Classification of Elements and Periodicity in Properties · Lesson 5 of 10

Atomic and Ionic Size

“Explain size trends by balancing nuclear attraction, shielding, shell number, and electron repulsion.”

Learning Objectives

• Distinguish covalent, metallic, and non-bonded measures of atomic size. • Calculate a radius from an appropriate internuclear distance. • Explain atomic-radius trends across periods and down groups. • Compare atoms with their cations and anions. • Order isoelectronic species using nuclear charge.

What does the radius of an atom mean?

A solid ball has a surface where it ends. An atom’s electron cloud has no comparable sharp edge: the probability of finding an electron gradually becomes small farther from the nucleus. Atomic radius is therefore an operational measure inferred from distances between neighbouring atoms, not a direct measurement of a hard boundary.

Many physical quantities, including melting and boiling points, heats of fusion and vaporisation, and atomization energies, can vary periodically. This chapter develops a selected set of atomic properties in detail because they help explain chemical behaviour. We begin with size, then connect it to the energy of removing or adding electrons.

Atoms are also extremely small. A representative atomic radius is of order $1 0^{- 10} m$ , or about one ångström. The picometre is convenient for tabulating atomic distances: $1 pm = 1 0^{- 12} m$ and $1 \overset{a}{˚} ngstr \overset{o}{¨} m = 100 pm$ . The exact assigned radius depends on how the neighbouring atoms interact.

Definition

Covalent radius

For two identical atoms joined by a single covalent bond, half the distance between their nuclei. This gives a useful measure of atomic size in that bonding situation.

Definition

Metallic radius

Half the internuclear distance between neighbouring atoms in a metallic crystal. It is a measure appropriate to metallic bonding.

For either of these particular equal-atom situations, the measured separation is shared equally between the two atoms. That gives a simple relationship. Interatomic separations can be inferred using X-ray diffraction or suitable spectroscopic methods. The halving rule should not be applied blindly to a bond between two different elements, whose contributions need not be equal.

Radius from an equal-atom separationLaTeX

r = \frac{d}{2}

d

is the internuclear separation and

r

the appropriate covalent or metallic radius, expressed in the same length unit.

Example — Chlorine’s covalent radius

Problem
The internuclear distance in a chlorine molecule is 198 pm. Find the single-bond covalent radius.

1.The two bonded atoms are identical, so divide the separation equally.
2. $r = 198/2 = 99 pm$ .
3.The result describes chlorine in the specified covalent situation, not a sharply bounded isolated sphere.

Example — Copper’s metallic radius

Problem
Two neighbouring copper atoms in the metal are separated by 256 pm. Find the metallic radius in pm and metres.

1.Half the equal-atom separation is $256/2 = 128 pm$ .
2.Using $1 pm = 1 0^{- 12} m$ , the radius is $128 \times 1 0^{- 12} m$ .
3.In standard scientific notation this is $1.28 \times 1 0^{- 10} m$ .

Interpreting a bonded-atom distance— The nuclei are separated by d; each equal atom is assigned a radius d/2. The circles illustrate the convention, not a sharp electron-cloud surface.

Why atomic radii change across and down the table

Across a main-group period, electrons are added to the same outer shell while the number of protons increases. Inner electrons screen part of the nuclear attraction, but their number does not rise enough to cancel the added nuclear charge. The outer cloud is pulled in more strongly, so the radius generally decreases.

Definition

Shielding and effective nuclear charge

Shielding, or screening, is the reduction in nuclear attraction experienced by an electron because of other electrons. Effective nuclear charge is the net positive attraction experienced after that screening is considered. It is not simply the formal charge on an ion.

Period 2 element	Li	Be	B	C	N	O	F
Atomic radius / pm	152	111	88	77	74	66	64

Period 3 element	Na	Mg	Al	Si	P	S	Cl
Atomic radius / pm	186	160	143	117	110	104	99

Atomic radius across the second period— The overall fall reflects increasing nuclear attraction within the same outer shell. The values use the chapter’s radius table.

Down a group, an additional occupied shell places the valence electrons farther from the nucleus. More inner electrons provide more shielding. Although the nucleus has more protons too, the added shell and shielding dominate the main-group size trend, so atomic radius increases.

Group 1	Radius / pm	Group 17	Radius / pm
Li	152	F	64
Na	186	Cl	99
K	231	Br	114
Rb	244	I	133
Cs	262	At	140

Atomic size down two families— At each step to a later period, both families gain an outer shell. These points use the same radius table as the preceding comparison.

Noble gases require special care in size comparisons. Their quoted non-bonded, or van der Waals, radii come from atoms that are not joined by an ordinary covalent bond. These values are often much larger than neighbouring covalent radii. Comparing unlike radius conventions can create a false break in the trend. Radius values also vary somewhat with bonding and structural environment.

