# Physics307L:People/Allen/Balmer

SJK 22:04, 4 October 2009 (EDT)
22:04, 4 October 2009 (EDT)
I know you lost a bunch of your notes, but even so, you have an excellent primary lab notebook. Very good notes during your analysis, and commentary on possible problems with the lab. Good job! Make sure to take a look at David's pages as well, because I didn't always copy over comments that were relevant to both.

## Balmer Notes

In this Lab, I worked with David Weiss, with many thanks for his help. We started by learning some of the elementary set-up of the spectrometer and its parts, the adjustment of the prism, its original setting on a known spectral wavelength, and then the use of the calibrated knob to take readings of other spectral lines. We spoke with Professor Koch and Pranav Rathi about safety concerns, especially with regards to the vapor lamp which carries 5000 volts.
We set up the spectroscope to align with the vapor lamp such that the slit to allow in the light was at the center of the vapor tube. We chose to calibrate based on the central green line of the Mercury vapor tube at 546.1 nm, and adjusted the prism until this line met the cross hairs when the calibrated dial was set at that reading. We then measured the other known spectral lines to assess the accuracy of the scale and the systemic considerations for the readings of Hydrogen and deuterium.
On day one we practiced centering the spectral lines and reading the scale on the spectrometer, taking readings on both hydrogen and deuterium. At this time, I was observing the lines and taking the readings and David was recording the data and writing the notes.
On day two, David was setting the spectral lines, and I was reading the scale. We took multiple readings for each spectral line in both the hydrogen and the deuterium in order to determine the error. It was informative to see how much the multiple readings varied for the same set up taken in series. We moved off the line and took the readings from the same direction each time to minimize the error from the play in the adjustment knob.
Unfortunately my notes were lost both days, but I was able to copy the data from David's notes.

## Equipment

SJK 16:52, 29 September 2009 (EDT)
16:52, 29 September 2009 (EDT)
Good job on the equipment, safety and setup!
• Constant-Deviation Spectrometer[[1]]
• Spectrum Tube Power Supply Model SP200 5000V
• Spectrum Tube, Mercury Vapor S-68755-30-K
• Spectrum Tube, Hydrogen S-68755-30-G
• Spectrum Tube, Deuteruim S-68755-30-E

## Safety

• Electrical Shock: The main safety concern of this lab is with respect to the Vapor Lamp which operates on 5000 volts, enough to cause serios injury.
• Breakage: The glass vapor tubes are fragile and can break, possibly causing cuts. Also the spectrometer needs to be treated with care to keep it working well and to avoid damaging the prism.
• Toxicity: The Mercury Vapor Tube contains toxic gas that can cause harm if inhaled, so it is especially important to take care with that tube.

## Set Up

Set Up of Balmer Lab

We set up the spectrometer on the desk between two computers and set the vapor lamp on books until it was to a height where the center of the vapor tube was at the level of the slit that received the light into the spectrometer.

I noticed that the slit adjustment narrowed the spectral line only from the left and thought it might be better to measure from the right edge rather than from the center, but we disagreed, and as it seemed the instructions suggested David's method, I took the measurements from the center of the narrowed line.
SJK 01:57, 29 September 2009 (EDT)
01:57, 29 September 2009 (EDT)
Hmmm... I don't think I understood you at the time! I like your thinking that you should measure from the edge that does not move with slit width. If you're going to vary the slit width at all, that sounds like a much better idea.

We put the mercury vapor tube into the lamp, turned it on, and moved the prism until the green spectral line was at the cross-hairs when the guage was set at 546.1 nm. We found the other spectral lines for Mercury Vapor as follows.

Calibration for day one:

• Red...........701.0 nm
• Yellow1.......578.5 nm
• Yellow2.......576.4 nm
• Green.........546.1 nm ~ the calibration line
• Violet1.......404.5 nm
• Violet2.......435.9 nm

Calibration for day two:

• Red...........697.0 nm
• Yellow1.......579.7 nm
• Yellow2.......577.0 nm
• Green.........546.1 nm ~ the calibration line
• Violet2.......435.9 nm

## Data Day One

Notes from David: After we calibrated the Spectrometer, we then measured the spectral lines of the Hydrogen gas below. The first line we observed was the violet line followed by the blue-green line, then the red. We were a little confused about what the actual spectral lines were, but we decided upon two in the range of yellow spectral lines.
We then measured the Deuterium. The first spectral line we observed was the red line, followed by the violet line, then the blue-green line. A yellow line was observed followed by an orange line, but both of them were more faint than the others.

