# Physics307L:People/Klimov/Balmer

## Balmer Series Summary

SJK 00:14, 19 October 2008 (EDT)
00:14, 19 October 2008 (EDT)
Excellent lab all around. Great summary and great analysis and data taking.

Although line spectra had been acknowledged for a long time, a theoretical explanation for them was not developed until the early 1900s, after the development of 'classical' quantum mechanics. In the theory, which has withstood a century of experimentation, relies on the idea that atoms emit photons when electrons make transitions between excited states and lower energy states. The Balmer series is a set of photon emissions, unique to Hydrogen, that lie in the visible spectrum. Using the fact that the index of refraction of matter is wavelength dependent, we separated the Hydrogen emissions into a line spectrum (with the help of a spectroscope). The constant that relates these emissions to their respective energy transitions is called the Rydberg constant. Measuring the value of this constant was the main goal of this experiment.

## Results

The constant was first calculated for each transition separately. With some justification, the calculated constants were all averaged together and their SEM was calculated. These are the results:

$R_{exp}= 1.09634(21) \cdot 10^{7} m^{-1}$

$R_{act}=1.09677\cdot 10^{7} m^{-1}$

Error = 0.039% (Steve Koch: 0.04% discrepancy is really cool! You do have enough info, though, to make an argument about whether your number is consistent with the accepted value. What do you think?)

## Conclusions

• I am happy with our calculated Rydberg constant because it is very close to the accepted value. (Steve Koch:Yes, it is very close, and I think that's pretty cool! However, how close is it relative to your SEM, which is supposed to indicate the normally distributed errors of your mean?)
• I would argue that random error would dominate in this lab.SJK 00:10, 19 October 2008 (EDT)
00:10, 19 October 2008 (EDT)
So it does look like there is no "trend" perhaps. However, as I commented in your notebook: are your data points consistent with each other? How do you evaluate that kind of thing? I think I would argue that systematic error was a bit larger than random. It just happened to be biased low in the first transition and high in the second
I must admit that at first I thought the opposite, thinking that the device would limit our ability to accurately resolve some of the lower wavelengths. I though so because the higher energy emissions forced us to open the aperture of the device to a much greater extent than was necessary for higher wavelengths, which I thought would produce worse data. However, after plotting the calculated Rydberg constant versus the quantum number such a trend was not seen.
• As I mentioned in my lab notebook, the spectroscope is incredibly accurate (despite the fact that it looks like its at least 30 years old). Furthermore, if I had more time, I would like to mess around with some more gas samples and try to resolve some closely spaced emissions. And what is perhaps more relevant, I would like to see if it would be possible to get enough good data to tell the spectrum of deuterium apart from that of hydrogen; In our lab, we measured the SEM of several emissions to be less than the wavelength shifts in deuterium, suggesting that we could measure the difference between the two isotopes. Unfortunately our limited set of data for Deuterium did not allow us to make any conclusions.
• Lab manual question answered in detail in the Lab Notebook.