Posted by Samantha on Thursday, April 1, 2010 at 11:30pm.
1/wavelength = R*(1/N1^2 - 1/N2^2)
R = 1.0973732 x 10^7 when wavelength is in meters. This will allow you to solve for either N1 or N2. In this formula, N1<N2.
Im confused though, it says three lines result from transitions to the nf=2, which three lines?
I would plug in N1 = 2, then N2 = 3 and calculate the wavelength. Perhaps that will give you 1 of the lines. Then N = 4 (their running numbers like that, all whole numbers) and you can identify another of the lines. Then n = 5 and you can identify the next one. If nothing fits one of the number you insert, just make sure your arithmetic is ok and go to the next. Rydberg (the R in the formula) did that strictly on an empirical basis and found the constant R and the running series of the Balmer (which ends in N = 2), the Lyman (which ends in N = 1), the Paschen (which ends in N = 3) etc. It must have been tedious. You can read more about it here. In fact, you probably can pick out the lines you have from this site, also.
http://en.wikipedia.org/wiki/Hydrogen_spectral_series
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