The correct order of ionic size of `N^(3-), Na^(+), F^(-), Mg^(2+) and O^(2-)` and is :

Options

A. `Mg^(2+) gt NA^(+) gt F^(-) gt O^(2-) lt N^(3-)`
B. `N^(3-)gtF^(-)gt O^(2-) lt Na^(+) gt Mg^(2+)`
C. `Mg^(2+) lt Na^(+) lt F^(-) lt O^(2-) lt N^(3-)`
D. `N^(3-) gt O^(2-) gt F^(-) gt Na^(+) lt Mg^(2+)`

Explanation

To determine the correct order of ionic sizes for the ions \(N^{3-}, Na^{+}, F^{-}, Mg^{2+},\) and \(O^{2-}\), we need to analyze the number of electrons and protons in each ion, as well as the concept of effective nuclear charge.

### Step-by-Step Solution:

1. **Identify the Ions and Their Electron Configurations:**
- \(N^{3-}\): Nitrogen has 7 protons and gains 3 electrons, resulting in 10 electrons.
- \(Na^{+}\): Sodium has 11 protons and loses 1 electron, resulting in 10 electrons.
- \(F^{-}\): Fluorine has 9 protons and gains 1 electron, resulting in 10 electrons.
- \(Mg^{2+}\): Magnesium has 12 protons and loses 2 electrons, resulting in 10 electrons.
- \(O^{2-}\): Oxygen has 8 protons and gains 2 electrons, resulting in 10 electrons.

2. **Determine the Effective Nuclear Charge (Z_eff):**
- The effective nuclear charge increases with the number of protons while the number of electrons remains constant.
- \(N^{3-}\) has 7 protons, \(Na^{+}\) has 11 protons, \(F^{-}\) has 9 protons, \(Mg^{2+}\) has 12 protons, and \(O^{2-}\) has 8 protons.

3. **Analyze the Ionic Sizes:**
- The ionic size increases with the addition of electrons (more electron-electron repulsion) and decreases with the loss of electrons (higher effective nuclear charge).
- Thus, the order of ionic sizes will be inversely related to the number of protons (higher protons lead to smaller size).

4. **Order the Ions Based on Their Sizes:**
- \(N^{3-}\) (7 protons, largest size due to high electron repulsion)
- \(O^{2-}\) (8 protons)
- \(F^{-}\) (9 protons)
- \(Na^{+}\) (11 protons)
- \(Mg^{2+}\) (12 protons, smallest size)

5. **Final Order of Ionic Sizes:**
- The correct order of ionic sizes from largest to smallest is:
\[ N^{3-} > O^{2-} > F^{-} > Na^{+} > Mg^{2+} \]