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How does the line emission spectrum of an element relate to these flame tests?

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Hint:The line spectrum is formed when the method of spectroscopy is used to analyse the emissions occurring. The flame tests excite the electron which in return release the energy to form a line spectrum.

Complete step-by-step answer:Let us study the phenomenon in detail;
If an atom is exposed to higher amounts of energy, then the valence electrons will tend to move along the shells to adjust with the energy provided. In this process, they will emit some photons which when recorded gives the line spectrum on the spectroscope.
More specifically, the energy is provided by the flame during the flame test to each element. Every element produces a photon at a certain time and with a certain intensity which gives different colours which are visible to naked eyes while conducting the test.

Note:Do note that the excitation or coming back of the electron to the ground state only can involve the energy parameters otherwise one cannot induce energy differences in an atom.
The spectroscope helps to read the lines, but the flame test can excite the electron and that’s why it is important to be noted down.