The increasing order of the ionic radii of the given isoelectronic species is: Cl⁻, Ca²⁺, K⁺, S²⁻

An isoelectronic series is useful in understanding the effects of gained or loss electrons on atom size. Isoelectronic species are atoms or ions that have the same number of electrons. In this case, Cl⁻, Ca²⁺, K⁺, and S²⁻ all have 18 electrons. The ionic radii increase with increasing negative charge and decreasing positive charge. The greater the negative charge, the more electrons there are to repel each other, thus increasing the ionic radius. Conversely, a more positive charge leads to a smaller ionic radius because the electrons are held more tightly by the nucleus. Therefore, the order of increasing ionic radii is Ca²⁺ < K⁺ < Cl⁻ < S²⁻.