Which of the following isoelectronic ions has the lowest ionization energy?

Options

A. `K^+`
B. `Ca^(2+)`
C. `Cl^-`
D. `S^(2-)`

Explanation

To determine which of the isoelectronic ions has the lowest ionization energy among K⁺, Ca²⁺, Cl⁻, and S²⁻, we can follow these steps:

### Step 1: Identify the Isoelectronic Species
All the ions given (K⁺, Ca²⁺, Cl⁻, and S²⁻) are isoelectronic, meaning they all have the same number of electrons. The electronic configurations are as follows:
- K⁺ (Potassium ion): 18 electrons (same as Argon)
- Ca²⁺ (Calcium ion): 18 electrons (same as Argon)
- Cl⁻ (Chloride ion): 18 electrons (same as Argon)
- S²⁻ (Sulfide ion): 18 electrons (same as Argon)

### Step 2: Arrange the Ions in the Periodic Table
Next, we arrange these ions according to their position in the periodic table:
- K⁺ is in Group 1 (alkali metal)
- Ca²⁺ is in Group 2 (alkaline earth metal)
- Cl⁻ is in Group 17 (halogen)
- S²⁻ is in Group 16 (chalcogen)

### Step 3: Understand the Trend of Ionization Energy
Ionization energy generally increases across a period (left to right) and decreases down a group (top to bottom). Since all ions are isoelectronic, we need to consider their nuclear charge:
- K⁺ has a nuclear charge of +19 (19 protons)
- Ca²⁺ has a nuclear charge of +20 (20 protons)
- Cl⁻ has a nuclear charge of +17 (17 protons)
- S²⁻ has a nuclear charge of +16 (16 protons)

### Step 4: Compare the Ionization Energies
The greater the nuclear charge, the higher the ionization energy because the electrons are held more tightly. Therefore:
- K⁺ (19 protons) will have a higher ionization energy than S²⁻ (16 protons).
- Ca²⁺ (20 protons) will have the highest ionization energy.
- Cl⁻ (17 protons) will have a higher ionization energy than S²⁻ but lower than K⁺ and Ca²⁺.
- S²⁻ (16 protons) will have the lowest ionization energy because it has the least nuclear charge.

### Conclusion
Thus, among the given isoelectronic ions, S²⁻ has the lowest ionization energy.

**Final Answer: S²⁻**