The species Ar, K⁺, and Ca²⁺ are isoelectronic, meaning they all possess the same number of electrons (18 electrons).

1. Concept: For isoelectronic species, the ionic radius is inversely proportional to the effective nuclear charge. As the atomic number (number of protons) increases, the attraction between the nucleus and the electrons increases, pulling the electron cloud closer and reducing the radius.
2. Analysis:

• Argon (Ar): Atomic number Z = 18 (18 protons).
• Potassium Ion (K⁺): Atomic number Z = 19 (19 protons).
• Calcium Ion (Ca²⁺): Atomic number Z = 20 (20 protons).

3. Trend: Since Calcium has the highest nuclear charge (20), it pulls the 18 electrons the strongest, resulting in the smallest radius. Argon has the lowest nuclear charge (18), resulting in the largest radius. Order of decreasing size: Ar > K⁺ > Ca²⁺ Order of increasing size: Ca²⁺ < K⁺ < Ar.