4. the ionic radii of the ions $s^{2-}$, $cl^-$, and $k^+$ are 184, 181, 138 pm, respectively. explain why…

4. the ionic radii of the ions $s^{2-}$, $cl^-$, and $k^+$ are 184, 181, 138 pm, respectively. explain why these ions have different sizes even though they contain the same number of electrons.

4. the ionic radii of the ions $s^{2-}$, $cl^-$, and $k^+$ are 184, 181, 138 pm, respectively. explain why these ions have different sizes even though they contain the same number of electrons.

Answer

Brief Explanations:

These ions (( \text{S}^{2-} ), ( \text{Cl}^- ), ( \text{K}^+ )) are isoelectronic (same number of electrons, ( 18 ) electrons, electron configuration ( 1s^2 2s^2 2p^6 3s^2 3p^6 )). The difference in ionic radii comes from the nuclear charge (( Z )): ( \text{S}^{2-} ) has ( Z = 16 ), ( \text{Cl}^- ) has ( Z = 17 ), ( \text{K}^+ ) has ( Z = 19 ). Higher nuclear charge (more protons) pulls the same electron cloud more strongly, shrinking the ionic radius. So ( \text{K}^+ ) (highest ( Z )) has the smallest radius, ( \text{S}^{2-} ) (lowest ( Z )) the largest.

Answer: These ions are isoelectronic (same electron count, 18 electrons) but have different nuclear charges (proton numbers: ( \text{S}^{2-} = 16 ), ( \text{Cl}^- = 17 ), ( \text{K}^+ = 19 )). Higher nuclear charge (more protons) exerts a stronger pull on the identical electron cloud, reducing the ionic radius. Thus, ( \text{K}^+ ) (largest ( Z )) has the smallest radius, ( \text{S}^{2-} ) (smallest ( Z )) the largest, explaining the size differences.