Which of these ions is smallest in size?

Options

A. `O^(2– )`
B. `C^(4– )`
C. `F^– `
D. `N^(3–) `

Answer

To determine which of the given ions is the smallest in size, we need to analyze the ions based on their effective nuclear charge and the number of protons. The ions given are O²⁻, C⁴⁻, F⁻, and N³⁻.

### Step-by-Step Solution:

1. **Identify the Ions and Their Charges**:
- O²⁻ (Oxygen ion with a -2 charge)
- C⁴⁻ (Carbon ion with a -4 charge)
- F⁻ (Fluorine ion with a -1 charge)
- N³⁻ (Nitrogen ion with a -3 charge)

2. **Determine the Number of Protons**:
- Oxygen (O) has 8 protons.
- Carbon (C) has 6 protons.
- Fluorine (F) has 9 protons.
- Nitrogen (N) has 7 protons.

3. **Determine the Number of Electrons**:
- O²⁻: 8 protons + 2 extra electrons = 10 electrons.
- C⁴⁻: 6 protons + 4 extra electrons = 10 electrons.
- F⁻: 9 protons + 1 extra electron = 10 electrons.
- N³⁻: 7 protons + 3 extra electrons = 10 electrons.

4. **Compare the Ions**:
- All four ions (O²⁻, C⁴⁻, F⁻, N³⁻) have the same number of electrons (10 electrons).
- The size of an ion is influenced by the effective nuclear charge (Z-effective), which is determined by the number of protons.

5. **Calculate the Effective Nuclear Charge**:
- O²⁻: 8 protons (Z-effective = 8)
- C⁴⁻: 6 protons (Z-effective = 6)
- F⁻: 9 protons (Z-effective = 9)
- N³⁻: 7 protons (Z-effective = 7)

6. **Determine the Size of the Ions**:
- As the number of protons increases, the effective nuclear charge increases, which pulls the electrons closer to the nucleus, resulting in a smaller ionic radius.
- Therefore, the order of ionic size from largest to smallest is: C⁴⁻ > N³⁻ > O²⁻ > F⁻.

7. **Conclusion**:
- The smallest ion among the given options is F⁻ (Fluoride ion).

### Final Answer:
The smallest ion in size is **F⁻** (Fluoride ion).