The ionic radii of `O^(2-),F^(-) , Na^(+) and Mg^(2+)` are in the order :

Options

A. `O^(2-) gt F^(-) gt Mg^(2+) gt Na^(+)`
B. `Mg^(2+) gt Na^(+) gt F^(-) gt O^(2-)`
C. `O^(2-) gt F^(-) gt Na^(+) gt Mg^(2+)`
D. `F^(-) gt O^(2-) gt Na^(+) gt Mg^(2+)`

Answer

To determine the order of ionic radii for the ions \( O^{2-}, F^{-}, Na^{+}, \) and \( Mg^{2+} \), we need to analyze their electronic configurations and effective nuclear charges. Here’s a step-by-step solution:

### Step 1: Identify the number of protons and electrons in each ion
- **For \( O^{2-} \)**:
- Atomic number of oxygen (O) = 8
- Protons = 8
- Electrons = 8 + 2 = 10 (gains 2 electrons)

- **For \( F^{-} \)**:
- Atomic number of fluorine (F) = 9
- Protons = 9
- Electrons = 9 + 1 = 10 (gains 1 electron)

- **For \( Na^{+} \)**:
- Atomic number of sodium (Na) = 11
- Protons = 11
- Electrons = 11 - 1 = 10 (loses 1 electron)

- **For \( Mg^{2+} \)**:
- Atomic number of magnesium (Mg) = 12
- Protons = 12
- Electrons = 12 - 2 = 10 (loses 2 electrons)

### Step 2: Determine the effective nuclear charge
All four ions have the same number of electrons (10), but they differ in the number of protons:
- \( O^{2-} \): 8 protons
- \( F^{-} \): 9 protons
- \( Na^{+} \): 11 protons
- \( Mg^{2+} \): 12 protons

### Step 3: Analyze the relationship between effective nuclear charge and ionic radii
- The effective nuclear charge (Z_eff) increases with the number of protons.
- The greater the effective nuclear charge, the stronger the attraction between the nucleus and the electrons, resulting in a smaller ionic radius.

### Step 4: Compare the ionic radii based on effective nuclear charge
- **\( Mg^{2+} \)** has the highest number of protons (12), thus it has the smallest ionic radius.
- **\( Na^{+} \)** has 11 protons, so it has a larger ionic radius than \( Mg^{2+} \) but smaller than \( F^{-} \) and \( O^{2-} \).
- **\( F^{-} \)** has 9 protons, leading to a larger ionic radius than \( Na^{+} \).
- **\( O^{2-} \)** has the least number of protons (8), resulting in the largest ionic radius.

### Step 5: Write the order of ionic radii
Based on the analysis:
\[ O^{2-} > F^{-} > Na^{+} > Mg^{2+} \]

### Final Answer
The order of ionic radii is:
\[ O^{2-} > F^{-} > Na^{+} > Mg^{2+} \]