The ionic radius is a measure of the size of an ion. It is determined by the arrangement of electrons around the nucleus of an ion. In the case of K+ and Cl-, both species are isoelectronic, meaning they have the same number of electrons.
When an atom loses electrons to form a cation (such as K+), it becomes positively charged. In this process, the outermost electron shell is depleted, resulting in a smaller ionic radius compared to the parent atom. In the case of K+, the potassium atom loses one electron from its outermost shell (4s), leaving behind a stable electron configuration similar to that of the noble gas argon.
On the other hand, when an atom gains electrons to form an anion (such as Cl-), it becomes negatively charged. In this process, additional electrons occupy the outermost electron shell, increasing the electron-electron repulsion and causing the electron cloud to expand. As a result, the ionic radius of Cl- is larger than that of the chlorine atom.
Therefore, even though K+ and Cl- are isoelectronic (having the same number of electrons), the ionic radius of K+ is smaller than that of Cl- due to the different electronic configurations resulting from the loss or gain of electrons.