Deep in the semiconductor materials of the LED are "impurities", materials such as aluminum, gallium, indium and phosphide. When properly stimulated, electrons in these materials move from a lower level of energy up to a higher level of energy and occupy a different orbital. Then, at some point, these higher energy electrons give up their "extra" energy in the form of a photon of light, and fall back down to their original energy level. The light that has suddenly been produced rushes away from the electron, atom and the LED to color our world.
Typically, the light produced by a LED is only one color red or green being strong favorites. Although they are cheap, easy to make, don't cost a lot to run, LEDs are not usually used to light a room, because they cannot normally produce the wide range of different colors needed in "white" light.
This is because of the quantum nature of the atoms being used in the LED and the quantum energies of the electrons within them. When an excited electron within a LED gives up energy it must do so in those lumps called quanta. These are fixed packets of energy that cannot be changed or used in fractions; they must always be transferred in whole amounts. Thus, an excited electron has no option but to give off either 1 quanta or 2 quanta of energy, it cannot give up 1.
Also, the electron can only move to very limited orbitals within the atom; it must end up in an orbital where the wavelength is now uses is "in phase" with itself. These two restrictions limit the quality of the quanta of energy being released by the electron, and thus the nature of the photon of light that rushes away from the LED. Since the energy given off is strongly restricted to quanta, and quanta that allow the electron to move to a suitable place within the atom, the photons of light are similarly restricted to a tiny range of values of wavelength and frequency a property we see as "color".
Many LEDs have electrons that can only give up quanta of energy that, when converted into photons, produce light with a wavelength of about nm - which we then see as red light. These electrons are so restricted in the quanta they can emit that they never shine blue light, or green light, or yellow light, only red light. Long, long before their were LEDs in our lives, scientists trying to understand electrons in atoms noted a similar phenomenon when light was either shone on certain materials or given off by certain materials.
They used Bunsen's burner to strongly heat tiny pieces of various materials and minerals until they were so hot that they glowed and gave off light. Sodium, for example, when heated to incandescence, produced a strong yellow light, but no blue, green or red. When the tube is on, the electrons get excited and some will move to higher energies than others.
We call the higher energy levels the excited states. The energy of an electron in an atom is negative.
The negative sign indicates that we need to give the electron energy to move it from the hydrogen atom. Giving the electron energy will increase the amound of energy in the atom.
When the electrons return to lower energy levels, they emit energy in the form of light. The colour of the light depends on the difference in energy between the two levels. For example, the red, green, and blue lines in the spectrum of hydrogen arise when the electron drops to level 2 from levels 3, 4, and 5. Every element has a different number of electrons and a different set of energy levels. Thus, each element emits its own set of colours. See, for example, mercury and neon above.
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