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Atomic Spectra of Hydrogen and Mercury

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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.

Homework Equations


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!
 

Answers and Replies

  • #2
963
213
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.
you will have to consult the hydrogen energy level diagram and see the transitions from a m state to nstate -the wavelength you have measured correspond to specific set of m,n values.
so you take for two wavelengths and can calculate Rydberg constant and check.
 
  • #3
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you will have to consult the hydrogen energy level diagram and see the transitions from a m state to nstate -the wavelength you have measured correspond to specific set of m,n values.
so you take for two wavelengths and can calculate Rydberg constant and check.
Yes, but according to the professor, I need to calculate the m values for each transition as well. I too looked at the diagram and used the m values (that correspond to each color) that was given there, and then continued to calculate Rydberg's constant (for each wavelength) to see how close the values were to the "correct" one. But she wanted me to calculate m, and then the constant. This by comparing two wavelengths and then get the m value for those two. I have no idea how to do that because I don't know which equation to use (or to derive from) :/
 

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