The correct order of increasing thermal stability of `K_(2)CO_(3),MgCO_(3),CaCO_(3),` and `BeCO_(3)` is

Options

A. `K_(2)COltMgCO_(3)ltCaCO_(3)ltBeCO_(3)`
B. `BeCO_(3)ltMgCO_(3)ltK_(2)CO_(3)ltCaCO_(3)`
C. `BeCO_(3)ltMgCO_(3)ltCaCO_(3)ltK_(2)CO_(3)`
D. `MgCO_(3)ltBeCO_(3)ltCaCO_(3)ltK_(2)CO_(3)`

Explanation

To determine the correct order of increasing thermal stability of the carbonates \( K_2CO_3, MgCO_3, CaCO_3, \) and \( BeCO_3 \), we need to analyze the thermal stability of these carbonates based on the properties of the metal cations and their positions in the periodic table.

### Step-by-Step Solution:

1. **Understanding Thermal Stability**:
- Thermal stability of carbonates generally increases with the increase in the size of the cation. Larger cations can stabilize the carbonate ion better due to lower lattice energy.

2. **Position in the Periodic Table**:
- The carbonates in question are from Group 1 (alkali metals) and Group 2 (alkaline earth metals) of the periodic table.
- The order of cations from smallest to largest is: \( Be^{2+} < Mg^{2+} < Ca^{2+} < K^{+} \).

3. **Analyzing Each Carbonate**:
- **\( BeCO_3 \)**: Beryllium has a small ionic radius and a high charge density, leading to a less stable carbonate. It decomposes at relatively low temperatures.
- **\( MgCO_3 \)**: Magnesium is larger than beryllium, so \( MgCO_3 \) is more stable than \( BeCO_3 \) but still less stable compared to calcium and potassium carbonates.
- **\( CaCO_3 \)**: Calcium is larger than magnesium, thus \( CaCO_3 \) is more thermally stable than both \( BeCO_3 \) and \( MgCO_3 \).
- **\( K_2CO_3 \)**: Potassium is an alkali metal and has a larger ionic radius than the alkaline earth metals, leading to a very stable carbonate.

4. **Conclusion on Stability Order**:
- Based on the analysis, the order of increasing thermal stability is:
\[ BeCO_3 < MgCO_3 < CaCO_3 < K_2CO_3 \]

### Final Answer:
The correct order of increasing thermal stability is:
\[ BeCO_3 < MgCO_3 < CaCO_3 < K_2CO_3 \]