# Physics307L:People/Callow/Balmar

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## Contents |

## Balmar Lab summary

## Links to lab notebook and procedure use

^{SJK 18:56, 10 October 2009 (EDT)}## Purpose of the lab

The main purpose of the lab is to find the Rydberg constant for hydrogen using a spectrometer and a lit up hydrogen tube. Also in addition to this try to find a difference between deuterium and hydrogen's Rydberg constants if the spectrometer's resolution is good enough.

## Summary of my data

Using the data from my lab notes I found that the Rydberg constant for hydrogen is

R = (1.099+-.00025)*10^7/meters.

^{SJK 18:51, 10 October 2009 (EDT)}The error between my best estimate of 1.099*10^7 and the accepted value of 1.097*10^7 is only about .2%. As stated in the notes this estimation would likely have been even better if I had time to calibrate using a line of best fit as that would have raised many of my measurements by about 1nm. The values I measured for deuterium happened to be about 1nm above and its Rydberg constant was about

R = (1.097+-.00025)*10^7/meters.

I decided only to carry my estimations out to 4 digits since that was about what I could measure with the spectrometer. Anything beyond this though is a really small fraction of the accepted value so I feel safe rounding (actually I think things are supposed to be rounded at least similar to this). My rounding is also a little bit inconsistent in parts of my notebook too which I'll try to keep better track of in the future.(Steve Koch 18:53, 10 October 2009 (EDT):As mentioned above, if your uncertainty is really at the fourth decimal place, then you should also have a fourth decimal place on your mean (and thus 5 sig figs))

There seemed to be a definite difference between deuterium and hydrogen with the wavelengths of deuterium's lines being about 1nm above. From the calculations in the notebook this is roughly what is expected due to the difference in reduced mass. 1nm seems well within the spectrometer's ability to measure accurately and from the data this is probably true. (Steve Koch 18:54, 10 October 2009 (EDT): As mentioned in primary notebook, think you may have a calculation error regarding the 1nm?)

## The physics behind the experiment

From quantum mechanics the energy levels an electron may have are quantized. This means that it may only gain or give off specific values and manifests itself in the Rydberg constant formula as the (1/n^2 - 1/m^2). The energies being quantized is also why n,m must be whole natural numbers. Because R is just a constant this means only specific values for the wavelength of light given off may exist. This explains the very defined light lines seen with the spectrometer.

As explained a bit in the notebook the reason behind the different R values and the corresponding values in wavelength between hydrogen and deuterium are due to the differences in reduced mass which also is related to the mass. Because deuterium has two ~~neutrons~~nucleons instead of one it is expected that the values differ.

## What I learned

In this lab I learned how to use a spectrometer to take wavelength measurements. It was also a good way to really see some of the physics behind it. In general when dealing with anything on this small of scale or quantum mechanics it's kind of hard to see anything other than formulas and numbers in a textbook.

In general I became more experienced with putting in pictures and using the excel sheet. Also I think I'm doing better at quantifying error but I'm not certain I'm doing specific parts of the analysis right (mostly how do I deal with my error after using a formula).

Near the end of writing my lab notes I also tried to use the math formula notations/writing for wikipedia and had some success. I'll try to use that more in the future as it does look nice.

## What I'd do/could do if I did the experiment again

If I had more time I would have tried to get the line of best fit working for calibration. I needed a little bit more practice with maple but in the future I'll try and have something set up to do that. Also because I prefer maple over the google excel I might try to find a good way to do calculations with it and then put my maple worksheet or code in my notes. As I mentioned above I'll want to check to make sure I'm doing the error analysis correctly and try to figure out to what place to round off to before I start doing calculations.

Because I couldn't find the reduced mass for deuterium online I had to calculate it myself and doing so I saw that because the mass is related to the Rydberg constant and wavelengths of light it might be interesting to try and find the mass of a few other substances similar to hydrogen.