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When an electron absorbs energy, it will increase its energy level and as a result, have a higher energy(conserving the energy). When the electron loses energy by going from a high energy level to a lower one, the energy lost between the two energy levels will be emitted as light (therefore conserving the energy).
I think one of the main ideas is that when an electron "jumps" from a higher energy level to a lower one the energy given off is seen as light. That's why when doing a calculation of an electron moving between the different energy levels when an electron goes to lower one the energy of that electron is seen as negative because it is losing it. When an electron moves to a higher energy level the energy is seen as positive because it is gaining energy and not releasing an electromagnetic radiation.
When an electron gains energy it goes to a higher orbital (further from the nucleus). When an electron loses energy, it releases the energy as light (photons) and depending upon how much energy is released, the electron travels to a lower orbital.
When considering the release of energy, it is important to remember that energy can not be created nor destroyed, only transferred. With this in mind, the energy released from an excited electron does not disappear, but instead is released into the universe thus conserving the total energy from the beginning.
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