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From what Dr. Lavelle described on Wednesday, the reference point for the energy of an electron is 0 because we assume it is not interacting with anything. The negative energy of the electron represents that an electron bound to an atom has a lower energy than that of a "free" electron, one that is not connected to any atom.
The electrons have negative energies according to Rydberg's equation because we take our reference point off an electron that has been completely removed and is no longer interacting with the nucleus as E=0. The minus sign is because the electron's energy has decreased and the energy is released as electromagnetic radiation as it comes back down to the different energy levels.
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