Determination of Rydberg Constant via Graphical Method

[vodkasoup]

Homework Statement

Not sure if this belongs in the 'Advanced' section so apologies if it does not.

I am using a monochromator to measure spectrum lines from a rubidium lamp. From the data (wavelength of spectral lines plus transition number 'n') I am asked to use a graphical method to calculate both the Rydberg constant and the correction factor Δ due to the penetration of the outer valence electron into the inner electron cloud.

Homework Equations

1/λ = 1/λ_∞ - R/(n + Δ²)

where λ is the wavelength;
R is the Rydberg constant;
λ_∞ is the series limit (which I presume to be the highest wavelength at which transition can occur?)
n is transition number
and Δ is the correction factor.

The Attempt at a Solution

I am aware that by 'linearising' the equation ( ie. putting it into the form y = mx+c) I can find the Rydberg constant as the gradient of the line of best fit. I've used this method before in determining the Rydberg constant from Balmer lines of hydrogen.

The problem this time is that there are two unknowns, and my efforts to find the constant plus correction factor have not been successful. I'm not sure how to go about this - any advice much appreciated.

Cheers!

 

[drvrm]

why don't you consult the following study'

http://www2.vernier.com/sample_labs/VSPEC-08-COMP-rydberg_constant.pdf
www2.vernier.com/sample.../VSPEC-08-COMP-rydberg_constant.pdf
The Rydberg constant bears witness to his contribution to understanding the ... A second method of determining the Rydberg constant is to analyze a graph of ...

 

[vodkasoup]

Thank you for your reply drvrm.

I've read through the study you linked, and it seems to be concerned only with the determination using the Balmer series; as I mentioned, I was previously able to derive the Rydberg constant from the Balmer series of H via the same graphical method as described in the study.

However, I am being asked to find two unknowns here - the Rydberg constant, and the correction factor Δ due to the penetration of the outer valence electron into the electron cloud. The spectrum lines are from an alkali, hence the equation I am using is slightly more complex than that given in the vernier study you linked:

1/λ = 1/λ_∞ - R/(n + Δ²)

Apologies if I'm missing something, but the method described in the study doesn't seem to take this correction factor into account, so I am none the wiser.

 

[drvrm]

OSA | Polarization, penetration, and exchange effects in the ...
https://www.osapublishing.org/viewmedia.cfm?uri=josa-7-4...0...by CJ Sansonetti - ‎1981 - ‎Cited by 31 - ‎Related articles
By using these lines we determined a correction factor for each spectrum in order to ... and ΔTpol(n,l) is the perturbation of the term value that is due to polarization of ... R is the Rydberg constant for the atom of interest (109736.865 cm−1 for Cs), ... As Edlén[8] has pointed out, it is convenient for graphical purposes to rewrite ...

sorry it was another ref. for your case

 

[vodkasoup]

I managed to get access to the site linked using my uni library account and read the article; however again the correction factor mentioned is not the same as that in my experiment and the method differs from what I have been asked to do.

I thank you for being good enough to help me drvrm, but I feel I may have been sent on a couple of wild goose chases here :p