Nuclear attraction is often the deciding control factor for the association of neutral molecules to a given metal ion. Which onee of the following represents the correct order of stability of the ions?
`[Be(H_(2)O)_(4)]^(2+),[Mg(H_(2)O)_(4)]^(2+),[Ca(H_(2)O)_(4)]^(2+)` and `[Sr(H_(2)O)_(4)}^(2+)`

Options

A. `[Be(H_(2)O_(4)]^(2+) gt [Sr(H_(2)O_(4)]^(2+)gt [Mg(H_(2)O)_(4)]^(2+) gt [Ca(H_(2)O)_(4)]^(2+)`
B. `[Ca(H_(2)O)_(4)]^(2+) gt [Mg(H_(2)O)_(4)]^(2+) gt [Be(H_(2)O)_(4)]^(2+) gt gt[S(H_(2)O)_(4)]^(2+)`
C. `[Sr(H_(2)O)_(4)]^(2+) gt [Ca(H_(2)O)_(4)]^(2+) gt [Mg(H_(2)O)_(4)]^(2+) gt [Be(H_(2)O)_(4)]^(2+)`
D. `[Be(H_(2)O)_(4)]^(2+) gt [Mg(H_(2)O)_(4)]^(2+) gt [Ca(H_(2)O)_(4)]^(2+) gt [Srr(H_(2)O)_(4)]^(2+)`

Explanation

To determine the correct order of stability of the ions \([Be(H_2O)_4]^{2+}\), \([Mg(H_2O)_4]^{2+}\), \([Ca(H_2O)_4]^{2+}\), and \([Sr(H_2O)_4]^{2+}\), we need to consider the factors that influence the stability of these hydrated metal ions.

### Step-by-Step Solution:

1. **Understand the Concept of Hydration Energy**:
- Hydration energy is the energy released when water molecules surround and interact with a cation. The greater the hydration energy, the more stable the ion.

2. **Consider the Size of the Cations**:
- The size of the cation affects the degree of hydration. Smaller cations can attract water molecules more effectively compared to larger cations. The order of ionic size for the given cations is:
\[ Be^{2+} < Mg^{2+} < Ca^{2+} < Sr^{2+} \]
- As we move down the group in the periodic table, the size of the cations increases.

3. **Relate Size to Hydration Energy**:
- Smaller cations (like \(Be^{2+}\)) have higher charge density, which leads to stronger interactions with water molecules. Thus, they release more energy upon hydration.
- Conversely, larger cations (like \(Sr^{2+}\)) have lower charge density and interact less effectively with water, resulting in lower hydration energy.

4. **Order of Stability Based on Hydration Energy**:
- Since stability is directly related to hydration energy, the order of stability for the ions can be predicted as follows:
- \([Be(H_2O)_4]^{2+}\) will be the most stable due to its small size and high hydration energy.
- \([Mg(H_2O)_4]^{2+}\) will be next, as it is larger than beryllium but still relatively small.
- \([Ca(H_2O)_4]^{2+}\) will be less stable than magnesium due to its larger size.
- \([Sr(H_2O)_4]^{2+}\) will be the least stable because it is the largest cation among the four.

5. **Final Order of Stability**:
- Therefore, the correct order of stability of the ions is:
\[ [Be(H_2O)_4]^{2+} > [Mg(H_2O)_4]^{2+} > [Ca(H_2O)_4]^{2+} > [Sr(H_2O)_4]^{2+} \]