How does the radius of K+ compare to that of Ar?

[assaftolko]

How is it that these two have the same electron level array (1s^22s^22p^63s^23p^6), but K+ has bigger radius than Ar?
K+ has one more proton in its nuclei than Ar, so I would expect that if both have the same electron configuration - the one with more protons in its nuclei would have the smaller radius since the electric force between its nuclei and its electrons is bigger, hence pulling the two closer together...

 

[AGNuke]

Never heard K⁺ being larger than Ar. But K (atom) is certainly larger than Ar.

 

[epenguin]

I think this is a good question - you may even have opened a can of little maggots, and I will give my fairly amateur answer hoping for greater expertise to come along.

Firstly be reassured that the lines of your explanation are right and followed by all I have been able to read.

About the anomaly you do not give figures and you do not tell us where your ‘fact’ comes from.
This reference
http://www.chemguide.co.uk/atoms/properties/atradius.html
gives the radius of A greater than that of Na⁺ and Na⁺> Mg²⁺ > Al³⁺ in accord with your reasoning. The word used for such a series is ‘isoelectronic’.

However, the author is himself rather puzzled by anomalies with anions.

Anyway the essential point if there is a puzzle like this, the essential question to ask is how were these radii measured? How deduced from experimental measurements? Because atoms and ions are not hard billiard balls of exactly defined radius but more or less concentrated but fuzzy electron clouds (around a small nucleus). Because of that these dinensions like radius will be different according to the method (and the definition) used to determine them. So realize that a radius will be different according to the method used to determine it. The most useful thing you can learn therefore if you want to probe further is at least an appreciation of what these methods are. I do not know for sure, but I would guess (and the reference below seems to verify) that for ions like those above they are deduced from the interatomic distances determined in crystal structures of ionic crystals, aka salts. (And when I’ve said that I haven’t answered, maybe you can conjecture a complete answer.) Anyway see
http://catalog.flatworldknowledge.com/bookhub/4309?e=averill_1.0-ch07_s02#a verill_1.0-ch07_s02
or maybe someone has a better reference. Noble gases do not form salts so their radii must have been determined in a different way.

In fact the first reference comments “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.”And the second “One member of this isoelectronic series is not listed in Table 7.3 "Radius of Ions with the Neon Closed-Shell Electron Configuration": the neon atom. Because neon forms no covalent or ionic compounds, its radius is difficult to measure.”