Step 1: Understanding the Concept:
Qualitative inorganic analysis involves identifying cations and anions through a series of characteristic tests (flame tests, group reagents, and confirmatory tests).
Step 2: Detailed Explanation:
1. Flame Test: An "apple green" color in the flame test is the characteristic identification for Barium (\(Ba^{2+}\)) ions. (\(Ca^{2+}\) gives brick red, \(Sr^{2+}\) gives crimson red).
2. Cation Group Test: For Group V cations (\(Ba^{2+}, Sr^{2+}, Ca^{2+}\)), the carbonates are precipitated. The precipitate is dissolved in acetic acid. The addition of potassium chromate (\(K_2CrO_4\)) produces a yellow precipitate of \(BaCrO_4\). This confirms \(Ba^{2+}\).
3. Anion Test: The test with conc. \(HNO_3\) and ammonium molybdate which yields a canary yellow precipitate is the specific confirmatory test for Phosphate (\(PO_4^{3-}\)) ions. The precipitate formed is ammonium phosphomolybdate \((NH_4)_3[P(Mo_{12}O_{40})]\).
Combining these results, the salt contains \(Ba^{2+}\) and \(PO_4^{3-}\).
Step 4: Final Answer:
The cation and anion are \(Ba^{2+}\) and \(PO_4^{3-}\) respectively.