# 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

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

Solving for R
$\displaystyle R_\mathrm{H} = \frac{1}{\lambda} \times \frac{1}{\left(\frac{1}{2^2} - \frac{1}{n^2}\right)}$
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.

## Data

The calculated Rydberg Constant for hydrogen was $\displaystyle R_\mathrm{H} = 1093(5)\times10^{4} \frac{1}{m}$ and for deuterium $\displaystyle R_\mathrm{H} = 1097(1)\times10^{4} \frac{1}{m}$ . Both of these results fall within 1 standard error of the mean of the accepted value of $\displaystyle R_\mathrm{H} = 10973731.6 \frac{1}{m}$ . SJK 01:21, 22 December 2010 (EST)