How is shielding effect related to atomic radius?

If one does the calculations for hydrogen, with a single proton, one finds that the size of each electron shell increases as #n^2# where #n# is the principal quantum number of that shell.

Thus, an atom of hydrogen with its electron promoted to the fourth shell would be about 16 times larger than the ground state (#n=1#).

When we look at potassium however, we find an atom that is not 16 times larger than hydrogen, even though its valence electron is a #4s# electron.

This of course is due to the additional attraction of 19 protons on the electrons shells. At the same time, the electron distributions in the first three shells blocks or shields the outer electron from much of this attractive force, with the result that the actual size of the atoms increases (very roughly) in proportion to the number of the shell.

Within a row, the number of shielding electrons remains constant (as the only change in electron configuration is in the valence shell), which means the additional protons pull the valence shell inward, and the atomic radius gradually decreases.

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