Thermal stability of `MCO_(3)` is in order:

Options

A. `BeCO_(3)ltMgCO_(3)ltCaCO_(3)ltSrCO_(3)ltBaCO_(3)`
B. `MgCO_(3)ltBeCO_(3)ltCaCO_(3)ltSrCO_(3)BaCO_(3)`
C. `CaCO_(3)ltSrCO_(3)ltBaCO_(3)ltBeCO_(3)ltMgCO_(3)`
D. `BaCO_(3)gtSrCO_(3)gtCaCO_(3)gtMgCO_(3)ltBeCO_(3)`

Answer

To determine the thermal stability of alkaline earth metal carbonates (MCO₃), we can analyze the trend in stability as we move down the group in the periodic table. Here’s a step-by-step solution:

### Step 1: Identify the Carbonates
The alkaline earth metals are beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), and barium (Ba). Therefore, the carbonates we will consider are:
- BeCO₃ (Beryllium carbonate)
- MgCO₃ (Magnesium carbonate)
- CaCO₃ (Calcium carbonate)
- SrCO₃ (Strontium carbonate)
- BaCO₃ (Barium carbonate)

### Step 2: Understand Thermal Stability
Thermal stability of a compound refers to its ability to withstand heat without decomposing. In the case of carbonates, thermal stability can be influenced by the ionic and covalent character of the bonds within the compound.

### Step 3: Analyze Trends in Stability
As we move down the group from beryllium to barium:
- The size of the cation (M²⁺) increases.
- The carbonate ion (CO₃²⁻) remains the same size.

According to Fajans' rules, when the cation is smaller compared to the anion, the compound tends to have more covalent character. Conversely, as the cation size increases, the covalent character decreases, leading to an increase in ionic character.

### Step 4: Determine the Order of Stability
- **Beryllium carbonate (BeCO₃)** is the least thermally stable because Be²⁺ is small and has a high charge density, leading to more covalent character.
- **Magnesium carbonate (MgCO₃)** is more stable than BeCO₃ but less stable than the others.
- **Calcium carbonate (CaCO₃)** is more thermally stable than both BeCO₃ and MgCO₃.
- **Strontium carbonate (SrCO₃)** is more stable than CaCO₃.
- **Barium carbonate (BaCO₃)** is the most thermally stable due to the larger size of Ba²⁺, which results in a higher ionic character.

### Step 5: Write the Final Order
The increasing order of thermal stability of the alkaline earth metal carbonates is:
**BeCO₃ < MgCO₃ < CaCO₃ < SrCO₃ < BaCO₃**

### Conclusion
Thus, the correct order of thermal stability of MCO₃ is:
**Beryllium carbonate < Magnesium carbonate < Calcium carbonate < Strontium carbonate < Barium carbonate.**