The solubility of `Na_(2),SO_(4),BeSO_(4),MgSO_(4) and BaSO_(4)` will follow the order

Options

A. `BaSO_(4)gtBeSO_(4)gtMgSO_(4)gtNa_(2)SO_(4)`
B. `Na_(2)SO_(4)gtBeSO_(4)gtMgSO_(4)gtBaSO_(4)`
C. `BeSO_(4)gtMgSO_(4)gtBaSO_(4)gtNa_(2)SO_(4)`
D. `MgSO_(4)gtBeSO_(4)gtNa_(2)SO_(4)gtBaSO_(4)`

Explanation

To determine the solubility order of the sulfates `Na2SO4`, `BeSO4`, `MgSO4`, and `BaSO4`, we can analyze the solubility trends of these compounds based on the properties of their constituent cations.

### Step-by-Step Solution:

1. **Understanding Solubility Trends**:
- The solubility of sulfates generally decreases as we move down the group in the periodic table. This is due to the increasing size of the cations, which affects their ability to be hydrated by water molecules.

2. **Analyzing Cations**:
- The cations in question are `Na+`, `Be2+`, `Mg2+`, and `Ba2+`.
- Sodium (`Na+`) is an alkali metal and is highly soluble in water.
- Beryllium (`Be2+`) and magnesium (`Mg2+`) are alkaline earth metals, and both are known to have good solubility in sulfates.
- Barium (`Ba2+`), being lower in the group, has lower solubility due to its larger ionic size.

3. **Hydration Energy Consideration**:
- Smaller cations like `Be2+` and `Mg2+` have higher hydration energies compared to larger cations like `Ba2+`.
- Higher hydration energy leads to greater solubility in water.

4. **Establishing the Order**:
- Based on the above points, we can establish the following order of solubility:
- `Na2SO4` > `BeSO4` > `MgSO4` > `BaSO4`
- This means that sodium sulfate is the most soluble, followed by beryllium sulfate, magnesium sulfate, and finally barium sulfate, which is virtually insoluble.

5. **Conclusion**:
- The correct order of solubility for the sulfates is:
- `Na2SO4` > `BeSO4` > `MgSO4` > `BaSO4`

### Final Answer:
The solubility order is: `Na2SO4 > BeSO4 > MgSO4 > BaSO4`.