Which of the following can not be explained on the basis of polarisation :-

Options

A. `Ag_(2)S` is much less soluble than `Ag_(2)O`
B. `BeCO_(3)` is thermally less stable than `BaCO_(3)`
C. `BaCO_(3)` is less soluble than `MgCO_(3)`
D. Melting point of `AlCl_(3)` is much less than that of NaCl.

Explanation

To solve the question "Which of the following can not be explained on the basis of polarization?", we will analyze the statements provided and determine which one does not relate to the concept of polarization and covalent character.

### Step-by-Step Solution:

1. **Understanding Polarization and Covalent Character**:
- Polarization refers to the distortion of the electron cloud of an anion by the electric field of a cation. The degree of polarization is influenced by the size and charge of the ions involved.
- Covalent character in ionic compounds increases with the polarization of the anion by the cation. Smaller cations with higher charges can polarize larger anions more effectively.

2. **Analyzing Statement A**:
- **Statement**: Ag2S is much less soluble than Ag2O.
- **Analysis**: Ag+ is the common cation. Ag2S (with S2-) has a larger anion compared to Ag2O (with O2-). As the size of the anion increases, the covalent character increases, leading to decreased solubility. This can be explained by polarization.
- **Conclusion**: This statement can be explained by polarization.

3. **Analyzing Statement B**:
- **Statement**: BeCO3 is less stable than BaCO3.
- **Analysis**: Beryllium (Be2+) is smaller than Barium (Ba2+). Smaller cations have a greater ability to polarize the anion (CO3^2-), leading to increased covalent character in BeCO3, making it less stable. This is also related to polarization.
- **Conclusion**: This statement can be explained by polarization.

4. **Analyzing Statement C**:
- **Statement**: BaCO3 is less soluble than MgCO3.
- **Analysis**: As we move down the group in the periodic table, the size of the cation increases. Ba2+ is larger than Mg2+, which means BaCO3 would have a lower covalent character and thus should be more soluble than MgCO3. This contradicts the statement, indicating that it cannot be explained by polarization.
- **Conclusion**: This statement cannot be explained by polarization.

5. **Analyzing Statement D**:
- **Statement**: The melting point of AlCl3 is much less than NaCl.
- **Analysis**: NaCl is an ionic compound with high ionic character, while AlCl3 has significant covalent character due to the polarization of Cl- by Al3+. This results in a lower melting point for AlCl3 compared to NaCl. This can be explained by polarization.
- **Conclusion**: This statement can be explained by polarization.

### Final Answer:
The statement that cannot be explained on the basis of polarization is **Statement C: BaCO3 is less soluble than MgCO3**.

---