1_3 Atomic and Ionic Radii: Periodic Trends Explained
Size is the first periodic trend worth mastering, because so many others follow from it. How strongly an atom holds its outer electrons, how easily it forms ions, and how it bonds all depend on how far those electrons are from the nucleus. This lesson explains how atomic size is measured and why it changes the way it does across the table.
Measuring the Size of an Atom
An atom has no sharp edge: its electron cloud just thins out with distance. So we cannot measure one isolated atom with a ruler. Instead we measure the distance between the nuclei of two bonded atoms, which techniques such as X-ray diffraction give very precisely, and take half of it as the radius.
- Covalent radius: half the distance between two identical atoms joined by a single covalent bond, e.g. half the Cl–Cl bond length in
\mathrm{Cl_2}
. - Metallic radius: half the distance between neighbouring nuclei in a metal crystal.
- Ionic radius: the share of the distance between a cation and an anion in an ionic crystal that belongs to each ion.
Radii are tiny, so they are quoted in picometres (
1\ \mathrm{pm} = 10^{-12}\ \mathrm{m}
). Always compare values of the same type, because a covalent and a metallic radius for the same element can differ noticeably.Trends in Atomic Radius
Two competing effects set an atom's size. The nuclear charge pulls electrons inward. The inner electrons shield the outer ones from part of that charge, because they sit between the nucleus and the outer shell and repel the outer electrons. What an outer electron actually feels is the effective nuclear charge: the full nuclear charge minus the shielding.
Down a group, radius increases. Each new period starts a new shell, further from the nucleus. The extra protons are largely cancelled by the extra layer of shielding electrons, so the larger distance wins. The halogens show this clearly: the covalent radii of F, Cl, Br and I are about 72, 99, 114 and 133 pm.
Across a period, radius decreases. Each step adds one proton, but the new electron enters the same shell. Electrons in the same shell shield each other poorly, so the effective nuclear charge rises and the whole shell is pulled closer. From lithium to fluorine, the atoms shrink steadily even though they gain electrons.
The effect is especially marked across the lanthanides, where electrons enter the deep 4f subshell, which shields very poorly. The steady shrinking over these fourteen elements is called the lanthanide contraction. It cancels the size increase expected for the next period, so hafnium (
Z = 72
) is almost exactly the same size as zirconium (Z = 40
) above it, about 159 and 160 pm. That is why these two elements are so hard to separate.Ions Compared with Their Atoms
A cation is always smaller than its atom. When sodium loses its single 3s electron, the whole third shell is emptied, so the ion's outer shell is now the second one. The 11 protons also now pull on only 10 electrons, so each is held more tightly. The radius drops from about 157 pm for the atom to 95 pm for
\mathrm{Na^+}
.An anion is always larger than its atom. When fluorine gains an electron, the nuclear charge is unchanged but there is one more electron in the outer shell. The extra electron–electron repulsion pushes the cloud outward, so the radius grows from about 72 pm for the atom to 136 pm for
\mathrm{F^-}
.Ions with the same charge follow the same group trend as atoms, growing down a group:
\mathrm{Li^+}
60 pm,\mathrm{Na^+}
95 pm,\mathrm{K^+}
133 pm.Isoelectronic Ions
Ions that have the same number of electrons are called isoelectronic. Each ion below has 10 electrons, the configuration of neon, so the only thing that differs is the number of protons pulling on them. More protons means a smaller ion.
Ions with 10 electrons (ionic radii)
Ion | Protons | Radius (pm) |
N³⁻ | 7 | 171 |
O²⁻ | 8 | 140 |
F⁻ | 9 | 136 |
Na⁺ | 11 | 95 |
Mg²⁺ | 12 | 65 |
Al³⁺ | 13 | 50 |
This explains both halves of the period trend for ions. Positive ions in a period get smaller from left to right, and so do negative ions, because in each series the nuclear charge rises while the number of electrons stays fixed.
Tips for remembering
- Down = new shell, so bigger: each step down a group adds a whole electron shell, which outweighs the extra protons.
- Across = same shell, stronger pull: protons are added but the shell stays the same, so the electrons are drawn in and atoms shrink.
- Cations cut, anions add: losing electrons often removes a shell and lets the nucleus pull harder; gaining electrons adds repulsion and swells the ion.
- Isoelectronic: more protons, smaller ion: for the same number of electrons, the ion with the highest nuclear charge is the smallest.