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Electrons can move up and down energy levels and the changes in energy are modeled by the difference in En for the hydrogen atom. Make sure that when you're finding Efinal-Einitial, the negative sign in the equation for En doesn't get lost.
the electron could absorb energy and go to a higher level or emit energy and go to a lower level. The equation En=-hR/n2 simply calculates the energy of the specific level and it has nothing to do with the previous energy level. the difference between energy levels is calculated with deltaE= Efinal-Einitial . As long as you calculate the energy for each level and use it in the delta e equation, you should get the correct answer!
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