Arrange the following ions in order of their increasing radii : `Na^(+) , Mg^(2+) , Si^(4+) , Al^(3+)`

Options

A. `Na^(+) lt Mg^(2+) lt Al^(3+) lt Si^(4+)`
B. `Mg^(2+) lt Na^(+) lt Al^(3+) lt Si^(4+)`
C. `Al^(3+) lt Na^(+) lt Si^(4+) lt Mg^(2+) `
D. `Na^(+) gt Mg^(2+) gt Al^(3+) gt Si^(4+)`

Answer

To arrange the ions \( \text{Na}^+, \text{Mg}^{2+}, \text{Si}^{4+}, \text{Al}^{3+} \) in order of their increasing radii, we can follow these steps:

### Step 1: Identify the Atomic Numbers
- Sodium (\( \text{Na} \)): Atomic number 11
- Magnesium (\( \text{Mg} \)): Atomic number 12
- Aluminum (\( \text{Al} \)): Atomic number 13
- Silicon (\( \text{Si} \)): Atomic number 14

### Step 2: Understand the Charge and Its Effect on Ionic Size
- The ions are all cations (positively charged).
- As the positive charge of a cation increases, the ionic radius decreases. This is because the removal of electrons increases the effective nuclear charge felt by the remaining electrons, pulling them closer to the nucleus.

### Step 3: List the Charges
- \( \text{Na}^+ \): +1 charge
- \( \text{Mg}^{2+} \): +2 charge
- \( \text{Al}^{3+} \): +3 charge
- \( \text{Si}^{4+} \): +4 charge

### Step 4: Compare the Ionic Sizes
- The order of ionic sizes based on the charge is as follows:
- \( \text{Si}^{4+} \) (smallest, due to +4 charge)
- \( \text{Al}^{3+} \)
- \( \text{Mg}^{2+} \)
- \( \text{Na}^+ \) (largest, due to +1 charge)

### Step 5: Write the Final Order
Thus, the order of increasing ionic radii is:
\[ \text{Si}^{4+} < \text{Al}^{3+} < \text{Mg}^{2+} < \text{Na}^+ \]

### Conclusion
The final answer is:
\[ \text{Si}^{4+} < \text{Al}^{3+} < \text{Mg}^{2+} < \text{Na}^+ \]