• Hydrogen Vapor Spectral Lines:

Red: 660nm

Yellow: 580.8nm

Orange: 604.8nm

Blue-Green: 486nm

Violet: 434.1nm

• Deuterium Vapor Spectral Lines:

Red: 659.1nm

Orange: 618.8nm

Yellow: 584.1nm

Blue-Green: 486.3nm

Volet: 434.3nm

## Data Day Two

• Hydrogen Vapor Spectral Lines

Red: 657.6nm, 657.0nm, 657.6nm, 577.7nm, 657.4nm

Orange: 603.3nm, 604.0nm, 603.9nm, 603.7nm, 603.6nm

Yellow: 582.4nm, 582.7nm, 582.6nm, 582.9nm, 582.4nm

Blue-Green: 486.3nm, 486.0nm, 486.2nm, 485.9nm, 485.9nm

Viloet: 433.8nm, 434nm, 433.9nm, 434.2nm, 434.3nm

• Deuterium Vapor Spectral Lines

Red: 657.8nm, 656.7nm, 657.2nm, 658.2nm, 656.6nm

Orange:

Yellow:

Blue-Green: 485.2nm, 485.6nm, 485.2, 485.2nm, 485.2nm

Violet:

## Data Analysis

My thanks to David Weiss for setting up the data analysis.

• Hydrogen

Red: 657.88+/-0.43nm

Orange: 603.88+/-0.2nm

Yellow: 582.3+/-0.31nm

Blue-Green: 486.05+/-0.07nm

Violet: 434.05nm+/-.07nm

SJK 02:02, 29 September 2009 (EDT)
02:02, 29 September 2009 (EDT)
As a note here, I don't see the calculation of the mean in your spreadsheet...obviously it's not a mystery how to do it, but just a note that some things seem to be missing. Also, for the Deuterium red, there seems to be a value that is obviously a typo. You could have discussed that and deleted it -- in a few weeks, we'll learn slightly more objective ways of dealing with bad points, too.
• Deuterium

Red: 660.6+/-3.06nm

Orange: 618.8nm

Yellow: 584.1nm

Blue-Green: 485.45+/-.18nm

Violet: 434.3nm

## Calculating the Rhydberg Constant

Rydberg formula for hydrogen:

${\displaystyle {\frac {1}{\lambda }}=R_{H}({\frac {1}{2^{2}}}-{\frac {1}{n^{2}}})}$

Using this formula(from Wikipedia) you can calculate the approximate value for the Rydberg Constant by knowing the transitions from the excited levels to the non excited states(ground states) by the following calculations:

${\displaystyle {\frac {\frac {1}{\lambda }}{({\frac {1}{2^{2}}}-{\frac {1}{n^{2}}})}}=R_{H}}$

where ${\displaystyle R_{H}}$ is the Rydberg Constant for hydrogen, ${\displaystyle \lambda }$ is the observed wavelength, and n is the excited energy state that the electron was in. You can find out what states that the electron was in by looking that up on a table. David used the Wiki page on Balmer Series Wiki Article and looked at the lines for the Balmer series.
The n=5 line represents the violet color that is emitted, the n=4 line represents the blue-green line that is emitted. The n=3 represents the red line that is emitted.

