This page explains the various measures of atomic radius, and then looks at the way it varies around the Periodic Table - across periods and down groups. It assumes that you understand electronic structures for simple atoms written in s, p, d notation.

Unlike a ball, an atom does not have a fixed radius. The radius of an atom can only be found by measuring the distance between the nuclei of two touching atoms, and then halving that distance.

As you can see from the diagrams, the same atom could be found to have a different radius depending on what was around it. The left hand diagram shows bonded atoms. The atoms are pulled closely together and so the measured radius is less than if they are just touching. This is what you would get if you had metal atoms in a metallic structure, or atoms covalently bonded to each other. The type of atomic radius being measured here is called the metallic radius or the covalent radius depending on the bonding.

The right hand diagram shows what happens if the atoms are just touching. The attractive forces are much less, and the atoms are essentially "unsquashed". This measure of atomic radius is called the van der Waals radius after the weak attractions present in this situation.

### Trends in atomic radius in the Periodic Table

The exact pattern you get depends on which measure of atomic radius you use - but the trends are still valid. The following diagram uses metallic radii for metallic elements, covalent radii for elements that form covalent bonds, and van der Waals radii for those (like the noble gases) which don't form bonds.

#### Trends in atomic radius down a group

It is fairly obvious that the atoms get bigger as you go down groups. The reason is equally obvious - you are adding extra layers of electrons.

#### Trends in atomic radius across periods

You have to ignore the noble gas at the end of each period. Because neon and argon don't form bonds, you can only measure their van der Waals radius - a case where the atom is pretty well "unsquashed". All the other atoms are being measured where their atomic radius is being lessened by strong attractions. You aren't comparing like with like if you include the noble gases.

Leaving the noble gases out, atoms get smaller as you go across a period. If you think about it, the metallic or covalent radius is going to be a measure of the distance from the nucleus to the electrons which make up the bond. (Look back to the left-hand side of the first diagram on this page if you aren't sure, and picture the bonding electrons as being half way between the two nuclei.)

From lithium to fluorine, those electrons are all in the 2-level, being screened by the 1s2 electrons. The increasing number of protons in the nucleus as you go across the period pulls the electrons in more tightly. The amount of screening is constant for all of these elements.

In the period from sodium to chlorine, the same thing happens. The size of the atom is controlled by the 3-level bonding electrons being pulled closer to the nucleus by increasing numbers of protons - in each case, screened by the 1- and 2-level electrons.

### Trends in the transition elements

Although there is a slight contraction at the beginning of the series, the atoms are all much the same size. The size is determined by the 4s electrons. The pull of the increasing number of protons in the nucleus is more or less offset by the extra screening due to the increasing number of 3d electrons.

Ionic radii are difficult to measure with any degree of certainty, and vary according to the environment of the ion. For example, it matters what the co-ordination of the ion is (how many oppositely charged ions are touching it), and what those ions are. There are several different measures of ionic radii in use, and these all differ from each other by varying amounts. It means that if you are going to make reliable comparisons using ionic radii, they have to come from the same source.

What you have to remember is that there are quite big uncertainties in the use of ionic radii, and that trying to explain things in fine detail is made difficult by those uncertainties. What follows will be adequate for UK A level (and its various equivalents), but detailed explanations are too complicated for this level.

#### Trends in ionic radius in the Periodic Table

Trends in ionic radius down a group: This is the easy bit! As you add extra layers of electrons as you go down a group, the ions are bound to get bigger. The two tables below show this effect in Groups 1 and 7.

electronic structure of ion ionic radius (nm)
Li+ 2 0.076
Na+ 2, 8 0.102
K+ 2, 8, 8 0.138
Rb+ 2, 8, 18, 8 0.152
Cs+ 2, 8, 18, 18, 8 0.167

electronic structure of ion ionic radius (nm)
F- 2, 8 0.133
Cl- 2, 8, 8 0.181
Br- 2, 8, 18, 8 0.196
I- 2, 8, 18, 18, 8 0.220

#### Trends in ionic radius across a period

Let's look at the radii of the simple ions formed by elements as you go across Period 3 of the Periodic Table - the elements from Na to Cl.

Na+ Mg2+ Al3+   P3- S2- Cl-
no of protons 11 12 13   15 16 17
electronic structure of ion 2,8 2,8 2,8   2,8,8 2,8,8 2,8,8
ionic radius (nm) 0.102 0.072 0.054   (0.212) 0.184 0.181

The table misses out silicon which does not form a simple ion. The phosphide ion radius is in brackets because it comes from a different data source, and I am not sure whether it is safe to compare it. The values for the oxide and chloride ions agree in the different source, so it is probably OK. The values are again for 6-co-ordination, although I can't guarantee that for the phosphide figure.

First of all, notice the big jump in ionic radius as soon as you get into the negative ions. Is this surprising? Not at all - you have just added a whole extra layer of electrons. Notice that, within the series of positive ions, and the series of negative ions, that the ionic radii fall as you go across the period. We need to look at the positive and negative ions separately.

• The positive ions: In each case, the ions have exactly the same electronic structure - they are said to be isoelectronic. However, the number of protons in the nucleus of the ions is increasing. That will tend to pull the electrons more and more towards the center of the ion - causing the ionic radii to fall. That is pretty obvious!
• The negative ions: Exactly the same thing is happening here, except that you have an extra layer of electrons. What needs commenting on, though is how similar in size the sulphide ion and the chloride ion are. The additional proton here is making hardly any difference.

The difference between the size of similar pairs of ions actually gets even smaller as you go down Groups 6 and 7. For example, the Te2- ion is only 0.001 nm bigger than the I- ion.

As far as I am aware there is no simple explanation for this - certainly not one which can be used at this level. This is a good illustration of what I said earlier - explaining things involving ionic radii in detail is sometimes very difficult.

### Trends in ionic radius for some more isoelectronic ions

This is only really a variation on what we have just been talking about, but fits negative and positive isoelectronic ions into the same series of results. Remember that isoelectronic ions all have exactly the same electron arrangement.

N3- O2- F-   Na+ Mg2+ Al3+
no of protons 7 8 9   11 12 13
electronic structure of ion 2, 8 2, 8 2, 8   2, 8 2, 8 2, 8
ionic radius (nm) (0.171) 0.140 0.133   0.102 0.072 0.054

Note:  The nitride ion value is in brackets because it came from a different source, and I don't know for certain whether it relates to the same 6-co-ordination as the rest of the ions. This matters. My main source only gave a 4-coordinated value for the nitride ion, and that was 0.146 nm.

You might also be curious as to how the neutral neon atom fits into this sequence. Its van der Waals radius is 0.154 or 0.160 nm (depending on which source you look the value up in) - bigger than the fluoride ion. You can't really sensibly compare a van der Waals radius with the radius of a bonded atom or ion.