The decreasing size of `K^(+) , Ca^(2+) , Cl^(-)` & `S^(2-)` follows the order :

Options

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

Answer

To determine the decreasing size of the ions \( K^+, Ca^{2+}, Cl^{-}, \) and \( S^{2-} \), we need to analyze the number of protons and electrons in each ion, as well as the effective nuclear charge experienced by the electrons.

### Step-by-Step Solution:

1. **Identify the number of protons and electrons in each ion:**
- \( K^+ \): Potassium has 19 protons. As a cation (\( K^+ \)), it has lost one electron, so it has 18 electrons.
- \( Ca^{2+} \): Calcium has 20 protons. As a cation (\( Ca^{2+} \)), it has lost two electrons, so it has 18 electrons.
- \( Cl^{-} \): Chlorine has 17 protons. As an anion (\( Cl^{-} \)), it has gained one electron, so it has 18 electrons.
- \( S^{2-} \): Sulfur has 16 protons. As an anion (\( S^{2-} \)), it has gained two electrons, so it has 18 electrons.

2. **Calculate the effective nuclear charge (Z_eff):**
- The effective nuclear charge can be understood as the net positive charge experienced by the electrons in an atom or ion. It can be approximated as the number of protons minus the number of shielding electrons.
- For \( K^+ \): \( Z_{eff} = 19 - 0 = 19 \)
- For \( Ca^{2+} \): \( Z_{eff} = 20 - 0 = 20 \)
- For \( Cl^{-} \): \( Z_{eff} = 17 - 0 = 17 \)
- For \( S^{2-} \): \( Z_{eff} = 16 - 0 = 16 \)

3. **Analyze the relationship between nuclear charge and ionic size:**
- As the effective nuclear charge increases, the attraction between the nucleus and the electrons increases, resulting in a smaller ionic size.
- Therefore, the order of ionic sizes will be inversely related to the effective nuclear charge.

4. **Arrange the ions in decreasing order of size:**
- The ion with the least effective nuclear charge will be the largest, and the one with the highest effective nuclear charge will be the smallest.
- Thus, the order from largest to smallest is:
- \( S^{2-} \) (16 protons, largest size)
- \( Cl^{-} \) (17 protons)
- \( K^+ \) (19 protons)
- \( Ca^{2+} \) (20 protons, smallest size)

5. **Final order of ionic sizes:**
- The decreasing size order is:
\[ S^{2-} > Cl^{-} > K^+ > Ca^{2+} \]