The correct sequence which shows decreasing order of the ionic radii of the elements is

Options

A. `Al^(3+)gtMg^(2+) gt Na^(+) gt F^(-)gtO^(2-)`
B. `Na^(+) gtMg^(2+) gtAl^(3+) gt O^(2-) gt F^(-)`
C. `Na^(+) gt F^(-)gt Mg^(2+) gt O^(2-)gt Al^(3+)`
D. `O^(2-)gtF^(-) gt Na^(+) gt Mg^(2+) gt Al^(3+)`

Answer

To determine the correct sequence showing the decreasing order of ionic radii for the given elements (Al³⁺, Mg²⁺, Na⁺, F⁻, O²⁻), we will follow these steps:

### Step 1: Identify the Ionic Species and Their Electron Configuration
All the given ions are isoelectronic, meaning they have the same number of electrons. In this case, all of them have 10 electrons. The ions are:
- Al³⁺ (Aluminum ion)
- Mg²⁺ (Magnesium ion)
- Na⁺ (Sodium ion)
- F⁻ (Fluoride ion)
- O²⁻ (Oxide ion)

### Step 2: Determine the Atomic Numbers
Next, we will identify the atomic numbers of each element:
- Aluminum (Al) has an atomic number of 13.
- Magnesium (Mg) has an atomic number of 12.
- Sodium (Na) has an atomic number of 11.
- Fluorine (F) has an atomic number of 9.
- Oxygen (O) has an atomic number of 8.

### Step 3: Calculate the Z/E Ratio
The ionic radius is influenced by the charge of the ion and the atomic number. We will calculate the Z/E ratio (where Z is the atomic number and E is the number of electrons) for each ion:
- For O²⁻: Z/E = 8/10 = 0.8
- For F⁻: Z/E = 9/10 = 0.9
- For Na⁺: Z/E = 11/10 = 1.1
- For Mg²⁺: Z/E = 12/10 = 1.2
- For Al³⁺: Z/E = 13/10 = 1.3

### Step 4: Analyze the Relationship Between Z/E Ratio and Ionic Radii
From our calculations, we can conclude:
- A lower Z/E ratio corresponds to a larger ionic radius.
- A higher Z/E ratio corresponds to a smaller ionic radius.

### Step 5: Arrange the Ions in Decreasing Order of Ionic Radii
Based on the Z/E ratios calculated:
- O²⁻ (0.8) > F⁻ (0.9) > Na⁺ (1.1) > Mg²⁺ (1.2) > Al³⁺ (1.3)

Thus, the correct sequence showing the decreasing order of ionic radii is:
**O²⁻ > F⁻ > Na⁺ > Mg²⁺ > Al³⁺**

### Final Answer:
The correct sequence is: **O²⁻ > F⁻ > Na⁺ > Mg²⁺ > Al³⁺**

---