Physics307L:People/Phillips/Balmer

Balmer Series Summary

Data & Results

The notebook entry for this lab can be found here, along with an Excel file: Balmer.xlsx.

For this lab we were trying to compare values of the Rydberg constant, R, for Hydrogen and Deuterium. Here are the results we ended up with:

[math]\displaystyle{ R_{accepted} = 1.0967758 \times 10^7 m^{-1} }[/math]

[math]\displaystyle{ R_{Hydrogen} = 1.0941321 \pm .004225 \times 10^7 m^{-1} }[/math]

[math]\displaystyle{ R_{Deuterium} = 1.0951129 \pm .003278 \times 10^7 m^{-1} }[/math]

We used just the standard deviations as the reported error. This is because of two things: it's what the lab manual suggested and it made more sense to us because our SEMs were very small.

We also calculated some percent errors to show how close each value was to the accepted value:

[math]\displaystyle{ %error_{H} = 0.241 % }[/math]

[math]\displaystyle{ %error_{Deu} = 0.152 % }[/math]

Some Conclusions

One of the things that the manual was directing us to find was the difference in the Rydberg constant and the difference in the red wavelength between the Hydrogen and Deuterium spectra. As soon as we started doing the data analysis, we concluded that there was no measurable difference in the values for the Rydberg constant. This was made especially clear after doing the error part of the analysis when we found out that the Standard Deviation and percent error were lower for Deuterium than for Hydrogen, even though being compared to the given value for Hydrogen. This seemed to suggest to us that the Rydberg constant does not depend on the mass of the atom (since that's really the only difference between Hydrogen and Deuterium), or at least not very significantly. This also seemed to fit with our intuitions, though we couldn't find any reason to have such intuitions.