How would you rank these ions according to atomic radius: #K^+#, #Ca^+2#, #P^-3#, #S^-2#, #Cl^-# (from smallest to largest)? Please explain why you chose this order.

All five ions have an equal number of electrons and therefore share the same electron configuration. For example, a neutral calcium atom (#Z=20#) has #20# electrons; it loses #color(purple)("two")# of them to form a #"Ca"^(color(purple)(2+)# cation, which would thus contain #20-2=18# electrons. Similarly, a phosphorus atom (#Z=15#) gains #color(navy)("three")# electrons to form a #"P"^(color(navy)(3-))# anion that contains #15+3=18# electrons.

Positively-charged protons in the nuclei attract the negatively-charged electron cloud. Each proton carries a #+1# charge; the more protons an atom or ion contains the stronger the attraction it poses on its electron cloud. A nucleus of strong positive charge pulls its electron cloud towards itself tightly such that the latter would have a small radius.

The periodic table is arranged in the order of increasing proton number. Phosphorus comes the first among the five species and contains the least number of protons. Its ion would be the largest among the five. Calcium comes the last and forms the smallest ion.

• Number of protons per nucleus #"P"<"S"<"Cl"<"K"<"Ca"#
• Strength of Electrostatic attraction on the electron cloud #"P"<"S"<"Cl"<"K"<"Ca"#
• Ionic radius #"P"^(3-)>"S"^(2-)>"Cl"^(-)>"K"^(+)>"Ca"^(2+)#