Which of the following correctly represents the order of atomic radii

Options

A. `Mg^(2+)ltNa^+ltF^-ltO^(2-)`
B. `Na^+ltF^-ltMg^(2+)ltO^(2-)`
C. `Na^+ltMg^(2+)ltO^(2-)ltF^-`
D. `O^(2-)ltF^-ltNa^+ltMg^(2+)`

Answer

To determine the correct order of atomic radii among the given options, we will analyze the atomic radii of the isoelectronic species provided in the question. The species we are considering are:

1. Magnesium ion (Mg²⁺)
2. Sodium ion (Na⁺)
3. Fluoride ion (F⁻)
4. Oxide ion (O²⁻)

### Step-by-Step Solution:

**Step 1: Identify the number of electrons in each species.**
- **Mg²⁺**: Magnesium has an atomic number of 12. After losing 2 electrons, it has 10 electrons.
- **Na⁺**: Sodium has an atomic number of 11. After losing 1 electron, it has 10 electrons.
- **F⁻**: Fluorine has an atomic number of 9. After gaining 1 electron, it has 10 electrons.
- **O²⁻**: Oxygen has an atomic number of 8. After gaining 2 electrons, it has 10 electrons.

**Step 2: Recognize that all species are isoelectronic.**
All four species have the same number of electrons (10 electrons), which means they are isoelectronic.

**Step 3: Understand the effect of nuclear charge on atomic radius.**
In isoelectronic species, the atomic radius is inversely related to the nuclear charge (the number of protons in the nucleus). The more protons present, the stronger the attraction between the nucleus and the electrons, leading to a smaller atomic radius.

**Step 4: Determine the nuclear charge for each species.**
- **Mg²⁺**: 12 protons (nuclear charge = +12)
- **Na⁺**: 11 protons (nuclear charge = +11)
- **F⁻**: 9 protons (nuclear charge = +9)
- **O²⁻**: 8 protons (nuclear charge = +8)

**Step 5: Order the species based on nuclear charge.**
Since the atomic radius decreases with increasing nuclear charge, we can arrange the species in order of increasing atomic radius:
- **Mg²⁺** (smallest radius, highest nuclear charge)
- **Na⁺**
- **F⁻**
- **O²⁻** (largest radius, lowest nuclear charge)

**Final Order of Atomic Radii:**
Mg²⁺ < Na⁺ < F⁻ < O²⁻

### Conclusion:
The correct order of atomic radii from smallest to largest is:
**Mg²⁺ < Na⁺ < F⁻ < O²⁻**