Positive ions have smaller atomic radii while negative ions have larger atomic radii. Why
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Positive ions have more numbers of protons in its nucleus then number of electrons so it has less atomic radius where as negative ions have more electrons than protons hence has less atomic radius.
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Let's take an example: 
Sodium has 11 electrons, 2,8,1. One electron is in the M shell. When we remove that electron, the size of $Na^{+}$ decreases, since there are now two shells, but earlier there were three.
If we add an electron to make $Na^{-}$, we have repulsion due to the extra electron, which makes the ion bigger than original atom.
Sodium has 11 electrons, 2,8,1. One electron is in the M shell. When we remove that electron, the size of $Na^{+}$ decreases, since there are now two shells, but earlier there were three.
If we add an electron to make $Na^{-}$, we have repulsion due to the extra electron, which makes the ion bigger than original atom.
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