Ionic Radius and Crystal Packing
How ion sizes compare to parent atoms, isoelectronic series, and using radius ratios to predict crystal coordination.
Quick answer
Ionic radius follows charge: cations are much smaller than their atoms (lost outer shell), anions much larger (added repulsion). In an isoelectronic series, size decreases as proton count rises — and the cation/anion radius ratio predicts crystal coordination geometry.
Example: Na (186 pm) → Na⁺ (102 pm); Cl (99 pm) → Cl⁻ (181 pm). NaCl's ratio (~0.56) predicts octahedral coordination — each Na⁺ touches 6 Cl⁻.
What you will learn
- Compare cation and anion sizes to parent atoms with reasons.
- Order isoelectronic series by nuclear charge.
- Apply the radius ratio rule to predict coordination numbers.
- Explain transition metal ion size dependence on oxidation state.
Cations shrink, anions swell — by a lot
Ion formation resizes atoms dramatically. Cations are always smaller than their parent atoms — often strikingly so. Sodium (186 pm) becomes Na⁺ (102 pm): the entire shell is gone, and the ten remaining electrons experience less mutual repulsion under the same 11 protons.
Anions are always larger: chlorine (99 pm) becomes Cl⁻ (181 pm). No shell is lost, but the added electron increases repulsion among electrons sharing the same nuclear attraction — the cloud inflates.
The magnitudes matter for everything built from ions. Table salt's crystal structure, a battery electrolyte's conductivity, a mineral's density — all depend on ionic radii, not atomic ones. Using atomic radii for ionic compounds is a category error the size data punishes immediately.
The isoelectronic series: pure nuclear charge
The isoelectronic series N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²⁺, Al³⁺ holds electron count fixed at 10 while protons run from 7 to 13. Radii fall smoothly: 146 → 140 → 133 → 112 → 102 → 72 → 54 pm.
With shielding constant (same electrons), the only variable is nuclear charge — this is in its purest form. The series also crosses the cation/anion boundary seamlessly: F⁻ (133 pm) to Na⁺ (102 pm) drops sharply because sodium lost its outer shell, a structural change atop the charge trend.
Exam questions love this series because it tests whether you reason from charge and shells rather than memorizing. Protons up → pull up → size down, with shell-loss steps at the boundary.
Radius ratios predict crystal structures
In ionic crystals, geometry follows size. The radius ratio predicts the coordination number — how many anions surround each cation:
- 0.225–0.414 → 4-coordinate (tetrahedral), e.g. ZnS
- 0.414–0.732 → 6-coordinate (octahedral), e.g. NaCl (102/181 ≈ 0.56)
- 0.732–1.0 → 8-coordinate (cubic), e.g. CsCl (181/167 ≈ 1.08, effectively cubic)
The logic is packing: small cations fit in small holes between larger anions. It is a hard-sphere model — real ions deform and polarize — but it correctly predicts the three great ionic structure types, connecting picometer data to macroscopic crystal shapes.
Size selectivity in technology and biology
Lithium-ion batteries work because Li⁺ (76 pm) is tiny enough to shuttle between electrode layers — larger ions would wedge the structure apart. Ion-exchange resins separate ions partly by size: smaller, higher-charged ions bind tighter.
In biology, the Na⁺/K⁺ pump and ion channels discriminate exquisitely by ionic radius and hydration energy — nerve signaling is applied ionic-size chemistry. From grid storage to neurons, who fits where decides what works.
Common mistakes
The changes are huge: Na⁺ (102 pm) is 45% smaller than Na (186 pm); Cl⁻ (181 pm) is 83% larger than Cl (99 pm). Ion formation is a major resizing event, not a minor adjustment — crystal structures depend on it.
Higher charge means smaller ion: Fe²⁺ (92 pm) vs Fe³⁺ (69 pm); Sn²⁺ vs Sn⁴⁺ similarly. Each removed electron raises the effective charge on the rest. Oxidation state is part of the size specification.
It is a geometric guideline assuming hard spheres — real ions polarize and bonds have covalent character. It predicts NaCl and CsCl correctly but fails for some compounds with highly polarizable ions. Useful first guess, not a law.
Real-world applications
Predicting crystal structures from cation/anion radius ratios
Explaining solubility trends in ionic salts
Understanding why Li⁺ moves fastest in battery electrolytes
Designing ion-exchange resins with size-selective pores
Frequently asked questions
Why do cations shrink but anions grow?
Cations lose their outermost shell entirely (Na → Na⁺ drops n = 3), and fewer electrons share the nuclear pull. Anions keep all shells but add repulsion: more electrons, same protons, expanded cloud. Shell loss dominates for cations; repulsion dominates for anions.
How do I order an isoelectronic series by size?
List them by proton count: for N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²�⁺, Al³⁺ (all 10 electrons), radius falls as Z rises from 7 to 13. Same electron count means shielding is constant, so rising nuclear charge is the only variable — a pure Z_eff demonstration.
What is the radius ratio rule?
The radius ratio (cation/anion) predicts how many anions fit around each cation: 0.225–0.414 → tetrahedral (4), 0.414–0.732 → octahedral (6), > 0.732 → cubic (8). NaCl (ratio ~0.56) is octahedral; CsCl (~0.93) is cubic. Geometry follows size.
Do transition metal ion sizes follow the trend?
Transition metal cations shrink across the period (rising Z_eff, same shell loss), then jump at each oxidation state change: Fe²⁺ (92 pm) > Fe³⁺ (69 pm) — higher charge pulls the remaining electrons tighter. Charge matters as much as identity.