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N1 is supposed to be the initial energy level it starts at, for instance if we say if it is the Lyman Series, then N1 starts at energy level 1 so then it absorbs energy and it excited to a higher energy level. You can use that equation to find the frequency required to make each jump, however Lavelle recommends that we don't use that equation because he wants use to understand conceptually why there is negative energy when an electron returns to its ground state. The equation you put there is to calculate the frequency from one energy level to the next and therefore we can convert the frequency to the energy difference between both energy levels.
My TA said it was all right to use the smaller n-value given for the n1 value, that way you will always get a positive number for your value of frequency (if you do not include the negative sign in front of R ). I usually just write a note on the side indicating which is n-initial and n-final.
I've tried using both. The formula with frequency worked more like a one step problem for me. I personally like using the shorter -hR/n^2 equation twice and taking the difference between the initial and final energies, because it feels like a step by step process. In the end, it's up to your preference.
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