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The wavelength of the light emitted will always be positive and the energy of the photon will be positive as well. However, the change in energy of the electron as it changes states can be negative. The energy is negative when the electron emits energy when moving down energy levels. The absolute value of this energy would equal the energy per photon of the light needed to excite the electron.
Electromagnetic radiation will only be emitted if the electrons move down from a higher transition level to a lower transition level (ground state). The reason why the energy for this electromagnetic radiation emitted is always positive is because there is a conservation of energy . So when an electron goes down from a higher energy level, it's energy will only become more negative, which means that the energy released/emitted must have a positive value.
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