# Physics307L F07:People/Gooden/Balmer

## Overview

The objective of this experiment was to determine the Rydberg Constant for Hydrogen and Deuterium using a constant-angle spectrometer. The Rydberg Constant appears in the Balmer Series which gives the inverse of the wavelength associate with certain atomic transitions. By using the spectrometer and looking at a gas-tube filled with hydrogen and then deuterium(deuterium being an isotope of hydrogen) we found the associated spectral lines for each element and the wavelength for that spectral line. Then continueing till we found all the spectral lines and recorded a wavelength for each. Once we had accomplished this we used the Rydberg formula(given directly below) to calculate the Rydberg Constant knowing what transition each spectral line corresponded too.

${\displaystyle {\frac {1}{\lambda }}={\frac {4}{B}}\left({\frac {1}{2^{2}}}-{\frac {1}{n^{2}}}\right)=R_{\mathrm {H} }\left({\frac {1}{2^{2}}}-{\frac {1}{n^{2}}}\right),n=3,4,5,...}$

## Results

From this experiment we found that the Rydberg Constant for Hydrogen to be: ${\displaystyle R_{H}=\left(1.0953\pm .0039\right)\times 10^{7}{m^{-}1}}$ in excellent agreement with the accepted value which can be found on the labnote book referenced at the bottom of this lab summary. Then we also searched for the Rydberg Constant associated with Deuterium, an isotope of hydrogen and from the experiment concluded that it is: ${\displaystyle R_{D}=\left(1.0953\pm .0039\right)\times 10^{7}{m^{-}1}}$ again in excellent agreement with the accepted value.

## Analysis

The experiment was very simple to set up and begin taking data with. The data obtained from this experiment produced results for the Rydberg Constants of Hydrogen and Deuterium that are in excellent agreement with the accepted values given in our lab notebook. Any discrepancy of our reported values and the accepted values of the two constants in most likely due to random error involved in using the equipment. Such as in perfectly alligning the spectral line with the crosshairs of the eye piece or accurately reading the dial to find the associated wavelength. Other random sources of error could be from the allignment of the prism in the calibration portion of this experiment, which has a large impact on the accuracy. However due to the high accuracy of our results we dont believe there was much error in the allignment of the prism. If given more time we would have liked to attempt the experiment on several other elements, to determine the Rydberg constant for those.

Steve Koch 21:34, 1 December 2007 (CST):Great job with this experiment! Very nice data...pretty amazing how accurate and precise you can get using spectroscopy, huh?