# Balmer Lab Summary

## Motivation

In 1885 Johann Balmer wrote an equation that described the spectral lines from hydrogen emission. These lines were peculiar because they were always the same and they were very narrow. This meant that there were only certain wavelengths of light (and therefore energy) that hydrogen would emit in the visible spectrum. At the time this was a strange phenomena because energy was thought to be continuous. Now we know that energy is quantized and the narrow emission lines are a result of quantum mechanics. In this lab our goal was to measure the Rydberg Constant in the Balmer equation.

## Theory

The equation for the Balmer Series is

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

Solving for R
$R_\mathrm{H} = \frac{1}{\lambda} \times \frac{1}{\left(\frac{1}{2^2} - \frac{1}{n^2}\right)}$
Here n represent the quantum states. The lowest n (starting at 2+1) represents the lowest change in energy (the red lines) the larger the n the larger the energy change.

## Methods

A constant deviation spectrometer was used to measure the wavelengths of the emission of hydrogen and deuterium. The spectrometer was first calibrated using a mercury lamp calibrating at 435.8nm. Measurements were then taken over the coarse of two days. The first day's data will be omitted due to the fact that Tyler wasn't present and my eyesight is not very good. See the Lab Notebook for further details on the calibration and subsequent data collection.

## Results

The calculated Rydberg Constant for hydrogen was $R_\mathrm{H} = 1093(5)\times10^{4} \frac{1}{m}$ and for deuterium $R_\mathrm{H} = 1097(1)\times10^{4} \frac{1}{m}$. Both of these results fall within 1 standard error of the mean of the accepted value of $R_\mathrm{H} = 10973731.6 \frac{1}{m}$. SJK 01:21, 22 December 2010 (EST)
01:21, 22 December 2010 (EST)
Note, if you're going to use that many significant digits, hydrogen and deuterium actually have different accepted values, due to the reduced mass correction!
The respective errors in these calculations were 0.37% and 0.053% respectively.

## Error

There was very little error in this lab. The spectroscope, at best, gives 4 significant figures when determining the wavelength. Considering this our reported values have 4 significant figures and are within 1 standard error of the accepted value. All things considered we were able to get very good results considering the limitations of the equipment and our own physical limitations. There was an issue with contamination in the hydrogen bulb so we saw many more spectral lines than we should have. Knowing all of these didn't correspond to hydrogen (per lab notebook and internet), we took measurements with the deuterium bulb and were able to pick out the four distinct lines. Knowing the wavelengths of these lines were were able to see which lines on the hydrogen spectrum were due to hydrogen and which lines were due to contamination. Once the contaminated lines were removed the data fell very neatly into place.