Correct order of ionic radii among the following is

Options

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

Answer

To determine the correct order of ionic radii among the given ions, we need to analyze the number of protons and electrons in each ion and how they affect the ionic size.

### Step-by-Step Solution:

1. **Identify the Ions**: Let's assume the ions in question are:
- \( \text{Mg}^{2+} \)
- \( \text{Na}^{+} \)
- \( \text{F}^{-} \)
- \( \text{O}^{2-} \)

2. **Determine the Number of Protons and Electrons**:
- **For \( \text{Mg}^{2+} \)**:
- Protons: 12 (magnesium has an atomic number of 12)
- Electrons: 10 (2 electrons are removed)
- **For \( \text{Na}^{+} \)**:
- Protons: 11 (sodium has an atomic number of 11)
- Electrons: 10 (1 electron is removed)
- **For \( \text{F}^{-} \)**:
- Protons: 9 (fluorine has an atomic number of 9)
- Electrons: 10 (1 electron is added)
- **For \( \text{O}^{2-} \)**:
- Protons: 8 (oxygen has an atomic number of 8)
- Electrons: 10 (2 electrons are added)

3. **Analyze the Effective Nuclear Charge**:
- All four ions have the same number of electrons (10), but they differ in the number of protons.
- The effective nuclear charge (Z-effective) increases with the number of protons:
- \( \text{Mg}^{2+} \) has the highest Z-effective (12 protons).
- \( \text{Na}^{+} \) has 11 protons.
- \( \text{F}^{-} \) has 9 protons.
- \( \text{O}^{2-} \) has 8 protons.

4. **Determine the Ionic Radius Order**:
- The greater the number of protons, the stronger the attraction on the electrons, leading to a smaller ionic radius.
- Therefore, the order from smallest to largest ionic radius is:
- \( \text{Mg}^{2+} < \text{Na}^{+} < \text{F}^{-} < \text{O}^{2-} \)

5. **Final Order**:
- The correct order of ionic radii is:
- \( \text{Mg}^{2+} < \text{Na}^{+} < \text{F}^{-} < \text{O}^{2-} \)