Which element/ion has the biggest atomic/ionic size na or na+1

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.

The relative sizes of ions and atoms

You probably won't have noticed, but nowhere in what you have read so far has there been any need to talk about the relative sizes of the ions and the atoms they have come from. Neither (as far as I can tell from the syllabuses) do any of the current UK-based exams for 16 - 18 year olds ask for this specifically in their syllabuses.

However, it is very common to find statements about the relative sizes of ions and atoms. I am fairly convinced that these statements are faulty, and I would like to attack the problem head-on rather than just ignoring it.

Important!

For 10 years, until I rewrote this ionic radius section in August 2010, I included what is in the box below. You will find this same information and explanation in all sorts of books and on any number of websites aimed at this level. At least one non-UK A level syllabus has a statement which specifically asks for this.

However, I was challenged by an experienced teacher about the negative ion explanation, and that forced me to think about it carefully for the first time. I am now convinced that the facts and the explanation relating to negative ions are simply illogical.

As far as I can tell, no UK-based syllabus mentions the relative sizes of atoms and ions (as of August 2010), but you should check past papers and mark schemes to see whether questions have sneaked in.

The rest of this page discusses the problems that I can see, and is really aimed at teachers and others, rather than at students.

If you are a student, look carefully at your syllabus, and past exam questions and mark schemes, to find out whether you need to know about this. If you don't need to know about it, stop reading now (unless, of course, you are interested in a bit of controversy!).

If you do need to know it, then you will have to learn what is in the box, even if, as I believe, it is wrong. If you like your chemistry to be simple, ignore the rest of the page, because you risk getting confused about what you need to know.

If you have expert knowledge of this topic, and can find any flaws in what I am saying, then please contact me via the address on the about this site page.

Choosing the right atomic radius to compare with

This is at the heart of the problem.

The diagrams in the box above, and similar ones that you will find elsewhere, use the metallic radius as the measure of atomic radius for metals, and the covalent radius for non-metals. I want to focus on the non-metals, because that is where the main problem lies.

You are, of course, perfectly free to compare the radius of an ion with whatever measure of atomic radius you choose. The problem comes in relating your choice of atomic radius to the "explanation" of the differences.

It is perfectly true that negative ions have radii which are significantly bigger than the covalent radius of the atom in question. And the argument then goes that the reason for this is that if you add one or more extra electrons to the atom, inter-electron repulsions cause the atom to expand. Therefore the negative ion is bigger than the atom.

This seems to me to be completely inconsistent. If you add one or more extra electrons to the atom, you aren't adding them to a covalently bound atom. You can't simply add electrons to a covalently-bound chlorine atom, for example - chlorine's existing electrons have reorganised themselves into new molecular orbitals which bind the atoms together.

In a covalently-bound atom, there is simply no room to add extra electrons.

So if you want to use the electron repulsion explanation, the implication is that you are adding the extra electrons to a raw atom with a simple uncombined electron arrangement.

In other words, if you were talking about, say, chlorine, you are adding an extra electron to chlorine with a configuration of 2,8,7 - not to covalently bound chlorine atoms in which the arrangement of the electrons has been altered by sharing.

That means that the comparison that you ought to be making isn't with the shortened covalent radius, but with the much larger van der Waals radius - the only available measure of the radius of an uncombined atom.

So what happens if you make that comparison?

Group 7

As we have already discussed above, measurements of ionic radii are full of uncertainties. That is also true of van der Waals radii. The table uses one particular set of values for comparison purposes. If you use data from different sources, you will find differences in the patterns - including which of the species (ion or atom) is bigger.

These ionic radius values are for 6-co-ordinated ions (with a slight question mark over the nitride and phosphide ion figures). But you may remember that I said that ionic radius changes with co-ordination. Nitrogen is a particularly good example of this.

4-co-ordinated nitride ions have a radius of 0.146 nm. In other words if you look at one of the co-ordinations, the nitride ion is bigger than the nitrogen atom; in the other case, it is smaller. Making a general statement that nitride ions are bigger or smaller than nitrogen atoms is impossible.

So what is it safe to say about the facts?

For most, but not all, negative ions, the radius of the ion is bigger than that of the atom, but the difference is nothing like as great as is shown if you incorrectly compare ionic radii with covalent radii. There are also important exceptions.

I can't see how you can make any real generalisations about this, given the uncertainties in the data.

And what is it safe to say about the explanation?

If there are any additional electron-electron repulsions on adding extra electrons, they must be fairly small. This is particularly shown if you consider some pairs of isoelectronic ions.

You would have thought that if repulsion was an important factor, then the radius of, say a sulphide ion, with two negative charges would be significantly larger than a chloride ion with only one. The difference should actually be even more marked, because the sulphide electrons are being held by only 16 protons rather than the 17 in the chlorine case.

On this repulsion theory, the sulphide ion shouldn't just be a little bit bigger than a chloride ion - it should be a lot bigger. The same effect is shown with selenide and bromide, and with telluride and iodide ions. In the last case, there is virtually no difference in the sizes of the 2- and 1- ions.

So if there is some repulsion playing a part in this, it certainly doesn't look as if it is playing a major part.

What about positive ions?

