ce{Rb+}$ (37), so $\ce{Sr^2+} < \ce{Rb+}$ .
Down a group, ionic radius increases due to added electron shells, so $\ce{Ca^2+} < \ce{Sr^2+}$ (Group 2) and $\ce{K+} < \ce{Rb+}$ (Group 1).

Putting these relationships together using actual measured radii ( $\ce{Ca^2+} \approx 100$ pm, $\ce{Sr^2+} \approx 118$ pm, $\ce{K+} \approx 138$ pm, $\ce{Rb+} \approx 152$ pm):

$\ce{Ca^2+} < \ce{Sr^2+} < \ce{K+} < \ce{Rb+}$

This matches choice (C).

Assumes ionic radius depends only on group position (same charge groups compared separately) and ignores that higher charge for the same electron configuration shrinks the ion; incorrectly ranks $\ce{Rb+}$ before the $2+$ ions and swaps $\ce{Ca^2+}$ / $\ce{Sr^2+}$ position relative to $\ce{K+}$ .

Mixes up the isoelectronic pairing—compares $\ce{K+}$ to $\ce{Ca^2+}$ correctly (smaller charge = larger radius) but then incorrectly places $\ce{Rb+}$ before $\ce{Sr^2+}$ , forgetting that $\ce{Sr^2+}$ 's extra proton makes it smaller than $\ce{Rb+}$ , not larger.

Correctly uses isoelectronic comparisons (higher charge = smaller radius for same electron count) and group trends (radius increases down a group) to get $\ce{Ca^2+} < \ce{Sr^2+} < \ce{K+} < \ce{Rb+}$ .

Incorrectly interleaves the ions by treating $2+$ and $1+$ charges as if they alternate by period only, placing $\ce{K+}$ between $\ce{Ca^2+}$ and $\ce{Sr^2+}$ without properly comparing isoelectronic species; ignores that $\ce{Sr^2+}$ (Kr core) is smaller than $\ce{K+}$ ... actually reverses the correct $\ce{Sr^2+}<\ce{K+}$ relationship, showing confusion about which ions share electron configurations.

Concept · Periodic trends: ionic radius (isoelectronic series and group trends)