# Physics307L:People/Andrego/Balmer Series

## BALMER SERIES LAB SUMMARY

^{SJK 12:48, 24 October 2009 (EDT)}

Please note that Anastasia Ierides was my lab partner for this lab. Her version of this lab can be found here. You can also find her lab summary by following this link.

### Brief Overview

In this lab we observed and measured the spectra lines of the hydrogen and deuterium atoms using hydrogen and deuterium bulbs underobservation through a spectroscope. By using electrical stimulation to excite our atoms to higher energy levels in the bulbs we were able to measure the emitted photons of wavelengths equivalent to the energy of our excited electrons. With our measurements we were able to experimentally determine Rydberg's constant, R, that is used in the following equation:

- [math]\displaystyle{ \frac{1}{\lambda }=R(\frac{1}{m^2}-\frac{1}{n^2}) }[/math]

- [math]\displaystyle{ m=1,2,3,...\,\! }[/math]
- [math]\displaystyle{ n=2,3,4,5,...\,\! }[/math]
- [math]\displaystyle{ n\gt m\,\! }[/math]

- [math]\displaystyle{ m=1,2,3,...\,\! }[/math]

- [math]\displaystyle{ \frac{1}{\lambda }=R(\frac{1}{m^2}-\frac{1}{n^2}) }[/math]

### Data Results

The average value of our measured Rydberg's Constant for both hydrogen and deuterium are as follows...

- [math]\displaystyle{ R_{Hydrogen,average}\approx1.0972781\pm 0.0025\times10^7 m^{-1}\,\! }[/math]
- [math]\displaystyle{ R_{Deuterium,average}\approx1.0983221\pm 0.0007\times10^7 m^{-1}\,\! }[/math]

^{SJK 12:50, 24 October 2009 (EDT)}

### Error

For ALL RECORDED accounts of error in our experiment methods and procedures please see the Notes about Our Uncertainty section in our Balmer Series Lab Notebook.

**Calculated Error Percentage**

- [math]\displaystyle{ R=1.0967758\times 10^7 m^{-1}\,\! }[/math]

- The error for our measured values of the Rydberg Constant relative to the accepted value given on page 30 of Professor Gold's Manual is...

- [math]\displaystyle{ \% error=\frac{R_{accepted}-R_{measured}}{R_{accepted}} }[/math]
- [math]\displaystyle{ \% error_{Hydrogen}\approx0.046%\,\! }[/math]
- [math]\displaystyle{ \% error_{Deuterium}\approx0.141%\,\! }[/math]

### Conclusions

Based on our extremely low percentage of calculated error for our measurements of the Balmer Series in the hydrogen atom, we can conclude that we were able to successfully observe the spectral lines and calculate a fairly accurate Rydberg's Constant. Our biggest source of discrepancy for the measured values of the wavelengths was found in the red spectra line. We are however not certain as to why only these measurements had such a large variance. From our data analysis and conclusions it is apparent that our calculated values of both our Rydberg Constants and wavelengths seemed to be shifted from the hydrogen values to the values measured for the deuterium atoms. This appeared shift could be a result of having to recalibrate our spectrometer for day two of our experimentation. From this lab I learned that using tools that need calibration it is probably a good idea to try to take all measurements within the same day to avoid an apparent shift in results as we saw in this lab.