# Physics307L:People/Allen/Balmer/Balmer Series Lab Summary

## Balmer Series Lab Summary

SJK 18:57, 4 October 2009 (EDT)
18:57, 4 October 2009 (EDT)
This is an excellent summary! Actually is more than required, but that's OK, of course, I enjoy seeing all of the thoughts about the experiments. Only things missing are noted below (e.g., numerical uncertainy will be required next time, and need to cite the source of the accepted value.

The Balmer Series is specific to Hydrogen spectral line emissions, and supports the concept of quantized energy as light emission occurs only at specific wavelengths that are determined by the energy differences between two electron states. Spectroscopy and especially the Balmer Series finds application in astronomy to analyze the composition of stars and calculate their surface temperatures from the relative strength of spectral lines. Wiki Article on Balmer Series

This lab was taken on to determine the Rhydberg Constant for Hydrogen and Deuterium by applying the Rhydberg Formula to the spectral lines of the Balmer Series measured in the lab. We used a constant deviation spectrometer which we calibrated with the known wavelength measurements of the spectral lines for Mercury vapor and then measured the wavelengths emitted from the Hydrogen and Deuterium vapor tubes.

We found an average value for the Rhydberg Constant for Hydrogen of 1.0965640$\displaystyle *10^{7}m^{-1}$
and for Deuterium of 1.0950235$\displaystyle *10^{7}m^{-1}$ .

The accepted value for the Rhydberg Constant for Hydrogen is 1.0973732$\displaystyle *10^{7}m^{-1}$ , so our finding has an error of 0.7%.SJK 18:20, 4 October 2009 (EDT)
18:20, 4 October 2009 (EDT)
What you have here is a final value and a discussion of discrepancy (difference from accepted value). However, in order to fully evaluate this discrepancy, you need to compare with the uncertainty on your final value (which you don't report here).
SJK 18:43, 4 October 2009 (EDT)
18:43, 4 October 2009 (EDT)
Where are you getting this value? You should cite your source, which would also probably clarify whether you're using the Rinfinity or Rhydrogen value. You're using the infinity value, which is actually not correct, since you're studying hydrogen and deuterium (and this would be the source of any difference between the two). Seems like you didn't notice this concept, but more importantly, you didn't cite the source of your accepted value, which is critical to do.

## Data

• Hydrogen

Red: 657.88+/-0.43nm

Orange: 603.88+/-0.2nm

Yellow: 582.3+/-0.31nm

Blue-Green: 486.05+/-0.07nm

Violet: 434.05nm+/-.07nm

• Deuterium

Red: 660.6+/-3.06nm

Orange: 618.8nm

Yellow: 584.1nm

Blue-Green: 485.45+/-.18nm

Violet: 434.3nm

## Analysis

Putting these into the formula for the Rhydberg Constant for Hydrogen:

$\displaystyle \frac{\frac{1}{\lambda }}{(\frac{1}{2^2}-\frac{1}{n^2})}=R_{H}$

where $\displaystyle R_{H}$ is the Rydberg Constant for Hydrogen, $\displaystyle \lambda$ is the observed wavelength, and n is the excited energy state that the electron was in.

We calculated the constants for the various spectral lines as follows:

Rydberg Constant for Hydrogen($\displaystyle R_{H}$ )

• $\displaystyle R_{H}$ for the red spectral line = 1.0944245+/-.00071$\displaystyle *10^{7}m^{-1}$
• $\displaystyle R_{H}$ for the blue-green spectral line = 1.0972808+/-.000158005$\displaystyle *10^{7}m^{-1}$
• $\displaystyle R_{H}$ for the violet spectral line = 1.0979866+/-.0001769$\displaystyle *10^{7}m^{-1}$

Rydberg Constant for Deuterium($\displaystyle R_{D}$ )

• $\displaystyle R_{D}$ for the red spectral line = 1.0899183+/-.00507$\displaystyle *10^{7}m^{-1}$
• $\displaystyle R_{D}$ for the blue-green spectral line = 0.910980157+/-.00028CNote: Due to a typo, this was miscalculated. Using the proper averaged measurement for the wavelength, 485.54nm, the Rhydberg constant is found to be 1.0986370$\displaystyle *10^{7}m^{-1}$
• $\displaystyle R_{D}$ for the violet spectral line = 1.09645516$\displaystyle *10^{7}m^{-1}$ (no +/- due to only seeing the two spectral lines and having only one data point)

This gives an average value for the Rhydberg Constant for Hydrogen of 1.0965640$\displaystyle *10^{7}m^{-1}$
and for Deuterium of 1.0950235$\displaystyle *10^{7}m^{-1}$ .
The accepted value for the Rhydberg Constant for Hydrogen is 1.0973732$\displaystyle *10^{7}m^{-1}$ , so our finding has an error of 0.7%.