# User:David K. O'Hara/Notebook/physics 307 lab/balmer conclusion

## Objective

The object of this experiment was to calculate the Rydberg Constant using the measured wavelengths of the Balmer series of spectral lines.

## Results

All data and calculations are viewable in my lab notebook,[[1]]

The Rydberg constant that i calculated for hydrogen from my data was 1.0965283e7 m-1 +/-4300 SJK 20:30, 14 November 2009 (EST)
20:30, 14 November 2009 (EST)
It is very difficult to read this the way you've written it. First, too many digits of precision on your mean value. Second, it's tough to read error with one being in scientific notation, and the other not. This is a perfect time to use the shorthand notation, like so: 1.0965(4) E7 m-1
This has the same meaning as 1.0965 +/- 0.0004 E7 m-1

The Rydberg constant that i calculated using my dueterium data was 1.0976325e7 m-1 +/-4500

With the accepted value for that constant as Rh=1.097272 x 107m-1 [|Ryderg constant wiki page] SJK 20:27, 14 November 2009 (EST)
20:27, 14 November 2009 (EST)
This is actually the Rydberg constant for an infinitely heavy nucleus. For hydrogen, it's actually smaller (due to reduced mass), and that's the one you'd want to compare with

Both values for the constant calculated off my measurements are within .001% of the accepted value which is remarkable considering the nostalgic equipment, but it just makes the original work done by Balmer that much more impressive.SJK 20:33, 14 November 2009 (EST)
20:33, 14 November 2009 (EST)
First, YES! It is really impressive how close you can get. But, for one thing, I think you missed that Hydrogen and Deuterium will have slightly different constants, both of them different from the R_infinity value. Finally, While it is very impressive accuracy, are your measurements consistent with the accepted value? To answer this question, you need to compare your discrepancy from the accepted value with the size of your uncertainty. Based on a normally distributed mean, how is it likely that your answer is consistent with the accepted value?

## Conclusion

The objective of this experiment was to calculate the rydberg constant by measuring the Hydrogen spectal lines using a specrometer and using the measured wavelengths to find the rydberg constant by plugging the measured wavelength into an equation based on which energy transition was being observed.

There were several sources of systemic error in this experiment, including:

1. Slippage of the gears on the measuring device. The way this spectrometer measures the wavelengths requires rotating the prism table to center the spectral line on crosshairs of the eyepiece. The mechanism for this rotation had what the manual called slippage (what I would call slop) that would allow the measurement gauge to move without moving the prism table.
2. The way you held your head when taking measurements could induce parallax which could have a fairly large impact on where the line appeared in relation to the crosshairs.
3. Also the measuring gauge was not very well divided. Particularly when trying to read the measurement for the higher wavelengths the gauge simple did not have the precision on its scale to engender a high confidence level.

Which, considering some of these issues, I was very happy with the value I calculated for the constant.