The correct set of decreasing ionic size is

Options

A. `Be ^(2+) gt Mg ^(2+) gt S ^(2-) gt Cl^(-)`
B. `S ^(2-) gt Cl ^(-)gt Na ^(+) gt Mg ^(2+)`
C. `Cl^(-) gt S ^(2-) gt Mg ^(2+) gt Be ^(2+)`
D. `S ^(2-) gt Cl ^(-) gt Mg^(2+) gt Na ^(+)`

Answer

To determine the correct set of decreasing ionic sizes among the given ions (Be²⁺, Mg²⁺, S²⁻, Cl⁻), we need to analyze the ionic sizes based on their charges and the number of protons and electrons they have.

### Step-by-Step Solution:

1. **Identify the Ions and Their Charges:**
- Beryllium ion (Be²⁺) has a +2 charge.
- Magnesium ion (Mg²⁺) also has a +2 charge.
- Sulfide ion (S²⁻) has a -2 charge.
- Chloride ion (Cl⁻) has a -1 charge.

2. **Understand the Concept of Ionic Size:**
- Cations (positively charged ions) are generally smaller than their parent atoms because they lose electrons, leading to a decrease in electron-electron repulsion and a stronger attraction between the remaining electrons and the nucleus.
- Anions (negatively charged ions) are generally larger than their parent atoms because they gain electrons, which increases electron-electron repulsion.

3. **Compare the Sizes of Cations:**
- Between Be²⁺ and Mg²⁺, magnesium is larger than beryllium. This is because as you move down a group in the periodic table, the ionic size increases due to the addition of electron shells. Therefore, Mg²⁺ > Be²⁺.

4. **Compare the Sizes of Anions:**
- Between S²⁻ and Cl⁻, both ions have the same number of electrons (18), but S²⁻ has fewer protons (16) compared to Cl⁻ (17). The greater positive charge in Cl⁻ pulls the electrons closer, making Cl⁻ smaller than S²⁻. Thus, S²⁻ > Cl⁻.

5. **Combine the Comparisons:**
- Now we can arrange the ions based on their sizes:
- S²⁻ is the largest (due to the increased electron-electron repulsion).
- Cl⁻ is smaller than S²⁻ but larger than the cations.
- Mg²⁺ is smaller than Cl⁻.
- Be²⁺ is the smallest.

6. **Final Order of Decreasing Ionic Size:**
- The correct order of decreasing ionic size is:
- S²⁻ > Cl⁻ > Mg²⁺ > Be²⁺.

### Conclusion:
The correct set of decreasing ionic size is S²⁻ > Cl⁻ > Mg²⁺ > Be²⁺.