Physics307L:People/Klimov/Balmer

Balmer Series Summary

In this lab, the Balmer series was studied, which allowed us to determine the value of the Rydberg constant. This experiment made use of the fact that electrons emit photons when making a transition between an excited state and a lower energy state. Using a prism, and also the fact that the index of refraction of matter is wavelength dependent, we separated the different wavelengths into a line spectrum (with the help of a spectrometer of course).

• Lab Notebook

Results

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

[math]\displaystyle{ R_{exp}= 1.096343(21) \cdot 10^{7} m^{-1} }[/math]

[math]\displaystyle{ R_{act}=1.0967758(7)\cdot 10^{7} m^{-1} }[/math]

[math]\displaystyle{ Error = 0.039% }[/math]

Conclusions

• I am happy with our result because it is very close to the accepted value of the Rydberg constant.
• I would argue that random error would dominate in this lab. 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. However, after plotting the calculated Rydberg constant versus the quantum number such a trend was not seen.
• Although we identified several potential sources of systematic error, they all seem too unlikely to be of issue here.
• If we had more time with this experiment, I like to mess around with some other gasses to see how good our resolving power really is. Although we didn't have the sodium lamp to try to resolve its doublet, I would think that we could find another sample with a closely spaced doublet.