Step 1: Concept
The thermal stability of alkaline earth metal carbonates increases down the group as the size of the metal cation increases, reducing its polarizing power.
Step 2: Meaning
A highly polarizing small cation distorts the large oxygen electron cloud of the carbonate ion ($CO_{3}^{2-}$), making it break down into its corresponding oxide and carbon dioxide gas easily.
Step 3: Analysis
$Be^{2+}$ is the smallest cation in Group 2 and exerts a high polarizing action on the carbonate group. Because of this, $BeCO_{3}$ is highly unstable and decomposes even at room temperature. To prevent this reverse reaction and maintain it, it must be stored in a $CO_{2}$-rich atmosphere.
Step 4: Conclusion
Therefore, $BeCO_{3}$ is the specific carbonate that requires a $CO_{2}$ atmosphere to prevent spontaneous decomposition.
Final Answer: (D)