Final answer:
To place Ar, Ca2+, S2−, Cs, and S in order of increasing radius, consider cation/anion status and periodic table trends. Ca2+ is the smallest due to electron loss and nuclear charge, then Ar, S, S2-, and finally Cs, which is the largest.
Step-by-step explanation:
To determine the order of increasing ionic radii for Ar, Ca2+, S2−, Cs, and S, we have to consider two factors: whether the species is a cation or an anion, and its position on the periodic table.
Cations are smaller than their parent atoms because they have lost one or more electrons, resulting in a decreased electron cloud size due to increased nuclear attraction. Anions are larger than their parent atoms because the addition of electrons results in increased repulsion among them.
The general trends are that atomic and ionic size increase going down a group and decrease going across a period from left to right.
Here are the species arranged in order of increasing radius:
Ca2+ (lost 2 electrons, smaller than its parent element, and higher nuclear charge than other cations or anions listed)
Ar (noble gas, full valence shell)
S (to the right of Ca in the same period, but as a non-ionized atom, it will be larger than Ca2+)
S2− (gain of two electrons increases size beyond the neutral sulfur atom)
Cs (one of the largest elements in the periodic table, at the far left of a lower period)