The increasing order of the ionic radii of the given isoelectronic species is :-

Options

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

Answer

To determine the increasing order of ionic radii of the given isoelectronic species (Cl⁻, Ca²⁺, K⁺, S²⁻), we can follow these steps:

### Step 1: Identify the Species and Their Atomic Numbers
We have the following species:
- Chloride (Cl⁻) - Atomic number 17
- Calcium ion (Ca²⁺) - Atomic number 20
- Potassium ion (K⁺) - Atomic number 19
- Sulfide (S²⁻) - Atomic number 16

### Step 2: Determine the Number of Electrons
Since these species are isoelectronic, they all have the same number of electrons. Each of these ions has 18 electrons:
- Cl⁻: 17 (atomic number) + 1 (gained an electron) = 18 electrons
- Ca²⁺: 20 (atomic number) - 2 (lost two electrons) = 18 electrons
- K⁺: 19 (atomic number) - 1 (lost one electron) = 18 electrons
- S²⁻: 16 (atomic number) + 2 (gained two electrons) = 18 electrons

### Step 3: Understand Ionic Radii Trends
The ionic radius is influenced by the charge of the ion and the atomic number:
- Anions (negatively charged ions) are larger than their parent atoms because they have gained electrons, which increases electron-electron repulsion.
- Cations (positively charged ions) are smaller than their parent atoms because they have lost electrons, which decreases electron-electron repulsion.

### Step 4: Compare the Ionic Sizes
1. **Cations**:
- Ca²⁺ (20 protons) has the smallest radius because it has the highest positive charge and the highest atomic number, pulling the electrons closer.
- K⁺ (19 protons) is larger than Ca²⁺ but smaller than the anions.

2. **Anions**:
- Cl⁻ (17 protons) is larger than both cations due to its negative charge.
- S²⁻ (16 protons) is the largest because it has the most negative charge, leading to the greatest electron-electron repulsion.

### Step 5: Establish the Increasing Order of Ionic Radii
Based on the analysis:
- Ca²⁺ < K⁺ < Cl⁻ < S²⁻

### Conclusion
The increasing order of the ionic radii of the given isoelectronic species is:
**Ca²⁺ < K⁺ < Cl⁻ < S²⁻**