Which one among the following ions, is smallest in size

Options

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

Answer

To determine which ion is the smallest in size among the given options, we will follow these steps:

### Step 1: Identify the Ions and Their Electron Configuration
The ions provided are isoelectronic, meaning they have the same number of electrons. The ions we will consider are:
1. N³⁻ (Nitride ion)
2. O²⁻ (Oxide ion)
3. Fe²⁺ (Iron ion)
4. Na⁺ (Sodium ion)

### Step 2: Count the Electrons and Protons
Next, we will count the number of protons and electrons for each ion:
- **N³⁻**: 7 protons, 10 electrons
- **O²⁻**: 8 protons, 10 electrons
- **Fe²⁺**: 26 protons, 24 electrons
- **Na⁺**: 11 protons, 10 electrons

### Step 3: Calculate the Electron to Proton (E/P) Ratio
Now, we will calculate the E/P ratio for each ion:
- For **N³⁻**: E/P = 10/7 ≈ 1.43
- For **O²⁻**: E/P = 10/8 = 1.25
- For **Fe²⁺**: E/P = 24/26 ≈ 0.92
- For **Na⁺**: E/P = 10/11 ≈ 0.91

### Step 4: Compare the E/P Ratios
To find the smallest ion, we look for the ion with the highest E/P ratio, as a higher ratio indicates a larger effective nuclear charge per electron, leading to a smaller ionic radius.

### Step 5: Identify the Smallest Ion
From our calculations:
- N³⁻ has an E/P ratio of 1.43
- O²⁻ has an E/P ratio of 1.25
- Fe²⁺ has an E/P ratio of 0.92
- Na⁺ has an E/P ratio of 0.91

The smallest ion is the one with the lowest E/P ratio, which is **Na⁺**.

### Conclusion
Thus, the smallest ion among the options is **Na⁺**.

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