Common mistake

A larger atomic number does not always mean a larger atom. Across a period it usually means a smaller main-group atom; down a group it usually means a larger atom. First identify the direction of comparison and use comparable radius definitions.

Turning atoms into ions

Electron loss creates a cation and electron gain creates an anion, but neither process changes the nucleus. A cation has fewer electrons sharing the same nuclear attraction, and sometimes loses the outer shell entirely. An anion has more electron repulsion in the cloud. Consequently a cation is normally smaller than its parent atom, while an anion is larger.

Comparison	Parent atom radius / pm	Ion radius / pm	Interpretation
Na and $N a^{+}$	186	95	Electron loss contracts the cloud
F and $F^{-}$	64	136	Electron gain expands the cloud

Ionic radii are inferred from ion separations in crystals, with a convention for sharing those distances. They depend on charge and coordination environment, so different valid tables can assign somewhat different values. Use a consistent dataset for a numerical comparison; the robust ideas here concern direction and electron count.

Definition

Isoelectronic atomic species

Atoms or ions with the same number of electrons. For example, $O^{2 -}$ , $F^{-}$ , Ne, $N a^{+}$ , and $M g^{2 +}$ each contain ten electrons. They need not have the same nuclear charge or the same radius.

For an isoelectronic sequence, the electron count is held constant while proton number changes. More protons pull the same electron population more strongly, producing a smaller species. Always compare nuclear charge, rather than memorising separate and potentially confusing rules for the signs of anions and cations.

An isoelectronic comparison— Every species has ten electrons. From left to right the proton number rises, and the size decreases. Circle sizes are schematic.

Example — Ordering an isoelectronic series

Problem
Arrange $N^{3 -}$ , $O^{2 -}$ , $F^{-}$ , $N a^{+}$ , $M g^{2 +}$ , and $A l^{3 +}$ in increasing radius.

1.Count electrons: $7 + 3$ , $8 + 2$ , $9 + 1$ , $11 - 1$ , $12 - 2$ , and $13 - 3$ all give ten.
2.Their nuclear charges rise from 7 for nitrogen to 13 for aluminium.
3.With the same electron count, radius decreases as nuclear charge increases.
4.The increasing-radius order is $A l^{3 +} < M g^{2 +} < N a^{+} < F^{-} < O^{2 -} < N^{3 -}$ .

Example — Combining atom and ion comparisons

Problem
Among Mg, $M g^{2 +}$ , Al, and $A l^{3 +}$ , identify the largest and smallest species.

1.Across period 3, neutral Mg is larger than neutral Al.
2.Each cation is smaller than its corresponding neutral atom, so neutral Mg is largest.
3. $M g^{2 +}$ and $A l^{3 +}$ each have ten electrons; aluminium has the greater nuclear charge, so $A l^{3 +}$ is smaller.
4.Thus Mg is the largest and $A l^{3 +}$ the smallest. The isoelectronic rule applies to the two ions, not indiscriminately to all four species.

Quick check

Why does atomic radius need an operational definition?

Quick check

A single bond between two identical atoms is 150 pm long. What is each covalent radius?

Quick check

Why does atomic size generally decrease across a main-group period?

Quick check

Which pair is isoelectronic?

Quick check

Which is smallest in the ten-electron series $O^{2 -}$ , $F^{-}$ , $N a^{+}$ , $M g^{2 +}$ ?

Quick check

Why can a noble-gas radius appear unexpectedly large beside a halogen radius?

Practice Problems

Explain why atomic radius is not the radius of a hard sphere.
An equal-atom bond distance is 242 pm. Calculate the corresponding covalent radius in pm and metres.
Explain the opposite size trends across period 3 and down Group 1.
Give one ten-electron species isoelectronic with $F^{-}$ and one eighteen-electron species isoelectronic with Ar.
Find a species isoelectronic with $R b^{+}$ and explain your electron count.
Explain why $N a^{+}$ is smaller than Na and $F^{-}$ larger than F without changing the number of protons.
Rank $A l^{3 +}$ , $M g^{2 +}$ , and $N a^{+}$ by radius and identify the controlled variable in your comparison.

Key Takeaways

Atomic radii are inferred from interatomic distances and depend on the chosen convention. Across a main-group period increasing effective nuclear attraction usually contracts the atom; down a group additional shells enlarge it. Cations are normally smaller and anions larger than their parent atoms. For isoelectronic species, a larger nuclear charge gives a smaller radius. Compare radii using consistent definitions and structural environments.

Previous · Lesson 4

Element Blocks, Metals, and Non-metals

Next · Lesson 6

Ionization Enthalpy and Electron Removal

What does the radius of an atom mean?

Why atomic radii change across and down the table

Turning atoms into ions

Quiz

Practice Problems

Key Takeaways