The correct order of ionic radii.

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 for the given ions (Na⁺, Mg²⁺, F⁻, O²⁻), we will analyze the ionic sizes based on their charge and the number of protons and electrons they contain.

### Step-by-Step Solution:

1. **Identify the Ions and Their Charges**:
- Sodium ion (Na⁺): 1 positive charge
- Magnesium ion (Mg²⁺): 2 positive charges
- Fluoride ion (F⁻): 1 negative charge
- Oxide ion (O²⁻): 2 negative charges

2. **Determine the Number of Protons and Electrons**:
- Na⁺:
- Protons = 11 (atomic number of Na)
- Electrons = 11 - 1 = 10
- Mg²⁺:
- Protons = 12 (atomic number of Mg)
- Electrons = 12 - 2 = 10
- F⁻:
- Protons = 9 (atomic number of F)
- Electrons = 9 + 1 = 10
- O²⁻:
- Protons = 8 (atomic number of O)
- Electrons = 8 + 2 = 10

3. **Identify Isoelectronic Species**:
All four ions (Na⁺, Mg²⁺, F⁻, O²⁻) are isoelectronic, meaning they all have the same number of electrons (10 electrons).

4. **Analyze the Effective Nuclear Charge**:
- The effective nuclear charge (Z_eff) is the net positive charge experienced by electrons in a multi-electron atom. It is influenced by the number of protons (positive charge) and the number of electrons (negative charge).
- For isoelectronic species, the size of the ion is inversely related to the number of protons. More protons mean a stronger attraction to the electrons, resulting in a smaller ionic radius.

5. **Order the Ions Based on Their Sizes**:
- Mg²⁺: 12 protons → smallest size (strongest attraction)
- Na⁺: 11 protons → larger than Mg²⁺
- F⁻: 9 protons → larger than Na⁺
- O²⁻: 8 protons → largest size (weakest attraction)

6. **Final Order of Ionic Radii**:
The correct order of ionic radii from smallest to largest is:
**Mg²⁺ < Na⁺ < F⁻ < O²⁻**

### Conclusion:
The correct order of ionic radii is **Mg²⁺ < Na⁺ < F⁻ < O²⁻**.