# Physics307L:People/Ierides/Balmer Series

## Balmer Series

SJK 12:42, 24 October 2009 (EDT)
12:42, 24 October 2009 (EDT)
Overall, excellent job on this lab!

The main overview and summary of the procedure and lab is provided by this link:

Prof. Gold's Lab Manual
The following link leads to my Balmer Series Lab entry that includes the data, procedure, and observations that were made:
Balmer Series Lab Notebook Entry

### Data Summary & Observations

The purpose of this lab was to view the difference between the spectra of Hydrogen and Deuterium in the Balmer Series. The measurement of the different wavelengths viewed could be used to calculate the Rydberg constant. The different wavelengths are the production of the emission of photons from excited electrons through different levels of the atom. My understanding of the shift of the wavelengths is that it could be due to the fact that the deuterium atom is heavier, but I'm not quite sure as to why this is. It could be due to some oversight of the dependence of the wavelength on the reduced mass placed in the Rydberg constant calculation:

$R=\frac{\mu e^4}{8\epsilon _0^2ch^3}\,\!$

According to our calculations found in the Calculations section of [1] we had:

• The average value of our measured Rydberg's constant as:
$R_{Hydrogen,average}\approx1.0973\pm 0.0025\times10^7 m^{-1}\,\!$
$R_{Deuterium,average}\approx1.0983\pm 0.0007\times10^7 m^{-1}\,\!$
$R_{accepted}=1.0967758\times 10^7 m^{-1}\,\!$

• The error for our measured value relative to the accepted value is then given by:
$\% error_{Hydrogen}\approx0.046%\,\!$
$\% error_{Deuterium}\approx0.141%$
SJK 12:46, 24 October 2009 (EDT)
12:46, 24 October 2009 (EDT)
The percent error is interesting for illustrating the amazing precision you can obtain with optical spectroscopy. However, what's missing is a statistical comparison with the accepted value, using the SEM to determine whether your measurements are consistent with the accepted value. This then indicates whether systematic error is important. Also, it looks like you missed the difference between hydrogen and deuterium.

### Conclusion

According to our data, although the Deuterium spectral lines varied from the Hydrogen lines in wavelength, as seen by the percentage error in the Rydberg Constant of each, the variance is slight. The largest value by which the wavelengths varied was designated in the red wavelength measurement as seen in our data tables [2]. But also according to our data, the wavelength measurements of each color seemed to be shifted from the Hydrogen in the Deuterium spectrum.