# Balmer Series: Observing the Visible Spectra of Hydrogen

SJK 22:01, 29 November 2009 (EST)

22:01, 29 November 2009 (EST)
Overall, a good start on the report. Obviously a lot of things to improve and add, as noted in the margins. I think you'd benefit from looking over a few published peer-reviewed reports, to get more feeling for how they're typically written. Proceedings of the National Academy of Sciences may be a good place to try to find some interesting articles to flip through. Aside from the introduction (which will take some work, especially in citing peer-reviewed research), I think most of your work will go into making a better presentation of the results, including several figures. Also, I did note one idea for your extra data session.
Author: Alexandra S. Andrego

Experimentalists: Alexandra S. Andrego & Anastasia A. Ierides

Junior Lab, Department of Physics & Astronomy, University of New Mexico

Albuquerque, NM 87131

aandrego@unm.edu

The visible spectrum of Hydrogen

SJK 15:42, 29 November 2009 (EST)

15:42, 29 November 2009 (EST)
Typically, a formal publication does not have a title image. However, it is true that sometimes very nice images are put on the cover of the journal issue. So, I think you can leave this image in here. HOWEVER, and this is very important: you should very clearly cite the source of the image! Other than that, good job with Title, author.

## Abstract

SJK 15:41, 29 November 2009 (EST)

15:41, 29 November 2009 (EST)
Overall, very good start on abstract. As noted below, some parts of your abstract were not essential. Besides the comments below, it seems to me that motivation is missing. Why is Rydberg or Balmer series important? You can say that first. Then, you can say directly that you set out to measure R using __ method. The OpenCourseWare example abstract says, "The abstract is essential. It should briefly mention the motivation, the method and most important, the quantitative result with errors. Based on those, a conclusion may be drawn. "
The Balmer series is the designation of visible specral lines of the emission of hydrogen atoms. The Balmer series contains eight spectral lines though only four are observable under the conditions of this experiment. The four visible spectral lines are categorized by Ultra Violet, Violet, Blue-Green, and Red, depending on the value of the light wavelength. The use of a spectrometer allows us to observe and classify spectra lines of the hydrogen atom. By using electrical stimulation to excite the hydrogen atoms to higher energy levels, measurements of the emitted photons with wavelengths equivalent to the energy of our excited electrons can be made. Through such measurements it is possible to experimentally determine Rydberg's constant, R, that is used in the Balmer-Rydberg equation for hydrogen: SJK 15:23, 29 November 2009 (EST)
15:23, 29 November 2009 (EST)
The first equation is OK to put in, but the second one should be left out of the abstract. There is almost always pressure to make the abstract as concise as possible. Also, sometimes formatted equations will not be allowed in the abstract (plain text is preferred), but hopefully that will change as things get modernized.
$\displaystyle{ \frac{1}{\lambda}=R(\frac{1}{2^2}-\frac{1}{n^2}), n=3,4,5,..\,\! }$
That is more generally stated by:
$\displaystyle{ \frac{1}{\lambda}=R(\frac{1}{m^2}-\frac{1}{n^2}) }$
$\displaystyle{ m=1,2,3,...\,\! }$
$\displaystyle{ n=2,3,4,5,...\,\! }$
$\displaystyle{ n\gt m\,\! }$

SJK 15:28, 29 November 2009 (EST)

15:28, 29 November 2009 (EST)
These next two sentences are probably superfluous, since you're focusing on using the above formula to measure the R, (as opposed to using R to predict lambdas)
The Balmer series, often referred to as "H-alpha", predicts the four visible spectral lines of hydrogen with high accuracy. By using the Balmer-Rydberg equation it is possible to calculate the resulting wavelengths of photons caused by the absorption and/or emission of the photon and its energy by hydrogen atoms.
In this experiment we calculated the Rydberg constant to be approximately
$\displaystyle{ R_{average}\approx1.0972781\pm 0.0025\times10^7 m^{-1}\,\! }$SJK 15:15, 29 November 2009 (EST)
15:15, 29 November 2009 (EST)
You have too many digits on your mean. The uncertainty only goes to 4 digits, so same should be true of mean.
Which we found to only have a small error percentile of SJK 15:26, 29 November 2009 (EST)
15:26, 29 November 2009 (EST)
"error percentile" will be ambiguous to someone only reading the abstract. It would be better to say something like, "The accepted value of ___ is more than ___ SE away from our value, and is thus statistically significantly different (or something like that but worded better).
$\displaystyle{ \% error\approx0.046%\,\! }$

## Introduction

SJK 15:43, 29 November 2009 (EST)

15:43, 29 November 2009 (EST)
Sounds good -- take a look at other students rough drafts (perhaps from last year too) to see my comments.

--Alexandra S. Andrego 03:04, 16 November 2009 (EST)I know I need an introduction but I would like to conduct more research on the uses of the Balmer series and Deuterium before writing this up formally. I was unable to do much research due to the unfortunate and fairly inconvenient death of my 2wire, and lack of competency within the customer service department at Qwest. My apologies.

