# Atomic Spectra of Hydrogen and Mercury

## Homework Statement

Hi!

I have a a question regarding the Atomic Spectra of Hydrogen and Mercury. My problem involves the value of m and Rydberg's constant. I used a spectrometer for this lab and calculated all the necessary angles.

See below

## The Attempt at a Solution

average angle:
α1=(θ1+θ2)/2 (1) and α2= | θ1-θ2|/2 (2) (I measured the θ values)

The wavelength for every recorded line in the first order (n=1) :
nλ=d(sin(α1)+sin(α2)) (3)

d= line’s width on the diffraction grating in the spectrometer= 600 lines/mm. In order to compute the width of a single line all that is required is to divide this number by 1 (the inverse). n=2 for Hydrogen btw and it's constant. For Mercury, it's n=1,2,3... (or m=b,c,d,e...)

So, I calculated the wavelengths for every color. I also have the θ1 and θ2 values, which I measured.
Below are the results for the Hydrogen spectra (in nm) after using (3):
violet: 432.462
blue(ish): 486.598
Red: 696.906
Violet: 434.462
blue: 486.598
red: 696.906

Next step is to calculate values for m and then calculate Rydberg's constant. I have no idea how to do it, therefore I'm stuck. I assume that Rydberg's constant can be calculated by rearranging the following equation:
1/ λ=RH((1/m2)-(1/n2)) (guessing, might be wrong)

After I have m, I can calculate m for the second line (m=m+1), third (m=m+2) etc. And then Rydberg's constant for each of the m values and wavelengths.
According to my professor, I'll have two unknowns, which is m and R_H. Therefore, I should use two wavelengths (from above) and try to figure this out. If someone can help me with the Hydrogen spectra, I can continue with Mercury's alone.

Thanks!