Final answer:
The given atoms and ions are ordered by increasing size as Ca²⁺, K⁺, Ar, Cl⁻, and S²⁻; this order is determined by accounting for nuclear charge and the gain or loss of electrons.
Step-by-step explanation:
To order the given atoms and ions according to increasing size, we take into account their positions in the periodic table and the effects of their nuclear charge on their size. Generally, within a period, the size of atoms and ions decreases from left to right, whereas within a group, the size increases from top to bottom. Additionally, cations (positively charged ions) are smaller than their parent atoms due to the loss of electrons and thus the increased effective nuclear charge, while anions (negatively charged ions) are larger due to the gain of electrons and the subsequent electron-electron repulsion.
Following these trends and considering the fact that ions with the same number of electrons (isoelectronic species) will have sizes that vary with nuclear charge, we can arrange the given species in order of increasing size:
- Ca²⁺
- K⁺
- Ar
- Cl⁻
- S²⁻
Here, Ca²⁺ is the smallest due to the significant loss of electrons and increased nuclear charge without an increase in electron shielding. K⁺ is slightly larger as it has one more electron and slightly less nuclear charge. Ar is neutral and has the same number of electrons as K⁺, hence it is comparable in size. Cl⁻ has gained one electron compared to Ar, increasing its size, and finally, S²⁻ has gained two electrons, making it the largest due to increased electron-electron repulsion.