The correct order of the increasing ionic character is

Options

A. `BeCl_(2) lt MgCl_(2) ltCaCl_(2) lt BaCl_(2)`
B. `BeCl_(2) lt MgCl_(2) lt BaCl_(2) lt CaCl_(2)`
C. `BeCl_(2) lt BaCl_(2) lt MgCl_2 lt CaCl_(2)`
D. `BaCl_(2) lt CaCl_(2) lt MgCl_(2) lt BeCl_(2)`

Explanation

To determine the correct order of increasing ionic character among the given cations (Beryllium \( \text{Be}^{2+} \), Magnesium \( \text{Mg}^{2+} \), Calcium \( \text{Ca}^{2+} \), and Barium \( \text{Ba}^{2+} \)), we can follow these steps:

### Step 1: Understand Ionic Character
Ionic character refers to the extent to which a bond between two atoms has ionic characteristics. It is influenced by the size and charge of the ions involved. Smaller cations with higher charges tend to have more covalent character, while larger cations with lower charges have more ionic character.

### Step 2: Analyze the Cations
- **Beryllium \( \text{Be}^{2+} \)**: It is the smallest cation among the group. Its small size leads to a high charge density, which increases its ability to polarize anions, resulting in a greater covalent character and lower ionic character.
- **Magnesium \( \text{Mg}^{2+} \)**: Larger than \( \text{Be}^{2+} \), but still relatively small. It has a lower charge density than beryllium, hence it has slightly more ionic character than beryllium.
- **Calcium \( \text{Ca}^{2+} \)**: Larger than magnesium, leading to a further decrease in charge density and an increase in ionic character.
- **Barium \( \text{Ba}^{2+} \)**: The largest cation in this group, which results in the lowest charge density and the highest ionic character.

### Step 3: Order the Cations by Ionic Character
Based on the analysis:
1. \( \text{Be}^{2+} \) has the least ionic character.
2. \( \text{Mg}^{2+} \) has more ionic character than beryllium.
3. \( \text{Ca}^{2+} \) has more ionic character than magnesium.
4. \( \text{Ba}^{2+} \) has the most ionic character.

Thus, the order of increasing ionic character is:
\[ \text{Be}^{2+} < \text{Mg}^{2+} < \text{Ca}^{2+} < \text{Ba}^{2+} \]

### Final Answer
The correct order of increasing ionic character is:
\[ \text{Be}^{2+} < \text{Mg}^{2+} < \text{Ca}^{2+} < \text{Ba}^{2+} \]

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