Q.For each of the following pairs, indicate which of the two species is of large size:
a. Fe²⁺ or Fe³⁺
b. Mg²⁺ or Ca²⁺
Step 1a. Compare Fe²⁺ and Fe³⁺. Both come from the same element (same nuclear charge, Z=26), but Fe³⁺ has one fewer electron than Fe²⁺. Fewer electrons means less electron-electron repulsion (less internal shielding), so the remaining electrons in Fe³⁺ feel a LARGER effective nuclear charge and are pulled in more tightly — making Fe³⁺ SMALLER than Fe²⁺ (section 7.5.2.2's cation rule).
Step 2a. Answer. Fe²⁺ is larger than Fe³⁺.
Step 1b. Compare Mg²⁺ and Ca²⁺. Both carry the same +2 charge, but Mg is period 3 and Ca is period 4 — Ca²⁺ retains an extra electron shell compared to Mg²⁺ (down-group radius increase, section 7.5.2.1/7.5.2.2), even after both have lost 2 electrons.
Step 2b. Answer. Ca²⁺ is larger than Mg²⁺.
a. Fe²⁺ (larger) vs Fe³⁺ (smaller) — fewer electrons removed means less shielding lost, less effective-nuclear-charge increase. b. Ca²⁺ (larger) vs Mg²⁺ (smaller) — Ca sits one period below Mg, retaining an extra shell even as the same-charge ion.
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