Atomic and ionic radii

How big is an atom?

An atom has no sharp edge: its electron cloud fades away. So chemists measure the size of an atom from the distance between nuclei in a molecule or a solid.

• The covalent radius is half the distance between the nuclei of two atoms joined by a single bond. In a chlorine molecule the nuclei are $198\ \text{pm}$ apart, so the covalent radius of chlorine is $99\ \text{pm}$.
• The metallic radius is half the distance between neighbouring nuclei in a metal crystal. In copper the nuclei are $256\ \text{pm}$ apart, so its metallic radius is $128\ \text{pm}$.

One picometre, $1\ \text{pm}$, is $10^{-12}\ \text{m}$. Both are called the atomic radius.

Across a period

From left to right in a period, each element has one more proton and one more electron. The new electron goes into the same shell. Electrons in the same shell shield each other only a little, so the outer electrons feel a stronger pull. The cloud is drawn in, and the atom shrinks.

The noble gases are left out. They form no bonds, so only their much larger van der Waals radii can be measured.

Down a group

Down a group, each element has one more shell than the one above. The outer electrons are farther from the nucleus, and the inner shells screen them. So the atoms grow.

The size of an ion

• A cation is smaller than its atom. It has lost electrons, often a whole shell, and the same nuclear charge now holds fewer electrons. The sodium atom is $186\ \text{pm}$, but $\text{Na}^+$ is only $95\ \text{pm}$.
• An anion is larger than its atom. The added electrons repel each other, and the same nuclear charge holds more of them. Fluorine is $64\ \text{pm}$, but $\text{F}^-$ is $136\ \text{pm}$.

Isoelectronic species

Atoms and ions with the same number of electrons are isoelectronic. $\text{O}^{2-}$, $\text{F}^-$, $\text{Na}^+$, $\text{Mg}^{2+}$ and $\text{Al}^{3+}$ all have $10$ electrons, the arrangement of neon.

With the same electrons, the size depends only on the number of protons. More protons pull the same cloud tighter.

So the order of size is $\text{O}^{2-} > \text{F}^- > \text{Na}^+ > \text{Mg}^{2+} > \text{Al}^{3+}$.

Practise with new numbers

Try it in Python

The program steps across period 3 and down group 1, and prints how the radius changes at each step.

Common mistakes

• Thinking more electrons always mean a bigger atom. Across a period electrons are added, yet the atom shrinks, because the nuclear charge grows faster than the shielding.
• Comparing noble gases with the rest. Their radii are van der Waals radii, a different measure.
• Making a cation larger. Losing electrons always makes an ion smaller than its atom.
• Ordering isoelectronic ions by charge sign alone. Count the protons: the most protons give the smallest ion.
• Using the whole bond length as the radius. The covalent radius is half of it.

Remember these

• Covalent radius $=$ half the distance between two bonded nuclei. Metallic radius $=$ half the distance between neighbouring nuclei in a metal.
• Across a period the radius falls. Down a group it grows.
• Cations are smaller than their atoms, anions larger.
• Isoelectronic species: more protons, smaller size.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Which is the larger atom of each pair: magnesium or chlorine; lithium or potassium?

2. In a molecule of iodine, $\text{I}_2$, the nuclei are $266\ \text{pm}$ apart. What is the covalent radius of iodine?

3. Why is $\text{Mg}^{2+}$ so much smaller than the magnesium atom?

4. Arrange $\text{Na}^+$, $\text{F}^-$ and $\text{Mg}^{2+}$ from the largest to the smallest, and give the reason.

5. Why does the radius change so little from silicon to chlorine, but so much from sodium to aluminium?