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A potassium atom comprises 19 protons and 18 core electrons. Those electrons screen 18 protons worth of Coulomb force. Therefore, there is one proton worth of Coulomb force attracting the valence electron of potassium. Whereas, krypton comprises 36 protons and 28 core electrons. Its electrons screen 28 protons wroth of Coulomb force. Therefore, there are eight protons worth of Coulomb force attracting the valence electrons of krypton.

Consequently, there is more Coulomb force attracting the valence electrons of krypton than there is attracting the valence electron of potassium; accordingly, the atomic radius of krypton is smaller than the atomic radius of potassium.

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Your concept is close to the real answer. You should think it as no. of protons per electron over all. This is the way things have been done in literature and if you are not satisfied then consider the fact that not all electrons are shielding the nucleus to same extent. There are certain rules [slaters rule] made and which works in most cases by which you can actually predict how much of nuclear charge is acting on the electron. Even with that you will see valence electron for K is more shielded than for Kr. But the numbers you came up with don't make that much sense. It does a bit but better if you go by the way it has been discussed.

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  • $\begingroup$ If we just did total electrons/total protons, then wouldn't the electron:proton ratio be the same for K and Kr, and so wouldn't their radii be approximately the same? $\endgroup$
    – Hal
    May 30, 2015 at 20:59
  • $\begingroup$ How is 36/28 and 19/18 same ? 36/28 is greater than 19/18 man $\endgroup$
    – Punarbasu Roy
    May 31, 2015 at 4:55
  • $\begingroup$ I am not satisfied with your answer because if we look at the base of the proton then the radius of sodium should be larger than argon $\endgroup$
    – Sumit Choudhary
    Jul 15, 2018 at 12:51
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Due to the poor shielding effect, of "d" orbital of" Kr" so the "z"effect is increase and radius is decrease but in "K" no poor shielding effect so it's radius is greater than "Kr"

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