Mark out the correct increasing order of radius.

Options

A. `As^(3-)ltBr^(-) lt K^(+) lt Mg^(2+)`
B. `Mg^(2+) lt K^(+) lt Br^(-) lt As^(3-)`
C. `Mg^(2+)ltK^(+)ltAs^(3-) lt Br^(-)`
D. `K^(+) lt Mg^(2+) lt Br^(-) lt As^(3-)`

Answer

To determine the correct increasing order of ionic radii, we need to analyze the sizes of cations and anions based on their charge and the number of electrons they possess. Here's a step-by-step solution:

### Step 1: Understand the relationship between ions and their parent atoms
- Cations (positively charged ions) are smaller than their parent atoms because they lose electrons. This results in a higher effective nuclear charge acting on the remaining electrons, pulling them closer to the nucleus.
- Anions (negatively charged ions) are larger than their parent atoms because they gain electrons. This increases electron-electron repulsion and causes the electron cloud to expand.

**Hint:** Remember that cations are smaller than their neutral atoms, while anions are larger.

### Step 2: Compare the sizes of cations
- When comparing cations, the charge affects their size. A cation with a higher positive charge is smaller than one with a lower positive charge. For example, \(Mg^{2+}\) is smaller than \(K^{+}\) because \(Mg^{2+}\) has lost two electrons compared to \(K^{+}\), which has lost only one.

**Hint:** Higher positive charge means smaller size for cations.

### Step 3: Compare the sizes of anions
- When comparing anions, the opposite is true. Anions with a higher negative charge are larger than those with a lower negative charge. For example, \(As^{3-}\) is larger than \(Br^{-}\) because \(As^{3-}\) has three additional electrons compared to \(Br^{-}\), which has only one additional electron.

**Hint:** Higher negative charge means larger size for anions.

### Step 4: Combine the information
- Based on the above points, we can start to arrange the ions in increasing order of their radii.
- We know that \(Mg^{2+}\) is smaller than \(K^{+}\), and \(Br^{-}\) is smaller than \(As^{3-}\).

### Step 5: Final arrangement
- The correct increasing order of radius is:
\[ Mg^{2+} < K^{+} < Br^{-} < As^{3-} \]

### Conclusion
Thus, the correct increasing order of radius is \(Mg^{2+} < K^{+} < Br^{-} < As^{3-}\).