I need help on this problem that asks me to solve for [tex]n_1[/tex] and [tex]n_2[/tex] (the initial and final quantum numbers).(adsbygoogle = window.adsbygoogle || []).push({});

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

[tex]n_1[/tex] and [tex]n_2[/tex] are unknown for each one.

I've tried using this equation, the Rydberg Equation, to solve for [tex]n_1[/tex] and [tex]n_2[/tex]:

[tex] \frac {1}{\lambda} = (R_H)(\frac {1}{n^2_2} - \frac {1}{n^2_2})[/tex]

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

I've plugged in the numbers and (for the color red) I got

[tex]\frac {1}{656.4} = \frac {R_H}{n^2_1} - \frac{R_H}{n^2_2}[/tex]

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.

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# Homework Help: Line spectra

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