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 order of atomic radii for the given elements in their ionic forms, we will follow these steps:

### Step 1: Identify the Elements and Their Ionic Forms
The elements given are:
- Sodium (Na)
- Magnesium (Mg)
- Fluorine (F)
- Oxygen (O)

The ionic forms we are considering are:
- Na⁺ (sodium ion)
- Mg²⁺ (magnesium ion)
- F⁻ (fluoride ion)
- O²⁻ (oxide ion)

### Step 2: Determine the Number of Electrons in Each Ion
Next, we need to find out how many electrons each ion has:
- Na⁺: Sodium has an atomic number of 11, so it has 11 protons and 11 electrons. When it loses one electron to form Na⁺, it has 10 electrons.
- Mg²⁺: Magnesium has an atomic number of 12, so it has 12 protons and 12 electrons. When it loses two electrons to form Mg²⁺, it has 10 electrons.
- F⁻: Fluorine has an atomic number of 9, so it has 9 protons and 9 electrons. When it gains one electron to form F⁻, it has 10 electrons.
- O²⁻: Oxygen has an atomic number of 8, so it has 8 protons and 8 electrons. When it gains two electrons to form O²⁻, it has 10 electrons.

### Step 3: Identify the Isoelectronic Species
All four ions (Na⁺, Mg²⁺, F⁻, O²⁻) have the same number of electrons (10), making them isoelectronic species.

### Step 4: Understand the Relationship Between Atomic Radius and Number of Protons
For isoelectronic species, the atomic radius is inversely proportional to the number of protons. This means that as the number of protons increases, the atomic radius decreases due to the increased positive charge in the nucleus attracting the electrons more strongly.

### Step 5: Count the Number of Protons
- Na⁺ has 11 protons.
- Mg²⁺ has 12 protons.
- F⁻ has 9 protons.
- O²⁻ has 8 protons.

### Step 6: Determine the Order of Atomic Radii
Based on the number of protons:
- O²⁻ (8 protons) will have the largest radius because it has the least positive charge.
- F⁻ (9 protons) will be next.
- Na⁺ (11 protons) will be smaller than both O²⁻ and F⁻.
- Mg²⁺ (12 protons) will have the smallest radius.

Thus, the order of atomic radii from largest to smallest is:
O²⁻ > F⁻ > Na⁺ > Mg²⁺

### Final Answer
The correct order of atomic radii is:
**O²⁻ > F⁻ > Na⁺ > Mg²⁺**