Out of `BeF_(2), MgF_(2), CaF_(2), SrF_(2)` which has maximum solubility :

Options

A. `BeF_(2)`
B. `MgF_(2)`
C. `CaF_(2)`
D. `SrF_(2)`

Explanation

To determine which of the compounds \( \text{BeF}_2, \text{MgF}_2, \text{CaF}_2, \text{SrF}_2 \) has the maximum solubility, we need to consider the factors that affect solubility, particularly hydration enthalpy.

### Step-by-Step Solution:

1. **Identify the Compounds**: The compounds in question are \( \text{BeF}_2 \), \( \text{MgF}_2 \), \( \text{CaF}_2 \), and \( \text{SrF}_2 \). These are fluorides of group 2 elements (alkaline earth metals).

2. **Understand Hydration Enthalpy**: Hydration enthalpy is the energy released when ions are surrounded by water molecules. A higher hydration enthalpy generally indicates greater solubility because it means that more energy is released when the ions dissolve in water.

3. **Compare the Sizes of Cations**: The size of the cations increases as we move down the group from beryllium to strontium:
- \( \text{Be}^{2+} \) is smaller than \( \text{Mg}^{2+} \), which is smaller than \( \text{Ca}^{2+} \), which is smaller than \( \text{Sr}^{2+} \).

4. **Relate Size to Hydration Enthalpy**: Smaller cations have a higher charge density, which leads to stronger interactions with water molecules. Therefore, \( \text{Be}^{2+} \) will have the highest hydration enthalpy due to its small size.

5. **Evaluate Solubility**:
- \( \text{BeF}_2 \) has a high hydration enthalpy due to the small size of \( \text{Be}^{2+} \), making it highly soluble.
- In contrast, \( \text{MgF}_2 \), \( \text{CaF}_2 \), and \( \text{SrF}_2 \) have larger cations, resulting in lower hydration enthalpy and thus lower solubility. These compounds are generally considered to be almost insoluble in water.

6. **Conclusion**: Based on the above analysis, \( \text{BeF}_2 \) has the maximum solubility among the given compounds.

### Final Answer:
The compound with maximum solubility is \( \text{BeF}_2 \).