Which one of the following is the smallest in size?

Options

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

Answer

To determine which of the given ions is the smallest in size, we need to analyze the options provided: N³⁻, O²⁻, F⁻, and Na⁺.

### Step-by-Step Solution:

1. **Identify the Number of Electrons**:
- N³⁻ (Nitride ion): Nitrogen has an atomic number of 7. In N³⁻, there are 7 protons and 3 additional electrons, giving it a total of 10 electrons.
- O²⁻ (Oxide ion): Oxygen has an atomic number of 8. In O²⁻, there are 8 protons and 2 additional electrons, also giving it a total of 10 electrons.
- F⁻ (Fluoride ion): Fluorine has an atomic number of 9. In F⁻, there are 9 protons and 1 additional electron, resulting in 10 electrons.
- Na⁺ (Sodium ion): Sodium has an atomic number of 11. In Na⁺, there are 11 protons and 1 electron is removed, resulting in 10 electrons.

2. **Determine Isoelectronic Species**:
- All four ions (N³⁻, O²⁻, F⁻, Na⁺) have the same number of electrons (10 electrons). Therefore, they are isoelectronic species.

3. **Understanding Size Trends in Isoelectronic Species**:
- The size of isoelectronic species decreases with an increase in atomic number. This is because as the atomic number increases, the positive charge in the nucleus increases, pulling the electrons closer to the nucleus and resulting in a smaller ionic radius.

4. **Compare Atomic Numbers**:
- N³⁻ has an atomic number of 7.
- O²⁻ has an atomic number of 8.
- F⁻ has an atomic number of 9.
- Na⁺ has an atomic number of 11.

5. **Determine the Smallest Ion**:
- Since Na⁺ has the highest atomic number (11) among the isoelectronic species, it will be the smallest in size due to the stronger nuclear charge acting on the same number of electrons.

### Conclusion:
The smallest ion among the given options is **Na⁺**.