What is happening at the atomic level to give rise to the observed energies in the flame tests and in the emission spectra

See explanation

Explanation:

According to the Bohr model of the atom, electrons are found in energy levels. Energy is absorbed or emitted when an electron moves from one energy level to another.

During flame test, electrons absorb energy and move to higher energy levels; they quickly return to ground state and emit the energy previously absorbed as a photon of light. This is seen as the colour imparted to the flame by the metal.

The emission spectrum tells us about the range of wavelengths emitted by an atom or compound when it is excited. At an atomic level, the electrons are moved to higher energy levels and as they return to ground state, they emit the various wavelengths that comprise the emission spectrum of any particular substance.