Whether you choose to use van der Waals radii or metallic radii as a measure of the atomic radius, for metals the ionic radius is smaller than either, so the problem doesn't exist to the same extent. It is true that the ionic radius of a metal is less than its atomic radius (however vague you are about defining this).

The explanation (at least as long as you only consider positive ions from Groups 1, 2 and 3) in terms of losing a complete layer of electrons is also acceptable.

Conclusion

It seems to me that, for negative ions, it is completely illogical to compare ionic radii with covalent radii if you want to use the electron repulsion explanation.

If you compare the ionic radii of negative ions with the van der Waals radii of the atoms they come from, the uncertainties in the data make it very difficult to make any reliable generalisations.

The similarity in sizes of pairs of isoelectronic ions from Groups 6 and 7 calls into question how important repulsion is in any explanation.

Having spent more than a week working on this, and discussing it with input from some very knowledgable people, I don't think there is any explanation which is simple enough to give to most students at this level. It would seem to me to be better that these ideas about relative sizes of atoms and ions are just dropped.

At this level, you can describe and explain simple periodic trends in atomic radii in the way I did further up this page, without even thinking about the relative sizes of the atoms and ions. Personally, I would be more than happy never to think about this again for the rest of my life!

© Jim Clark 2000 (last modified January 2022)

1

The following generalizations apply to relating the sizes of atoms, ions and Periodic Table position of the elements involved.

1. Down a Group: Atomic radius increases down any Periodic Table Group because in each successive period the outer electrons occupy an orbit that is further from the nucleus. This effect is enhanced through the increased screening of the outer electrons by those occupying orbits closer to the nucleus, thereby preventing the outer electrons from experiencing the full effect of the attraction by the nucleus.
2. Across a period: Across any period of the Table from left to right, the atomic radius decreases. (Some small departures from this occur in the d-block.) This occurs because, for each additional proton added to the nucleus, the accompanying additional electron is allocated to the same set of outer orbitals which are being filled as that period is built up. The result is that as successive protons and electrons are added, all the outer electrons experience an increasing effective nuclear charge attracting them to the nucleus and hence the atomic radius decreases. (The "effective nuclear charge" is also referred to as "core charge".) When enough electrons have been added to attain the noble gas structure of

ns2 (n-1)d10 np6 in Group 18, the next added electron must occupy an orbital with principal quantum number n increased by one, corresponding to an element from Group 1, so it is further out from the nucleus and the cycle starts again.

Note that there is no comparable way of comparing the radii of the noble gases with those of other elements, so experimental values for their atomic radii are not normally listed.

3. Cation radius: The cation of a given element has a smaller radius than the neutral atom due to the excess positive nuclear charge compared with the negative charge of the electrons. The greater attraction between the nucleus and the electrons draws the electrons closer to the nucleus. The larger the cationic charge, the greater will be this contraction of radius. Where multiple cations of an element exist, the cationic radius decreases greatly as the cation charge increases.

E.g. Fe > Fe2+ > Fe3+

4. Anion radius: Simple anions always have a larger radius than the neutral atom of the same element due to the excess negative charge from the electrons as compared with the positive nuclear charge. Repulsion between the electrons allows them to move further away from the nucleus. The larger the excess negative charge, the greater is the resulting anionic radius.

(i) The sodium ion (Na+) is larger than the magnesium ion (Mg2+) due to two effects. The elements sodium and magnesium are in the same Period, therefore outer electrons of the Mg atom experience greater effective nuclear charge and, more importantly, the magnesium cation, Mg2+, has a greater cationic charge than the Na+ cation. This second effect is by far the more significant.

(ii) The sulfide ion (S2-) is larger than the oxygen atom (O) due to two effects. Sulfur is in the same Group as oxygen and one Period lower, so its outer electrons occupy orbitals from the n = 3 level while oxygen's outer electrons occupy orbitals from the n = 2 level. Consequently for the neutral atoms, S would be larger than O. For the sulfide ion, reinforcing this effect is the large, excess 2- charge that greatly increases the radius of S2- as compared with the neutral S atom.

(iii) The magnesium ion (Mg2+) is smaller than the sulfide ion (S2-). If one were comparing just the neutral atoms Mg and S, the S atom would be smaller as both elements are in the same period and sulfur is more to the right. However, the presence of the excess 2+ charge on Mg2+ greatly reduces its size while the presence of the excess 2- charge on S2- greatly increases its radius. The effects of excess + or - charge on the radius of ions compared with their neutral atoms is far greater than the reduction observed in radius for neutral atoms that results from increasing effective nuclear charge from left to right across any Period.

(iv) The calcium ion (Ca2+) is smaller than the barium ion (Ba2+). The elements calcium and barium are both in the same Group 2 with calcium being higher, so for the neutral atoms, Ca would have a smaller radius, its outer electrons being in the n = 4 level as compared with the n = 6 level for the Ba atom. Both cations have a 2+ charge, so the relationship between their radii in the cationic state would be the same as for the neutral atoms.

(v) The nitride ion (N3-) is smaller than the phosphide ion (P3-). The elements nitrogen and phosphorus are in the same Group 15 with nitrogen being higher, so for the neutral atoms, N with its outer electrons in the n = 2 level would have a smaller radius than P with its outer electrons in the n = 3 level. Both anions have a 3- charge, so the relationship between their radii in the anionic state would be the same as for the neutral atoms.