Mixed Radius and Ionisation Problems

Introduction

A mixed problem may ask which species is larger and which atom has lower first ionisation energy. The two answers may rely on different comparisons. Counting electrons, checking neutral or ionic state and naming the property prevents a single memorised arrow from being used twice where it does not belong.

Core explanation

For neutral atoms in one main group, compare outer principal shell numbers. Li has 2s¹ and Na 3s¹, so Na is generally larger and has lower first ionisation energy. The two trends share a distance-and-shielding explanation but are not numerically equivalent. Radius values need a consistent convention, while IE₁ values refer to gaseous neutral atoms.

For neutral atoms in one period, compare Z and core shielding, then inspect orbital exceptions. Na and Mg share a [Ne] core with outer n = 3; Mg has higher Z, generally smaller radius and higher IE₁. Mg and Al, however, illustrate why IE₁ can reverse locally: Al's 3p¹ electron is easier to remove than Mg's 3s electron. The radius trend may still broadly contract. Do not force both properties to follow the same exact neighbour-by-neighbour sequence.

For a parent atom and its ion, keep Z fixed and compare electron counts and occupied shells. Na⁺ is much smaller than neutral Na because the 3s outer electron is removed and the ion has [Ne]. Cl⁻ is generally larger than neutral Cl because one electron is added to the existing 3p shell. First ionisation energy, however, is defined for a gaseous neutral atom becoming X⁺; if a question asks energy to remove an electron from Na⁺, that is second ionisation energy, not Na's IE₁.

For isoelectronic ions, hold electron count constant and compare Z. F⁻, Na⁺ and Mg²⁺ each have ten electrons. Greater proton count generally contracts the distribution, so a compatible ionic-radius order is F⁻ > Na⁺ > Mg²⁺. This is not a comparison of first ionisation energies of the ions; removing an electron from each ion is a different charge-state process requiring appropriately defined energies.

The mixed question may contain a mass or isotope distractor. Isotopes of an element have the same Z and, at the same charge state, essentially the same introductory electron arrangement; their mass numbers do not determine first ionisation ordering in a simple classroom comparison. Small isotope effects can exist in precise spectroscopy, but “more neutrons means a stronger nuclear charge” is false. Protons, not neutrons, set bare nuclear charge.

Units and definitions provide final checks. Convert 0.10 nm to 100 pm before comparing radii. Do not mix a covalent radius of a neutral atom with an ionic radius from a lattice as though the same boundary were measured. IE₁ is commonly in kJ mol⁻¹, not pm; a table column of radius cannot be used directly as an energy. The physical model connects trends qualitatively, not through a direct unit conversion.

A useful decision tree asks: same neutral group, same neutral period, same element before/after ionisation, or same electron count among ions? Each branch has a leading factor: added shells, rising effective nuclear charge, changed electron number or different Z at fixed electrons. Select the branch before applying a rank.

When data are supplied, they override a simplistic shortcut within their defined scope. If a measured pair conflicts with an expected arrow, inspect orbital occupancy and data conventions. Report a qualified conclusion rather than changing the sign or ignoring the value. This turns a mixed exercise into evidence-based reasoning.

Step-by-step reasoning

1. Label each species with Z, charge, electron count and highest occupied shell. 2. Identify the comparison class for each requested property separately. 3. Use the appropriate shell, Z or ionisation-step model. 4. Check units, radius conventions and local orbital exceptions before final ranking.

Visual explanation

Draw a four-branch chart: neutral same group → outer n; neutral same period → Z/core; atom versus own ion → electron gain/loss; isoelectronic ions → Z at fixed e. Put IE₁ in a separate box labelled gas-phase neutral removal, so it is not accidentally applied to an already charged ion.

Real-world analogy

Ranking runners by height and by speed requires different measurements, even if height sometimes correlates with stride. Radius and ionisation energy are likewise related but distinct properties with separate definitions.

Real-world example

In ionic solids, Mg²⁺ and F⁻ may both have ten electrons but occupy different lattice roles and effective sizes. Their charge signs and proton counts matter. A comparison of their ion radii is not settled by saying both have neon-like configurations.

Why?

Why is Na⁺ versus Na a different radius problem from Na⁺ versus Mg²⁺? The first holds the nucleus fixed and changes electron count; the second holds electron count fixed and changes proton number.

Common misconception

“If an atom is smaller, its first ionisation energy must always be higher than another's.” The quantities correlate broadly, but subshell occupancy, charge state and data definitions can produce exceptions or make the comparison inapplicable.

Worked example

Rank F⁻, Na⁺ and Mg²⁺ by compatible ionic radius, then compare neutral Na and Mg first ionisation. The ions each have ten electrons and Z values 9, 11 and 12, so F⁻ > Na⁺ > Mg²⁺ in radius. Neutral Na [Ne]3s¹ and Mg [Ne]3s² share period three; Mg's higher effective attraction gives Mg the higher IE₁ in the broad and observed comparison. The two questions use different species sets and models.

Quick check

1. Is electron removal from Na⁺ described by sodium's first or second ionisation energy? Answer: Second ionisation energy, because the starting gas-phase species already has one positive charge.

Exam focus

Classify the comparison before ranking. Write electron counts for ions, note outer shells for neutral groups and check subshell exceptions for IE₁. Keep pm radius and kJ mol⁻¹ energy data separate.

Advanced insight

Exact ion sizes and ionisation energies arise from relaxed many-electron states. The simple comparison branches identify dominant variables, but quantitative predictions require empirical tables or detailed quantum calculations.

Summary

Mixed periodic problems require separate models for neutral group trends, neutral period trends, parent-ion changes and isoelectronic series. First ionisation energy refers specifically to a gaseous neutral atom. Define each property and species before comparing.

Practice questions

1. Which is larger, neutral Na or Na⁺? Answer: Neutral Na, whose n = 3 outer electron is absent from Na⁺. 2. Which is generally smaller among ten-electron ions, Na⁺ or Mg²⁺? Answer: Mg²⁺ because it has twelve rather than eleven protons. 3. Which has lower IE₁, Li or Na? Answer: Na in the broad group-one trend, with a more distant outer electron. 4. Can Mg/Al IE₁ be ranked by rising Z alone? Answer: No; Al's first removable 3p electron gives a local exception.