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Balmer Series

SJK Incomplete Feedback Notice
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My feedback is incomplete on this page for two reasons. First, the value of the feedback to the students is low, given that the course is over. Second, I'm running out of time to finish grading!
SJK 16:52, 18 December 2009 (EST)
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.


We measured wavelengths for 4 different spectral line colors 5 times using two different gas bulbs, Hydrogen and Deuterium. For Hydrogen I calculated:

[math]R = 1.09561(8) \times 10^7 \ \mathrm{m}^{-1},[/math]

For Deuterium I calculated:

[math]R = 1.0948(1) \times 10^7 \ \mathrm{m}^{-1},[/math]

These can be compared to the accepted value from wikipedia:

[math]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)
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


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.

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