The correct order of the size is

Options

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

Explanation

To determine the correct order of size among the given species (Ca²⁺, K⁺, Ar, Cl⁻, S²⁻), we will analyze their electron configurations and the effect of nuclear charge on their sizes.

### Step-by-Step Solution:

1. **Identify the Species and Their Electron Counts**:
- **Ca²⁺**: Calcium loses 2 electrons, resulting in 18 electrons.
- **K⁺**: Potassium loses 1 electron, resulting in 18 electrons.
- **Ar**: Argon has 18 electrons.
- **Cl⁻**: Chlorine gains 1 electron, resulting in 18 electrons.
- **S²⁻**: Sulfur gains 2 electrons, resulting in 18 electrons.

All these species have the same number of electrons (18), making them isoelectronic.

2. **Determine the Number of Protons**:
- **Ca²⁺**: 20 protons
- **K⁺**: 19 protons
- **Ar**: 18 protons
- **Cl⁻**: 17 protons
- **S²⁻**: 16 protons

3. **Understand the Concept of Isoelectronic Species**:
- In isoelectronic species, the size of the ions is influenced by the effective nuclear charge (Z_eff), which is the net positive charge experienced by electrons in the outer shell.
- The greater the number of protons (positive charge), the stronger the attraction between the nucleus and the electrons, leading to a smaller ionic size.

4. **Order the Species Based on Proton Count**:
- Since the effective nuclear charge increases with the number of protons, the order of ionic sizes from largest to smallest will be the opposite order of the number of protons:
- S²⁻ (16 protons) > Cl⁻ (17 protons) > Ar (18 protons) > K⁺ (19 protons) > Ca²⁺ (20 protons)

5. **Final Order of Sizes**:
- The correct order of size from largest to smallest is:
- S²⁻ > Cl⁻ > Ar > K⁺ > Ca²⁺

### Conclusion:
The correct order of size is: **S²⁻ > Cl⁻ > Ar > K⁺ > Ca²⁺**.