Which of the following arrangements represents the correct order of increasing radius?

Options

A. `Mg^(2+) lt K^(+) lt Se^(2-) lt S^(2-)`
B. `Mg^(2+) lt K^(+) lt S^(2-) lt Se^(2-)`
C. `Se^(2-) lt S^(2-) lt Mg^(2+) lt K^(+)`
D. `Mg^(2+) lt Se^(2-) lt K^(+) S^(2-)`

Explanation

To determine the correct order of increasing ionic radius among the given elements (Potassium, Magnesium, Sulfur, and Selenium), we can follow these steps:

### Step 1: Identify the Ions and Their Charges
- We have the following ions:
- Potassium (K⁺)
- Magnesium (Mg²⁺)
- Sulfur (S²⁻)
- Selenium (Se²⁻)

### Step 2: Determine the Number of Electrons
- K⁺ has lost one electron, so it has 18 electrons.
- Mg²⁺ has lost two electrons, so it also has 18 electrons.
- S²⁻ has gained two electrons, so it has 18 electrons.
- Se²⁻ has gained two electrons, so it also has 18 electrons.

### Step 3: Identify Isoelectronic Species
- All the ions (K⁺, Mg²⁺, S²⁻, and Se²⁻) are isoelectronic, meaning they all have the same number of electrons (18 electrons).

### Step 4: Compare Ionic Radii of Isoelectronic Species
- In isoelectronic species, the ionic radius decreases with increasing nuclear charge.
- Therefore, the order of ionic radii will be:
- S²⁻ > K⁺ > Mg²⁺
- Since Se²⁻ is in the same group as S²⁻, it will have a larger radius than S²⁻.

### Step 5: Final Arrangement of Ionic Radii
- The correct order of increasing radius is:
- Mg²⁺ < K⁺ < S²⁻ < Se²⁻

### Conclusion
Thus, the correct order of increasing radius is:
**Mg²⁺ < K⁺ < S²⁻ < Se²⁻**