[MissDee]

I'm having some trouble figuring out how to approach this, need some guidance please.

Three of the strongest lines in the He⁺ ion spectrum are observed at the following wavelengths: (1) 121.57 nm; (2) 164.12 nm; (3) 468.90 nm. Find the quantum numbers of the initial and final states for the transitions that give rise to these three lines. Do this by calculating, using Equation 1, the wavelengths of lines that can originate from transition involving any two of the four lowest levels. When a calculated wavelength matches an observed one, write down n_hi and n_lo for that line. Continue until you have assigned all three of the lines.

(1) _____________   ____________
(2) _____________   ____________
(3) _____________   ____________


Equation 1: N :delta: E =  :delta: E = NE_upper - NE_lower = E_upper - E_lower = Nhc/wavelength

How I approached it:
For (1): I took the (highest wavelength) - (lowest wavelength)= delta E
(468.90 nm) - (121.57 nm) = 365.33 nm = :delta: E (for [1]).

Nhc = 1.19627 x 10⁵ (this is what my book gave me):
(Nhc) / (wavelength):
(1.19627 x 10⁵) / (365.33 nm) = 327.45nm

Therefore, (1) 365.33 kJ/mol   327.45nm

I have a feeling this is extremely wrong, but I'm not sure how else to approach this. Help, please!

[Nicolas88]

check the Balmer-Rydberg-Ritz formula..

[tamim83]

Also .  So each wavelength you are given corresponds to a single transition.  

[MissDee]

check the Balmer-Rydberg-Ritz formula..

So do I use:

1.097 x 10⁷ (1/2² - 1/n²)

and substitute the n for  :delta: N?

Which would be:
(1) 365.33 nm
(2) 42.55 nm
(3) 0