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When an electron goes from a higher state to a lower state, it gives up energy equal to the difference of energy levels of the two states. This energy is in the form of a photon. If it goes directly from n=3 to n=1, then 1 photon is emitted. If it transitions from n=3 to n=2, then from n=2 to n=1, two (2) photons are emitted.

Energy level of n=3 for Hydrogen is -1.511 eV (electron volts)

Energy level of n=2 for Hydrogen is -3.4 eV (electron volts)

Energy level of n=3 for Hydrogen is -13.6 eV (electron volts)

The energy levels are 'more negative' at lower levels because the electron becomes more bound to the atom.

From n=3 to 1 (gives up 12.089 eV, or a photon with wavelength 102.518 nm - ultraviolet light)

From n=3 to 2 (gives up 1.889 eV, or a photon with wavelength 656.112 nm - red light)

From n=2 to 1 (gives up 10.2 eV, or a photon with wavelength 121.5 nm - ultraviolet)

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