Question
Arrange Fe, Fe²⁺, and Fe³⁺ in increasing order of ionic/atomic radius, and explain your reasoning.
Solution — Step by Step
Iron (Fe) has atomic number 26. The electronic configurations are:
- Fe (neutral atom): [Ar] 3d⁶ 4s² — 26 electrons, 26 protons
- Fe²⁺: [Ar] 3d⁶ — 24 electrons, 26 protons (loses both 4s electrons)
- Fe³⁺: [Ar] 3d⁵ — 23 electrons, 26 protons (loses both 4s electrons + one 3d electron)
All three species have 26 protons in the nucleus — the same positive charge pulling electrons inward.
What changes is the number of electrons:
- Fe: 26 electrons
- Fe²⁺: 24 electrons
- Fe³⁺: 23 electrons
Fewer electrons with the same nuclear charge → stronger pull per electron → electrons held closer to the nucleus → smaller radius.
Fe has the most electrons, so the nuclear charge is most “diluted” among the electrons — radius is largest.
Fe³⁺ has the fewest electrons with the same nuclear charge — they’re held most tightly — radius is smallest.
| Species | Radius (pm) |
|---|---|
| Fe (metallic/atomic) | ~126 pm |
| Fe²⁺ | ~77 pm |
| Fe³⁺ | ~65 pm |
The jump from Fe to Fe²⁺ is dramatic because the entire 4s shell is removed, losing the outermost shell entirely. The jump from Fe²⁺ to Fe³⁺ is smaller — both have the same shells, but one fewer 3d electron reduces shielding slightly.
Why This Works
The size of an ion depends on the balance between nuclear attraction (inward pull) and electron-electron repulsion (outward push). When electrons are removed, the remaining electrons experience less shielding from each other and more pull from the same number of protons — they contract inward.
This is why cations are always smaller than their parent atoms, and why higher-charged cations of the same element are smaller.
JEE Main and NEET frequently ask about isoelectronic species (same number of electrons) and isonuclear species (same number of protons). Here, Fe²⁺ and Fe³⁺ have the same nuclear charge (isonuclear) — making this a direct comparison of electron-proton balance. The species with fewer electrons is always smaller.
Alternative Method
Think of it as “more charge, less space.” The effective nuclear charge experienced per electron (often approximated by , where is the shielding constant) increases as electrons are removed. Higher per electron → contracted orbitals → smaller radius.
Common Mistake
Students often say “Fe³⁺ is larger because it has more charge.” This reverses the logic. More positive charge means stronger pull on fewer electrons — the ion contracts, not expands. Also, be careful not to compare Fe (neutral metal atom) on the same scale as ions without noting that the neutral atom includes the 4s shell, which is absent in both Fe²⁺ and Fe³⁺.