Final answer:
The different flame colors produced by calcium and barium are due to the unique electron configurations of these elements which cause electrons to emit light at specific wavelengths as they return to their ground state. Calcium emits red light, while barium emits green light, which is essential in identifying elements via atomic emission spectra.
Step-by-step explanation:
The colors seen during a flame test arise from electrons emitting different wavelengths of light as they return to their ground state. As metals such as calcium and barium are heated in a flame, electrons can be excited to higher energy levels. When these electrons fall back down to their lower energy states, they release energy in the form of light. The color of this light is specific to the metal due to its unique electron configuration. The variance between calcium's flame color and barium's flame color is due to the differences in their electron configurations and consequently, the different energies involved in their transitions.
Calcium typically produces a red flame, while barium produces a green flame. This is because the energy transitions in barium are different from those in calcium. The wavelengths of the emitted photons are specific to the element, as they depend on the particular spacing between energy levels, which in turn is determined by the element's electron configuration. Therefore, the different flame colors help identify the presence of specific elements in a sample and are crucial to atomic emission spectra experiments.