Which of the following ions has the smallest size?

Options

A. `Na^+ `
B. `Mg^(2+ )`
C. `Al^(3+) `
D. `P^(5+ )`

Answer

To determine which of the given ions has the smallest size, we need to analyze the ions provided: Na⁺, Mg²⁺, Al³⁺, and P⁵⁺.

### Step-by-Step Solution:

1. **Identify the Ions and Their Electron Configurations:**
- **Na⁺ (Sodium ion)**: Sodium (Na) has an atomic number of 11. When it loses one electron to form Na⁺, it has 10 electrons.
- **Mg²⁺ (Magnesium ion)**: Magnesium (Mg) has an atomic number of 12. When it loses two electrons to form Mg²⁺, it also has 10 electrons.
- **Al³⁺ (Aluminum ion)**: Aluminum (Al) has an atomic number of 13. When it loses three electrons to form Al³⁺, it has 10 electrons.
- **P⁵⁺ (Phosphorus ion)**: Phosphorus (P) has an atomic number of 15. When it loses five electrons to form P⁵⁺, it has 10 electrons.

2. **Determine Isoelectronic Species:**
- All four ions (Na⁺, Mg²⁺, Al³⁺, and P⁵⁺) have the same number of electrons (10 electrons), making them isoelectronic species.

3. **Analyze the Effect of Nuclear Charge:**
- The size of an ion is influenced by its nuclear charge (the number of protons in the nucleus). A higher nuclear charge means a stronger attraction between the nucleus and the electrons, which results in a smaller ionic size.
- The number of protons in each ion is as follows:
- Na⁺: 11 protons
- Mg²⁺: 12 protons
- Al³⁺: 13 protons
- P⁵⁺: 15 protons

4. **Order the Ions by Size:**
- Since all the ions have the same number of electrons, we can compare them based on their nuclear charge:
- P⁵⁺ (15 protons) will have the smallest size due to the highest nuclear charge.
- Al³⁺ (13 protons) will be larger than P⁵⁺ but smaller than Mg²⁺.
- Mg²⁺ (12 protons) will be larger than Al³⁺ but smaller than Na⁺.
- Na⁺ (11 protons) will have the largest size among these ions.

5. **Conclusion:**
- The order of ionic sizes from smallest to largest is:
- P⁵⁺ < Al³⁺ < Mg²⁺ < Na⁺
- Therefore, the ion with the smallest size is **P⁵⁺**.

### Final Answer:
The ion with the smallest size is **P⁵⁺**.