Which of the following 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 number of protons and electrons in each ion. The ions in question are derived from the elements carbon (C), nitrogen (N), oxygen (O), and fluorine (F).

### Step-by-Step Solution:

1. **Identify the ions and their electron configurations**:
- Carbon (C) forms the ion C^4-:
- Atomic number = 6 (6 protons)
- Electrons after gaining 4 electrons = 6 + 4 = 10 electrons.
- Nitrogen (N) forms the ion N^3-:
- Atomic number = 7 (7 protons)
- Electrons after gaining 3 electrons = 7 + 3 = 10 electrons.
- Oxygen (O) forms the ion O^2-:
- Atomic number = 8 (8 protons)
- Electrons after gaining 2 electrons = 8 + 2 = 10 electrons.
- Fluorine (F) forms the ion F^-:
- Atomic number = 9 (9 protons)
- Electrons after gaining 1 electron = 9 + 1 = 10 electrons.

2. **Count the number of protons and electrons**:
- All four ions have 10 electrons.
- The number of protons for each ion is as follows:
- C^4-: 6 protons
- N^3-: 7 protons
- O^2-: 8 protons
- F^-: 9 protons

3. **Determine the effective nuclear charge**:
- The effective nuclear charge (Z_eff) is the net positive charge experienced by electrons in an atom. It can be approximated by the number of protons since all ions have the same number of electrons.
- C^4- has 6 protons, N^3- has 7 protons, O^2- has 8 protons, and F^- has 9 protons.

4. **Analyze the relationship between protons and size**:
- As the number of protons increases while the number of electrons remains constant, the attraction between the protons and electrons increases.
- Therefore, the ion with the highest number of protons will have the smallest size due to stronger attraction pulling the electrons closer to the nucleus.

5. **Conclusion**:
- Among the ions, F^- has the highest number of protons (9). Thus, it will be the smallest in size compared to C^4-, N^3-, and O^2-.

### Final Answer:
The smallest ion in size is **F^- (fluoride ion)**.

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