# Balmer Series

SJK 01:02, 6 October 2008 (EDT)
01:02, 6 October 2008 (EDT)

### Introduction

This lab experiment tests the Balmer Series equation for Hydrogen and Deuterium. We started by calibrating a spectroscope using a mercury tube and the known values of wavelength for each color in the Mercury Spectrum. Then we took measurements for the Deuterium and Hydrogen spectrum having each of us take multiple measurements.

### Error

Using the dial near the end of the spectroscope we could shrink the color lines horizontally from the spectrum and therefore minimize the error we have from trying to measure the location of a line with width. Also our reading came from a dial that was turned by hand which had an error since we can only read the measurement up to one decimal place accurately. As the wavelengths got larger, the scale on the measuring dial for the spectroscope got a lot larger so our measurements became less and less accurate.SJK 00:52, 6 October 2008 (EDT)
00:52, 6 October 2008 (EDT)
You probably mean "precise"...although as you show below it turns out accuracy was lower too (I'm talking about terminology for random versus systematic errors here
Since every measurement was done with the human hand and eye inaccuracy's with be present. However our Data Analysis and multiple measurements should take account for our inaccuracy.

### Concepts

To calculate the Rydberg constant.

$\frac{1}{\lambda} = R \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$

Where

λ is the wavelength of the light emitted in vacuum,
R is the Rydberg constant for hydrogen,
n1 and n2 are integers such that n1 < n2,

and our n1 for this experiment will always be 2.

The mass of the nucleus has a small effect on the constant by

$R_M = \frac{R_\infty}{1+m_e/M} \$

Where,

$R_M \$ is the Rydberg constant for a certain atom with one electron with the rest mass $m_e \$
$M \$ is the mass of the atomic nucleus.

so as M increases we can see that our Rydberg constant also increases. It would follow that our data would represents this as well since Deuterium has a larger nucleus than Hydrogen and we took data for both of these elements. The difference is small ,but I hope to show it in my analysis.

The colors emitted are photon emitted from the excited atoms have a wave number proportional to the properties of the Hydrogen.SJK 00:54, 6 October 2008 (EDT)
00:54, 6 October 2008 (EDT)
What does this phrase mean? proportional to what? Did you mean to say wavenumber?

### Data Analysis

matlab code (Lab notes are a combined effort of Arianna Pregenzer-Wenzler and Daniel Young)

The blue line represents the accepted value for R∞ and we can see that most of our data points are in a close range with the accepted values. The error bars are the Standerd mean error which was found by taking our standerd devation and dividing the the squareroot of the number of data points we had. At first I was concerned that not all of our error bars cross the accepted value for the Rydberg constant however, the low values of n ( large wavelegth) have less presicsion than the higher one which seems alright since. Our mean values for the Rydberg constant were...

• Hydrogen
Color Dark Purple Purple Blue Red
Quantum Number n = 6 n = 5 n = 4 n = 3
Rydberg constant mean 1.0973e7 1.0958e7 1.0952e7 1.0814e7
• Deuterium
Color Purple Blue Red
Quantum Number n = 5 n = 4 n = 3
Rydberg constant mean 1.0973e7 1.0961e7 1.0831e7

{{SJK Comment|l=00:57, 6 October 2008 (EDT)|c=I like your tables, and your discussion of uncertainties. I can see that you're attempting to report a "final" value. However, it's not clear from where the final value comes...and also you don't have uncertainty estimates or units on the final value!}

 Percent Difference from accepted value= 0.4467%
mean Rydberg constant = 1.0923e+007

The Hydrogen and Deterium spectrum are different enough to be distinguishable. Since the error bars for Deuterium and Hydrogen of the same wavelength do not cross our values are different enough to be determined.SJK 00:24, 6 October 2008 (EDT)
00:24, 6 October 2008 (EDT)
from where are you getting the information about error bars overlapping? When I look at your data, I do not see uncertainties on the individual numbers...also, I see that you have the same value for H and D at dark purple???
As was predicted earlier our values for the n=3 (red line) are far off from our other values of R and the accepted value. I attribute this to the decrease in accuracy on the dial on the spectroscope as we approach higher wavelengths.SJK 00:50, 6 October 2008 (EDT)
00:50, 6 October 2008 (EDT)
And as Arianna mentioned, this lack of accuracy is probably due to the manner in which you calibrated. That is, it's systematic error that you could possibly reduce a bunch by calibrating differently