Step 1: Understanding the Concept:
Flame tests are a qualitative analytical method used in chemistry to identify the presence of certain metal ions.
When metal ions are heated in a flame, their electrons absorb energy and are excited to higher energy levels.
As these electrons return to their ground state, they emit light of specific wavelengths characteristic of the element's electronic configuration. This light corresponds to specific colors in the visible spectrum.
Step 2: Detailed Explanation:
(A) **Sodium (Na):** When sodium compounds are heated, they produce a very strong, brilliant yellow light. It is one of the most persistent and recognizable flame colors. Thus, (A) matches with (II).
(B) **Calcium (Ca):** Calcium salts impart a distinctive orange-red color to the flame, commonly described as "brick red." Thus, (B) matches with (III).
(C) **Barium (Ba):** Barium compounds produce a pale green light, often called "apple green" in chemical textbooks. Thus, (C) matches with (I).
(D) **Lithium (Li):** Lithium produces a deep, intense purplish-red flame color known as "crimson red." Thus, (D) matches with (IV).
Step 3: Final Answer:
By aligning each element with its characteristic emission color, we find the sequence: A-II, B-III, C-I, D-IV.
This matches option (b).