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To calculate the differences between two energy levels you take the difference in their frequencies and end up with v=R[1/nf^2-1/ni^2]. Frequency=change in E/ h, is given by the Bohr frequency condition. If we substitute v for E/h, we can multiply the other side of the equation by plank's constant to get E=Rh[1/nf^2-1/ni^2].
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