Which one of the following is the smallest in size?

Options

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

Explanation

To determine which of the given anions is the smallest in size, we can follow these steps:

### Step 1: Identify the Given Species
The species to compare are:
- Na⁺ (Sodium ion)
- N³⁻ (Nitride ion)
- O²⁻ (Oxide ion)
- F⁻ (Fluoride ion)

### Step 2: Determine the Number of Electrons
All the given species are ions and we need to check their electron count:
- Na⁺ has lost one electron from Na (atomic number 11), so it has 10 electrons.
- N³⁻ has gained three electrons from N (atomic number 7), so it has 10 electrons.
- O²⁻ has gained two electrons from O (atomic number 8), so it has 10 electrons.
- F⁻ has gained one electron from F (atomic number 9), so it has 10 electrons.

All these ions are isoelectronic, meaning they all have the same number of electrons (10 electrons).

### Step 3: Apply the Z/e Ratio
The size of an ion is inversely proportional to the ratio of its atomic number (Z) to the number of electrons (e). Since all the ions have the same number of electrons (10), we can compare their atomic numbers:
- Z for Na⁺ = 11
- Z for N³⁻ = 7
- Z for O²⁻ = 8
- Z for F⁻ = 9

### Step 4: Compare the Atomic Numbers
Since the size is inversely proportional to Z/e, the ion with the highest atomic number will be the smallest:
- Na⁺ has the highest atomic number (11), thus it will have the smallest size among the given ions.

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

### Final Answer
Na⁺ is the smallest in size.

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