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

Options

A. (a) `BeCO_3 lt MgCO_3 lt K_2CO_3 lt CaCO_3`
B. (b) `BeCO_3 lt MgCO_3 lt CaCO_3 lt K_2CO_3`
C. (c) `MgCO_3 lt BeCO_3 lt CaCO_3 lt K_2CO_3`
D. (d) `K_2CO_3 lt MgCO_3 lt CaCO_3 lt BeCO_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 compounds based on the properties of the metal ions involved.

### Step-by-Step Solution:

1. **Understand Thermal Stability**:
- Thermal stability refers to the ability of a compound to withstand heat without decomposing. A more thermally stable compound requires a higher temperature to decompose.

2. **Identify the Group of Each Compound**:
- \( K_2CO_3 \) (Potassium Carbonate) is an alkali metal carbonate from Group 1.
- \( MgCO_3 \) (Magnesium Carbonate) is an alkaline earth metal carbonate from Group 2.
- \( CaCO_3 \) (Calcium Carbonate) is also an alkaline earth metal carbonate from Group 2.
- \( BeCO_3 \) (Beryllium Carbonate) is from Group 2 as well.

3. **Trend of Thermal Stability**:
- For metal carbonates, thermal stability generally increases down the group in the periodic table. This is because as the size of the metal ion increases, the polarizing power decreases, making the carbonate more stable.
- Conversely, thermal stability decreases across a period due to the decrease in size and increase in polarizing power of the metal ions.

4. **Comparison of Carbonates**:
- Among the alkaline earth metals, the thermal stability order is \( BeCO_3 < MgCO_3 < CaCO_3 \) because as we move down the group, the size of the metal ion increases, leading to decreased polarizing power and increased thermal stability.
- Since \( K_2CO_3 \) is an alkali metal carbonate, it is generally more thermally stable than alkaline earth metal carbonates.

5. **Final Order of Increasing Thermal Stability**:
- Based on the above points, we can summarize the order of increasing thermal stability as:
\[ BeCO_3 < MgCO_3 < CaCO_3 < K_2CO_3 \]

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