Physics307L:People/Mahony/Balmer
Balmer Series
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SJK 16:52, 18 December 2009 (EST)
Good way of comparing using SEM and discussing systematic error.
In this experiment, my lab partner Ryan and I calculated the Rydberg constant by measuring the Balmer series spectral lines of Hydrogen and Deuterium using a spectrometer and following Professor Gold's manual.
Results
We measured wavelengths for 4 different spectral line colors 5 times using two different gas bulbs, Hydrogen and Deuterium. For Hydrogen I calculated:
- [math]\displaystyle{ R = 1.09561(8) \times 10^7 \ \mathrm{m}^{-1}, }[/math]
For Deuterium I calculated:
- [math]\displaystyle{ R = 1.0948(1) \times 10^7 \ \mathrm{m}^{-1}, }[/math]
These can be compared to the accepted value from wikipedia:
- [math]\displaystyle{ R = 1.097\;373\;156\;852\;5\;(73) \times 10^7 \ \mathrm{m}^{-1}, }[/math]
The Rydberg constant for Hydrogen was 21 SEM's away from the accepted value, and the one for Deuterium was 24 SEM's away.
SJK 16:51, 18 December 2009 (EST)
You'll still be many SEM's away, but you should be comparing to the values adjusted for reduced mass of hydrogen and deuterium, not the R_infinity value
Conclusions
Though my calculated Rydberg constants were too far from the accepted value to attribute this to random error, and there had to be some systematic error, I suspect I underestimated my error. Nevertheless my systematic error could include one of the following possibilities:
- Mis-calibration of the spectrometer: It is possible that in the process of aligning the spectrometer to the spectral lines from a Mercury source, we made an error (tightened the screw which turned the crystal or misread the dial)
- Gear Back lash (although we were careful to only measure values turning the gear one direction)
- Too large of a slit opening: The slit opens from one side, rather then evenly on both sides, so this may have skewed our data to one direction.
