Physics307L F09: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

^{SJK 00:59, 18 December 2008 (EST)}

00:59, 18 December 2008 (EST)
You missed the fact that the mass is important...it's just a small effect on the values! But if you had enough precision to measure it (and maybe you were seeing a hint of it in the red), this would reveal very important physics. I think you missed out on a lot of learning by not reading a little more about this.

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.

Something that did seem apparent though was that the values for the red wavelengths were consistently different for Hydrogen and Deuterium, though not by a lot. This would, in turn, affect the difference in the Rydberg constant for each if we only counted this particular wavelength at n=1. This seemed to puzzle us, but since we had some significant errors in our final calculations, we thought perhaps the mass difference mentioned above played enough of a role to shift the values ever so slightly so that we could not detect a difference in the average final values.

Some Comments

We thought this lab went very well, especially in comparison to some of our past experiences this semester. We had a fairly low error for both of our final values, we were able to calculate our Standard Deviation and SEM without much hassle, and we were able to take enough data that we were sure the average would be quite accurate. The only thing that seemed a little off-putting for us is that measuring dimmer bands was incredibly difficult (such as the "violet2" bands mentioned in our data) because of the light pollution from other groups and from outside the room (this effect actually prevented us from getting one piece of data for Deuterium, as seen in our notebook entry). To remedy this, I think just having a separate room just for the Balmer Series lab would work. That way, we wouldn't have to accommodate to the background light caused by other groups using flashlights or computers and we could close the door completely to block out hallway light. This would at least cut down the systematic error by some amount. However, seeing as our results were quite good, this is certainly not a necessary step to take for this particular lab.