The correct order of increasing ionic radii is

Options

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

Explanation

To determine the correct order of increasing ionic radii, we need to analyze the ionic sizes of different ions based on their charge and the number of electrons they possess. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Ions
The ions mentioned in the video transcript are:
- \( \text{N}^{3-} \) (Nitride ion)
- \( \text{O}^{2-} \) (Oxide ion)
- \( \text{F}^{-} \) (Fluoride ion)
- \( \text{N}^{+} \) (Nitrogen cation)
- \( \text{M}^{2+} \) (A cation with a +2 charge, unspecified)

### Step 2: Understand Isoelectronic Species
All these ions are isoelectronic, meaning they have the same number of electrons. In this case, they all have 10 electrons (since they are derived from elements in the same period of the periodic table).

### Step 3: Analyze Ionic Radii Trends
For isoelectronic species, the ionic radius decreases with increasing positive charge and increases with increasing negative charge. This is due to the effective nuclear charge experienced by the electrons:
- **Cations** (positive charge) have fewer electrons than protons, leading to a stronger attraction between the nucleus and the remaining electrons, resulting in a smaller radius.
- **Anions** (negative charge) have more electrons than protons, leading to increased electron-electron repulsion, which results in a larger radius.

### Step 4: Order the Ions by Charge
Based on the charge of the ions, we can arrange them in order of increasing ionic radii:
1. \( \text{M}^{2+} \) (smallest radius due to +2 charge)
2. \( \text{N}^{+} \) (next smallest due to +1 charge)
3. \( \text{F}^{-} \) (larger radius due to -1 charge)
4. \( \text{O}^{2-} \) (larger radius due to -2 charge)
5. \( \text{N}^{3-} \) (largest radius due to -3 charge)

### Step 5: Write the Final Order
Thus, the correct order of increasing ionic radii is:
\[ \text{M}^{2+} < \text{N}^{+} < \text{F}^{-} < \text{O}^{2-} < \text{N}^{3-} \]