# Balmer Series Lab Summary

### Summary of Activities

In this lab we measured the Rydberg constant for Hydrogen and for Deuterium. We this through observation of the spectral lines of the atoms. The procedure was very straightforward and consisted of looking for the positions of the spectral lines and recording the observed positions.

### Lab Notebook

My lab notebook is located here: My Lab Notebook.

### Results

We know from the Rydberg formula that R=1/((wavelength of the light)*(1/4-1/n^2)), the accepted value is 0.0109737316 nm^-1 for hydrogen. And using the definition of the Rydberg constant, it should be 0.01097072 for Deuterium.

For the first day:

We get for hydrogen:

R=0.01098308+/-0.000027, and the 68% confidence interval [0.01100972,0.0109565]; which includes the value.

Which gives a relative error of 0.00085 and a fractional error of 0.0024

and for Deuterium:

R=0.01098897 +/-0.000021 and the 68% confidence interval [0.01100954,0.0109684]; which also includes the value.

Which gives a fractional error of 0.0019 and a relative error of 0.00055

For the second day:

For H:

R=0.01099695+/- 0.000026, and the 68% confidence interval [0.01102343,0.01097048]; which includes the value.

Which gives a relative error of 0.0021 and a fractional error of 0.00241

For D:

R=0.01098152+/-0.000022, and the 68% confidence interval [0.01100343,0.0109596]; which includes the value.

Which gives a fractional error of 0.002 and a relative error of 0.001

Overall the data from both days and using both methods of calibration produced good accurate results for the value of the Rydberg constant. We assume we are safe in averaging the values we have for the Rydberg constant since we attempted to make the trials as independent as possible by making sure we always turned the gear until it reached the end, before turning it the other direction. That should ensure that each measurement was taken as independently as possible. Especially for the second day since we took one measurement only moving forwards, and one measurement only moving backwards. Therefore we should be safe in assuming the measurements are independent. Our fractional error is close to the relative error so our procedure was reasonable on both days. On each trial the actual value was within the 68% confidence interval, which means our measurements were very accurate.

### Improvements for Future Labs

In the future it would be nice to perform this lab with some better method of calibration, since both of the methods we chose still had a lot of variance in the observed values.