# User:Garrett E. McMath/Notebook/Junior Lab/2008/09/29

Balmer Series Main project page
Previous entry      Next entry

## Balmer Series Lab

Notes by: Paul Klimov and Garrett McMath In this lab, we will be measuring the Rydberg constant by observing the spectrum of several lamps. We will first calibrate with a Helium lamp.

Rydberg constant formula
$\frac{1}{\lambda}=R(\frac{1}{n^{2}}-\frac{1}{m^{2}})$


## Equipment

• Adam Hilger London Spectrometer. Serial Number 12610
• Spectrum II Power Supply. Model Sp200 5000V 10mA electro technic products.
• Helium Tube: Cenco Scientific Company.
• Hydrogen Tybe: Cenco Scientific Company.

## Calibration

We didn't find the hydrogen vapor lamp, so we will calibrate the device with Helium:

• 438.793 w
• 443.755 w
• 447.148 s
• 471.314 m
• 492.193 m
• 501.567 s
• 504.774 w
• 587.562 s
• 667.815 m

Taken from Hyper physics.

• We first turned on the helium lamp, and adjusted the aparture on the spectrometer which is facing the bulb.
• We notice that rotating measuring dial the lines are moved in the spectrometer.
• To calibrate we use the measuring dial and and turn the prism to line up the bright yellow line at 587nm
• Then, we went through and checked to make sure the other lines match up with the correct wavelength.
• this process was pretty painless, as it looked like all of the lines matched up quite well.

## Spectrum of Hydrogen

We noticed that the gears slip quite a bit. For this reason, one person took all measurements from one side, and the other person started from that side and went backwards. To get the measurement, we lined up the middle of the line with the crosshair

First Attempt(from left).
*412.1±.3nm
*435.4±.1nm
*486.3±.1nm
*659.5±.1nm

Second Attempt(from right).
*653.0±01nm
*484.8±.02nm
*436.0±.05nm
*413.7±.15nm


The spectrometer was re-calibrated at this point, before taking our next round of measurements.

Third Attempt(from right).
*656.0±.1nm
*485.5±.05nm
*433.9±.05nm
*411.4±.15nm

Fourth Attempt(from left).
*411.0±.05nm
*435.6±.05nm
*486.0±.02nm
*657.4±.02nm


After speaking with Dr. Koch we decided to take another set of data for Hydrogen again calibrating with helium. To ensure the accuracy of our data. In this set of data we calibrated going from the right

First New Attempt(from left, Paul)
*411.0±.1nm
*434.6±.1nm
*486.9±.1nm
*660.4±.3nm

First New Attempt(from right,Paul)
*657.0±.3nm
*486.1±.1nm
*434.3±.1nm
*410.3±.3nm

Second New Attempt(from left,Garrett)
*410.5±.5nm
*434.7±.1nm
*486.7±.1nm
*660.5±.4nm

Second New Attempt(from right,Garrett)
*657.5±.3nm
*486.3±.1nm
*434.2±.1nm
*410.7±.5nm

Third New Attempt(from left,Paul)
*410.7±.3nm
*434.7±.1nm
*486.8±.1nm
*661.0±.6nm

Third New Attempt(from right,Paul)
*657.1±.5nm
*486.0±.1nm
*434.2±.1nm
*410.2±.5nm

Fourth New Attempt(from left,Garrett)
*410.5±.3nm
*434.6±.1nm
*487.0±.1nm
*660.9±.6nm

Fourth New Attempt(from right,Garrett)
*657.9±.5nm
*486.0±.1nm
*434.3±.1nm
*410.6±.5nm

• Note:Given the direction we were turning the screw for calibration seems to have corresponds to much higher accuracy in the data taken from the same direction.

## Deuterium

First Attempt(from right)
*657.4±.03nm
*485.0±.04nm
*433.3±.04nm
*409.8±.05nm

Second Attempt(from left)
*410.1±.05nm
*433.9±.02nm
*485.95±.05nm
*657.7±.1nm


## Data Analysis

SJK 00:59, 19 October 2008 (EDT)
00:59, 19 October 2008 (EDT)
What are the results of your data analysis? You don't report them anywhere! Even in the excel file, I don't see what you think is the "final" value of your R and though I do see a standard deviation calculation, I don't see any standard error of the mean discussion. It seems like you ran out of time for this analysis and summary.
• After taking the second set of data being very careful with the calibration direction we decided that the correct set of data were those taken in the same direction as the calibration. Therefore the data analysis will be only of the data taken form the right and only the four sets taken on the second day of measurements.(Steve Koch:I agree with this assessment)
• The data analyisis was done in excel and is linked below

## Sources of Error and Uncertainty

• SJK 01:00, 19 October 2008 (EDT)
01:00, 19 October 2008 (EDT)
This is a really good point. I suspect it is the main source of systematic error in the red line as you point out.
Our first source of error was an obvious systematic one. At lower wavelengths we had to open the slit to allow in the wider wavelength. This caused immediate uncertainty due to wider lines in the spectroscope. But more importantly when closing the slit width to resolve lines more clearly the lines would consistly shift to the right. This caused a systematic error that is quite clear in the analysis of the data. At lower wavelengths our data was consistently higher than the accepted values while our data for the higher wavelengths were much more randomly ditributed around the accepted values.
• As mentioned above the line width we would observe caused uncertainty in the measurements which we tryed to display accuratly in the ± readings after each data point.
• Another source of expiremental error which we tryed very hard to avoid is the gears in the screw drive had what is called "gear backlash" in the lab manual. This ment that when making small back and forth adjustments on the screw did not nessesarily correspond to movement of the diffraction prism but actually was just slippage between two gears. We countered this by taking all of our measumements in one direction or another. We further tried to fix any discrepencies by taking two sets of data from each directions to average out any problems with the apparatus.
• There are many other sources of uncertainty and error (i.e heisenberg uncertainty principle, accuracy of the angles in the manufacturing of the prism, the purity of the gas in the lamps we use, etc.) but given the high accuracy of our data with the accepted values these sources are obviously extremely insignificant to this lab.

## Summary

SJK 00:55, 19 October 2008 (EDT)
00:55, 19 October 2008 (EDT)
Well, I did ask you to make your summary more concise, but this is far too concise! The most important missing thing is your final calculation of the Rydberg constant! Take a look at Paul's page for an example of how it can be clear and succinct and have all the important information.

In addition to missing the final value of R, you talk about comparisons with the accepted value, but you don't state the accepted value anywhere either. I did look at the Excel file, but it does not have the accepted value stated.

In conclusion our R-values were very accurate and seemed to have a trend in the higher quantum numbers. Our lowest quantum number was 3 and for that we had the most inaccurate r-value, but for the rest they seemed to have an asymtotic trend toward the accepted value. As for the deuterium we calculated that we would not have been able to resolve the difference as the difference was weel inside our visual margins of error. We did not have sodium lamps in the lab so we were unable to preform that expirement but given the accepted values for the split I think we would have easily been able to resolve and measure the difference.