ATOMIC AND IONIC RADIUS

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.
	Important!  If you aren't reasonable happy about electronic structures you should follow this link before you go any further.
ATOMIC RADIUS Measures of atomic radius Unlike a ball, an atom doesn't 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.
	Note:  If you want to explore these various types of bonding this link will take you to the bonding menu.
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 in Periods 2 and 3 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.
	Note:  You might possibly wonder why you don't get extra screening from the 2s2 electrons in the cases of the elements from boron to fluorine where the bonding involves the p electrons. In each of these cases, before bonding happens, the existing s and p orbitals are reorganised (hybridised) into new orbitals of equal energy. When these atoms are bonded, there aren't any 2s electrons as such. If you don't know about hybridisation, just ignore this comment - you won't need it for UK A level purposes anyway.
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.
	Note:  The 4s orbital has a higher energy than the 3d in the transition elements. That means that it is a 4s electron which is lost from the atom when it forms an ion. It also means that the 3d orbitals are slightly closer to the nucleus than the 4s - and so offer some screening. Confusingly, this is inconsistent with what we say when we use the Aufbau Principle to work out the electronic structures of atoms. I have discussed this in detail in the page about the order of filling 3d and 4s orbitals. If you are a teacher or a very confident student then you might like to follow this link. If you aren't so confident, or are coming at this for the first time, I suggest that you ignore it. Remember that the Aufbau Principle (which uses the assumption that the 3d orbitals fill after the 4s) is just a useful way of working out the structures of atoms, but that in real transition metal atoms the 4s is actually the outer, higher energy orbital.
IONIC RADIUS A warning! 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
	Note:  These figures all come from the Database of Ionic Radii from Imperial College London. I have converted them from Angstroms to nm (nanometres), which are more often used in the data tables that you are likely to come across. If you are interested, 1 Angstrom is 10-10 m; 1 nm = 10-9 m. To convert from Angstroms to nm, you have to divide by 10, so that 1.02 Angstroms becomes 0.102 nm. You may also come across tables listing values in pm (picometres) which are 10-12 m. A value in pm will look like, for example, for chlorine, 181 pm rather than 0.181 nm. Don't worry if you find this confusing. Just use the values you are given in whatever units you are given. For comparison purposes, all the values relate to 6-co-ordinated ions (the same arrangement as in NaCl, for example). CsCl actually crystallises in an 8:8-co-ordinated structure - so you couldn't accurately use these values for CsCl. The 8-co-ordinated ionic radius for Cs is 0.174 nm rather than 0.167 for the 6-co-ordinated version.
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
	Note:  The table misses out silicon which doesn't 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 centre 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-co-ordinated 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.
You can see that as the number of protons in the nucleus of the ion increases, the electrons get pulled in more closely to the nucleus. The radii of the isoelectronic ions therefore fall across this series.