Solving for n_1 and n_2 in Hydrogen Line Spectra

[bubbles]

I need help on this problem that asks me to solve for $$n_1$$ and $$n_2$$ (the initial and final quantum numbers).

This is the given information (the line spectra for Hydrogen):

color red known wavelength: 656.4 nm
color turquoise known wavelength: 486.3 nm
purple wavelength: 434.2 nm
purple wavelength: 410.3 nm

$$n_1$$ and $$n_2$$ are unknown for each one.

I've tried using this equation, the Rydberg Equation, to solve for $$n_1$$ and $$n_2$$:

$$\frac {1}{\lambda} = (R_H)(\frac {1}{n^2_2} - \frac {1}{n^2_2})$$

where $$\lambda$$ is the wavelength, $$n_1$$ and $$n_2$$ are the initial and final principal quantum numbers, with the initial one being larger than the final one. $$R_H$$ is Ryberg's constant.

I've plugged in the numbers and (for the color red) I got
$$\frac {1}{656.4} = \frac {R_H}{n^2_1} - \frac{R_H}{n^2_2}$$

I still can't find n1 and n2. Am I using the right formula? I just couldn't understand how to solve a problem with 2 variables.

 

[Astronuc]

Well n2 > n1, so pick n1 = 1, then solve for n2, which must be an integer.

If that doesn't work, then try n1 = 2, and solve for n2.

Alternatively, one can select n1=1, and then using n2 = 2, 3, 4, . . . solve for the wave lengths.

What value is one using for Rydberg's constant.

Try this reference - http://hyperphysics.phy-astr.gsu.edu/Hbase/hyde.html

Hint - the visible lines are in the Balmer series.

 

[GCT]

Also, consider the selection rules as well as the determination of the ionization energy.