science
posted by Samantha .
Five lines in the H atom spectrum have the following wavelengths in Ǻ: a). 1212.7, b). 4340.5, c).
4861.3 d). 6562.8 and e). 10938. Three lines result from transitions to the nf = 2. The other two
result from transitions in different series, one with nf = 1, and the other with nf = 3. Identify the initial
state for each line.

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