Theoretical Calculations (Hydrogen):

The Schronlinger equation (1925), using a simple
"Coulomb"potential between the electron and the nucleus (the proton), yields the
same values for the energy levels as the older Bohr model (1913). Despite the
difficulties with the Bohr model, it is still easier to "present" in a
short appendix than the more correct (and mathematically more involved) Schrodinger
solution. Bohr uses the energy-conservation that E=0 means the atom is ionized
(where the electron is "barely free" of the proton);
thus negative values of energy pertain to the bound state (the state of actually being a
hydrogen atom). With this convention, then and using electronvolts for units,
we have: En= -13.60 eV/n^2 with n=1 being the
lowest (and most stable) level. Make a fairly extensive list that includes
computations of En for n=1,2,3,4,5,6,7,8 and 9.
Be sure to keep 4 significant figures in each result. Now comes the very tedious
part: calculate and list __all__ the differences!! (like E2
- E1, E8-E7,
E8-E1, E7-E3,
and so forth) As you already know, each energy-level difference corresponds
to the emission of a photon of energy E photon and
wavelength l. Of course, E photon simply equals the energy level difference in each
case, and the Planck-Einstein relation E photon = hf relates this energy to the photon's
frequency (and to Planck's constant h=6.626 ´ 10^-34 joule.second, or h = 4.136E ´
10^-15 eV.second). But frequency is easily related to wavelength (f =c/ l where c =
299792458 m/s or c = 2.9979 ´ 10^17 nanometers/second); apologize for using "f"
for frequency to those of you who are more used to seeing "v" used for
frequency. Thus, conbining these relationships, we get Ephoton = hc/l which is
conveniently written aso Ephoton = (1240eV.nm)/l once we multiply out the constants. Using
this, then, "convert" all the energy differences you listed above into photon
wavelengths in nanometers!

Finally, compare this final list with your measured wavelengths for hydrogen, to decide which line came from which transition (from the electron "dropping" from which level to which level?). Then, calculate the percent differences between these few theoretical values of l which "match up" with the corresponding measured values (since I presume the ones that "match up" don't exactly match up perfectly). Then you're done!