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Hi I was a little confused when doing the Rydberg equation and finding the energy difference between the two levels I got a negative number which I know means that energy is being emitted to go to a lower energy level so I was wondering if when we state the energy difference would we state it as a positive number or a negative number? And to follow that up when finding from that energy level the frequency or wavelength of that energy would we make it positive or negative? Thanks!
Just the energy difference by itself can be stated as a negative number because, like you said, it just shows that light was being emitted. However, if you want to find the wavelength, you need to omit the negative signs because there is no such thing as a negative wavelength - same thing goes for frequencies.
So the negative number arises because you are thinking about photons in the Rydberg formula while the energy difference you find is that for the electron in the H-atom. Since electron lost its energy, by conservation of energy, the amount of energy loss is converted into photons.
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