For `N^(3-) gt O^(2-) gt F^(-)` and `Na^(+)`, the order in which their ionic radii varies is

Options

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

Explanation

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

### Step-by-Step Solution:

1. **Identify the Ions and Their Electron Configurations:**
- \(N^{3-}\): Nitrogen has an atomic number of 7. When it gains 3 electrons, its electron configuration becomes \(1s^2 2s^2 2p^6\) (total 10 electrons).
- \(O^{2-}\): Oxygen has an atomic number of 8. When it gains 2 electrons, its electron configuration becomes \(1s^2 2s^2 2p^6\) (total 10 electrons).
- \(F^{-}\): Fluorine has an atomic number of 9. When it gains 1 electron, its electron configuration becomes \(1s^2 2s^2 2p^6\) (total 10 electrons).
- \(Na^{+}\): Sodium has an atomic number of 11. When it loses 1 electron, its electron configuration becomes \(1s^2 2s^2 2p^6\) (total 10 electrons).

2. **Determine the Number of Protons:**
- \(N^{3-}\) has 7 protons.
- \(O^{2-}\) has 8 protons.
- \(F^{-}\) has 9 protons.
- \(Na^{+}\) has 11 protons.

3. **Analyze the Ionic Sizes:**
- All ions have the same electron configuration (10 electrons), but they differ in the number of protons.
- The more protons an ion has, the greater the effective nuclear charge acting on the electrons, which pulls the electrons closer to the nucleus and results in a smaller ionic radius.

4. **Order the Ions by Ionic Radius:**
- \(N^{3-}\) (7 protons) has the largest radius because it has the least effective nuclear charge.
- \(O^{2-}\) (8 protons) is smaller than \(N^{3-}\) but larger than \(F^{-}\).
- \(F^{-}\) (9 protons) is smaller than both \(N^{3-}\) and \(O^{2-}\).
- \(Na^{+}\) (11 protons) has the smallest radius due to the highest effective nuclear charge.

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