Physics307L:People/Cochran/Balmer series

Steve Koch 22:41, 21 December 2010 (EST):Good job on this lab, which turned into a nice formal report. For this summary, you would have wanted to compare how many SEMs away from accepted value were the results.

Summary

The purpose of this lab is to measure the Balmer series of hydrogen and deuterium (as well as their Rydberg constants) using a constant-deviation spectrometer. Cristhian Carrillo was my lab partner for this lab. We used a constant deviation spectrometer, a Model SP200 spectrum tube power supply (5000 V, 10mA), and spectral tubes filled with mercury, hydrogen and deuterium.

set up

My procedure for this lab is described here.

Procedure/Results

We followed the procedure described in Professor Gold's manual. We placed the mercury tube in the power supply and allowed it to heat up for a few minutes, then recorded the dial nanometer reading for spectral lines of mercury given in the manual. These values are given in our data table. Once we had recorded these measurements, we recorded the Balmer spectral lines - red, blue-green, and violet - for our hydrogen and deuterium tubes - 4 lines for hydrogen, 3 for deuterium, and 5 trials for each. We created a best-fit line for our calibrating factor, averaged our calibrated wavelengths, and used the Rydberg formula to obtain:

• [math]\displaystyle{ R_Haverage = 1.0911685 +/- 0.0070852*10^7 m^{-1} }[/math]
• [math]\displaystyle{ R_Daverage = 1.0991917 +/- 0.0018430*10^7 m^{-1} }[/math]

We also calculated the accepted value of the Rydberg constant for hydrogen and deuterium using their reduced masses, and obtained the following percent errors:

• [math]\displaystyle{ % error_H\approx 0.086% }[/math]
• [math]\displaystyle{ % error_D\approx 0.795% }[/math]

All this was done using a Google spreadsheet.

Conclusion

Our error for the Rydberg constant for hydrogen was lower than that for deuterium, but the standard error of the mean was higher for hydrogen than it was for deuterium. I believe that this means that our random error was greater for hydrogen and our systematic error was greater for deuterium. According to Wikipedia, the Rydberg constant is "currently the most accurately measured fundamental physical constant", so there is obviously still a great deal of room for improvement in our result. We had some difficulties determining which of the violet lines we should be measuring, which is why I chose not to use our first data set. This confusion may have contributed to our error, as well as gear backlash, though we did our best to avoid it by always turning the dial from left to right during a set of measurements.