Let's analyze the chemical reaction given in the problem: beryllium oxide (\( \text{BeO} \)) reacts with ammonia (\( \text{NH}_3 \)) and hydrogen fluoride (\( \text{HF} \)) to give a compound 'A'. The compound 'A' upon thermal decomposition yields beryllium fluoride (\( \text{BeF}_2 \)) and ammonium fluoride (\( \text{NH}_4\text{F} \)). We need to identify the compound 'A'.
To solve this, let's consider the components involved in the reaction:
- \(\text{BeO}\) reacts with \(\text{NH}_3\) and \(\text{HF}\) to form a beryllium-ammonium-fluoride compound.
- The product forms \(\text{BeF}_2\) and \(\text{NH}_4\text{F}\) upon decomposition, indicating that 'A' is likely a complex compound containing these ions.
- Let's consider the stoichiometry required to balance the creation and decomposition:
Since \(\text{A}\) when decomposed yields two products, \(\text{BeF}_2\) should have a single beryllium for stoichiometric balance. The formula \(\left( \text{NH}_4 \right)_2 \text{BeF}_4\) accommodates this:
- \(\left( \text{NH}_4 \right)_2 \text{BeF}_4\) decomposes to \(\text{BeF}_2\) and 2 \(\text{NH}_4\text{F}\).
- Thus, the breakdown is: \(\left( \text{NH}_4 \right)_2 \text{BeF}_4 \rightarrow \text{BeF}_2 + 2 \, \text{NH}_4\text{F}\).
- This matches the components given: a source for \(\text{BeF}_2\) and \(\text{NH}_4\text{F}\).
Thus, the correct compound 'A' is \(\left( \text{NH}_4 \right)_2 \text{BeF}_4\), because:
- It contains beryllium, ammonium, and fluoride ions adequately.
- On decomposition, it yields the exact products as described: \(\text{BeF}_2\) and \(\text{NH}_4\text{F}\).
Let's now evaluate other options:
- \(\left( \text{NH}_4 \right) \text{BeF}_3\): Contains only one ammonium ion, making it incapable of yielding \(\text{NH}_4\text{F}\) properly.
- \(\text{H}_3 \text{NBeF}_3\): This doesn't even contain sufficient ammonium for producing \(\text{NH}_4\text{F}\).
- \(\left( \text{NH}_4 \right) \text{Be}_2 \text{F}_5\): Incorrect ratio of beryllium and fluorine for the decomposition products given.
Therefore, the correct answer is: \(\left( \text{NH}_4 \right)_2 \text{BeF}_4\).