I tried this...
In an atom, such as Hydrogen, the electron can occupy determined states where it will not emit radiation. The electron will preferably occupy the ground state so that the energy of the atom will be a minimum.
Receiving energy the atom will become excited and its electron will jump up occupying excited states of higher energy.
The electron will go back (after a short time) to the ground state emitting the surplus energy in fixed amounts corresponding to the energy gap between the excited and ground state. This energy is emitted in form of photons of light that will form our spectrum.