Rydberg Constant for Hydrogen(${\displaystyle R_{H}}$)

SJK 02:08, 29 September 2009 (EDT)
02:08, 29 September 2009 (EDT)
I checked your value for the red hydrogen line and got the same value for the best estimate. I checked for the uncertainty and got almost the same value. From your lab notebook, I can't tell which method you used for getting your uncertainty. Assuming you used a spreadsheet, embedding the analysis spreadsheet would solve that problem! (I see the spreadsheet above, but it does not include these calculations.)
• ${\displaystyle {\frac {({\frac {1}{657.88nm}})}{({\frac {1}{2^{2}}}-{\frac {1}{3^{2})}}}}}$ = ${\displaystyle R_{H}}$ for the red spectral line = 1.0944245+/-.00071${\displaystyle *10^{7}m^{-1}}$
• ${\displaystyle {\frac {({\frac {1}{486.05nm}})}{({\frac {1}{2^{2}}}-{\frac {1}{4^{2})}}}}}$ = ${\displaystyle R_{H}}$ for the blue-green spectral line = 1.0972808+/-.000158005${\displaystyle *10^{7}m^{-1}}$
• ${\displaystyle {\frac {({\frac {1}{434.05nm}})}{({\frac {1}{2^{2}}}-{\frac {1}{5^{2})}}}}}$ = ${\displaystyle R_{H}}$ for the violet spectral line = 1.0979866+/-.0001769${\displaystyle *10^{7}m^{-1}}$

Rydberg Constant for Deuterium(${\displaystyle R_{D}}$)

• ${\displaystyle {\frac {({\frac {1}{660.6nm}})}{({\frac {1}{2^{2}}}-{\frac {1}{3^{2})}}}}}$ = ${\displaystyle R_{D}}$ for the red spectral line = 1.0899183+/-.00507${\displaystyle *10^{7}m^{-1}}$
• ${\displaystyle {\frac {({\frac {1}{585.45nm}})}{({\frac {1}{2^{2}}}-{\frac {1}{4^{2})}}}}}$ = ${\displaystyle R_{D}}$ for the blue-green spectral line = 0.910980157+/-.00028${\displaystyle *10^{7}m^{-1}}$
Note: Due to a typo, this was miscalculated. Using the proper averaged measurement for the wavelength, 485.54nm, the Rhydberg constant is found to be 1.0986370${\displaystyle *10^{7}m^{-1}}$
• ${\displaystyle {\frac {({\frac {1}{660.6nm}})}{({\frac {1}{2^{2}}}-{\frac {1}{5^{2})}}}}}$ = ${\displaystyle R_{D}}$ for the violet spectral line = 1.09645516${\displaystyle *10^{7}m^{-1}}$(no +/- due to only seeing the two spectral lines and having only one data point)

## Concerns and Sources of Error

SJK 02:10, 29 September 2009 (EDT)
02:10, 29 September 2009 (EDT)
This is a great discussion of sources of error! This shows very good experimentalist's skills and will be a good asset for you in the future.

The mercury calibration is a bit strange anyway...but one way of dealing with it is to have a conversion factor that interpolates between each of the "known" wavelengths. I can describe this better in person, and especially if you choose this lab for your formal report.
• Systematic Error: When we first calibrated the spectrometer, we noticed that we had not fully tightened the set screw on the prism, so there was some slippage of the prism as we moved through the range of our measurements. As a result we repeated the first calibration with the prism set properly. However, this may still be a concern on a small scale.
In addition, the scale on the dial to the wavelengths was difficult to read and did not have as much accuracy for the longer wavelengths. The dial had a significant amount of play in the gears as well, which we tried to minimize by always taking the readings from the same direction.
• Random Error: This could come from reading the markings or aligning the spectral lines slightly differently for each repitition of a data point, even though they were all taken from the same direction.
• The one outlier reading for the Deuterium red spectral line on day two may have been due to inaccurate reading of the scale markings or due to approaching the spectral line from the opposite direction, leading to error from the play in the adjustment gears. In addition, I did not know how to include the error of our readings for Mercury from its standard spectral line values into our data collected for Hydrogen and Deuterium It seems we should have adjusted our readings due to the amount that the Mercury readings varied across the scale. In doing future labs, I would work on developing this correction to obtain more accurate results with other calibrations.
• Another concern comes from the fact that we observed five spectral lines for Hydrogen, two of them yellow, whereas in the lab notes and other information thaat I've read there are only four listed, two of them violet. So it may be that our vapor tube was contaminated with another element. Although we still found the Rhydberg Constant within a small degree of error, this seems a major issue of uncertainty.