For any particular atom, that is any atom number, there are a fixed number of protons in the nucleus. That 'obliges' the electrons around the atom to take up certain 'orbits' (although that word is not to be taken as anything other than an analogy). Each of those orbits i.e. distance from the nucleus and the manner in which it 'orbits' is characteristic of an atom with that given number of protons.
The electrons can only exist in these orbital locations. Electrons with more energy occupy orbits further way from the nucleus.
For an electron to gain the energy to move up from a lower orbit to a higher, more energetic one, it must acquire the necessary energy from somewhere. Remember that the set of shell radii depends on the number of number of protons in the nucleus. The energy an electron has is usually referred to in 'electron-Volts', eV. So, if in a fictitious atom the two lowest energy levels were -8eV and -10eV, an electron with an energy level of -10eV would require to gain EXACTLY 2eV to jump up to -8eV. When it got up there, if it were to drop back down to -10eV, it would have to loose EXACTLY 2EV.
The acquisition and loss of energy by the electron are always done by the absorption or emission of a photon of light. Therefore such an electron would need to absorb a photon of EXACTLY 2EV to go up a level, or emit a photo of EXACTLY 2EV to go down a level.
The Energy of a photon determines its wavelength and therefore its frequency by this equation: E=h*frequency (h= Planck's constant). Rearranging the equation, you get frequency=E/h... SO... the frequency of the photons that constitute the radiation is directly related to the energy levels in the atom that the electron transitions to and from.
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