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We would use this equation in questions that ask us about a change in energy levels (n1 to n2). i.e. How much energy is required to excite an electron from energy levels 1 to 4? If ##J energy were used to excite an electron off of ground state, what will be the final energy level of the electron?
You use Rydberg's equation when the question talks about an electron transitioning from one energy level to another. Generally, you will use it to sole for the final or the initial energy level, based on the information that is provided. Sometimes, you will also be asked to calculate the frequency of light emitted/absorbed when the energy levels are given. I heard Lavelle say in class, though, that we should try to use the energy equation (E = -hR/n^2) as much as possible because you will better understand the concepts than if you stick to using the Rydberg equation.
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