The hydration energy of `Mg^(2+)` ions is lesser than that of:

Options

A. `Al^(3+)`
B. `Ba^(2+)`
C. `Na`
D. none of these

Answer

To determine which ion has greater hydration energy than `Mg^(2+)`, we need to understand the factors that influence hydration energy. Hydration energy is the energy released when ions are surrounded by water molecules. It is influenced by the charge and size of the ion.

### Step-by-Step Solution:

1. **Understanding Hydration Energy**: Hydration energy increases with the charge of the ion and decreases with the size of the ion. This means that smaller ions with higher charges will have higher hydration energies.

2. **Comparing Ions**: We need to compare the hydration energy of `Mg^(2+)` with other ions. The ions we will consider include `Na^+`, `Ba^(2+)`, and `Al^(3+)`.

3. **Charge and Size Analysis**:
- **`Mg^(2+)`**: Magnesium has a +2 charge and a relatively small ionic radius.
- **`Na^+`**: Sodium has a +1 charge and a larger ionic radius than `Mg^(2+)`. Therefore, `Na^+` will have lower hydration energy than `Mg^(2+)`.
- **`Ba^(2+)`**: Barium also has a +2 charge but has a larger ionic radius than `Mg^(2+)`. Hence, `Ba^(2+)` will have lower hydration energy than `Mg^(2+)`.
- **`Al^(3+)`**: Aluminum has a +3 charge and a smaller ionic radius compared to `Mg^(2+)`. Thus, `Al^(3+)` will have higher hydration energy than `Mg^(2+)`.

4. **Conclusion**: Since `Al^(3+)` has a higher charge and a smaller size compared to `Mg^(2+)`, it will have greater hydration energy. Therefore, the hydration energy of `Mg^(2+)` is lesser than that of `Al^(3+)`.

### Final Answer:
The hydration energy of `Mg^(2+)` ions is lesser than that of `Al^(3+)` ions.