## Required Equipment

SJK 15:48, 29 November 2009 (EST)

15:48, 29 November 2009 (EST)
Even though it may be helpful, the custom is not to include a list of required equipment in a formal publication. This probably is due to issues with space and page costs. What is done instead is the equipment is noted in a description of the procedure. For example, "Hyrdogen (S-68755-30-G) or Deuterium (S-68755-30-E) discharge tubes were inserted into the Spectrum Tube Power Supply (Company; Model Sp200). After warming up for more than ___ minutes, spectra were viewed with constant-deviation spectrometer (Company, model #)...etc."
The equipment that was used to perform this experiment is as follows:
-Constant-Deviation Spectrometer (SER #12610)
-Spectrum Tube Power Supply (Model SP200)
• 5000V
• 10 MA
-Spectrum Tubes:
• Spectrum Tube, Mercury Vapor (S-68755-30-K)
• Spectrum Tube, Hydrogen (S-68755-30-G)
• Spectrum Tube, Deuterium (S-68755-30-E)

## Methods

SJK 16:09, 29 November 2009 (EST)

16:09, 29 November 2009 (EST)
This figures are very helpful for understanding how you did the experiment. In a traditional publication, these kinds of photos are usually omitted (probably due to space/page costs). However, I think it'd be good for you to keep them. To make them better, you need to: (a) number every figure, and refer to the figure by number in text. For example, "...the slit width was adjusted blah blah (slit shown in Figure __)." and (b) Figure captions need more detail. You don't need to explain everything, but you need enough information that the reader can understand what the photo is and why you are showing it. For example, "Figure ___: the single-slit aperture. Slit was adjusted by the visible thumbscrew in order to balance precision (best with small slit) and visibility (best with large slit)
The Complete Set Up
The Slit Width for the Incident Light
The Open Prism Apparatus and Spectrometer Dial

SJK 16:22, 29 November 2009 (EST)

16:22, 29 November 2009 (EST)
The section labels "setup" and "experiment" are too informal. You should rename them something like "Spectromter calibration" and "Measurement of H and D spectral lines"

### Set Up

SJK 16:35, 29 November 2009 (EST)

16:35, 29 November 2009 (EST)
You have a mix of past and present tense here. For methods, it is standard to use past tense, since you are describing what you did. In more informal settings, people like to write a "how to" ("..next do this") kind of instructions, but that's not what's done in formal scientific publications. Take care to change it to past tense throughout. Also, refer to supporting figures or diagrams by number when necessary ("...as shown in Figure __").
To begin the experiment a few preliminary steps were taken. First adjusting the spectrometer by bringing the cross-hairs into focus and sliding the ocular to a position that suits our vision allows for no parallax to exist between the cross-hairs and the slit of the spectrometer when it is focused sharply. To bring the slit into focus while looking through the eye piece, it is possible to turn the large ring near the center of the viewing telescope. By attaching and positioning the mercury bulb into the spectrum tube power supply the apparatus is made functional. The spectrum tube power supply requires approximately five minutes to warm up the mercury bulb. Calibration of the spectrometer is a very important part of the set up for this experiment. It is done by the use of a wide slit setting. After finding a line of the the mercury spectrum and narrowing the slit until the line is focused sharply, the known values of light wavelengths for the spectral lines of mercury can be used to position the prism, bulb, and spectrometer to achieve minimal systematic error. The positioning is done by a series of small rotations of the prism and measurements from the spectrometer dial. (It is very important to understand the mechanics of a spectrometer to avoid causing unnecessary systematic error. Due to the use of gears in the spectrometer dial, "back lash" caused by the empty space between the teeth of the gears, can cause false data. It is important to always turn the dial back at least a quarter of a turn before rotating to the position at which a measurement needs to be taken. This insures that when the measurement is taken, the gears are continuously in contact). This is repeated until the positioning of all components yields correct measurements for the wavelengths of the corresponding mercury spectra. Once the calibration process is complete the mercury bulb may be removed and replaced with the hydrogen bulb, and experimentation may commence.
The calibration technique demonstrated in this experiment used the general data from the following table in Professor Gold's Manual, pg 29 SJK 16:39, 29 November 2009 (EST)
16:39, 29 November 2009 (EST)
The Table should be numbered ("Table 1") and referred to by number in text("Table 1 shows..."). Also, instead of linking to Gold's manual here, you should put it as a numbered reference and then in the reference link to his Manual.

Color Wavelength (nm)
Deep Violet (very hard to see) 404.7
Violet 435.8
Very Weak Blue-Green skip this one
Green 546.1
Yellow 1 577.0
Yellow 2 579.0
Red 690.75

### Experiment

SJK 16:48, 29 November 2009 (EST)

16:48, 29 November 2009 (EST)
A little more detail is necessary here, thinking of the "we did" versus "how to" style. Did you alternate partners? Did you take some data in week 1, other data in week 2? Did you take care about backlash? Was slit width left fixed?
After replacing the mercury bulb in the experiment with the hydrogen bulb (and waiting the five minutes to allow the bulb to warm up and keeping in mind the "back lash" effect), measurements for the visual spectral lines of hydrogen were easily taken.
Once sufficient data was obtained from the hydrogen bulb, the experiment was taken one level further, and the spectral lines of deuterium were observed through the same method as well.

SJK 17:10, 29 November 2009 (EST)

17:10, 29 November 2009 (EST)
Missing from the methods section is description of analysis. How were the data processed? What software applications were used? What formula were used for error propagation, etc.

## Raw Data

SJK 17:17, 29 November 2009 (EST)

17:17, 29 November 2009 (EST)
"Raw Data" is not a typical section of a formal publication. Providing raw data is becoming more common, but is still rare (a great thing for you to do, and hopefully commonplace early this century!). I think the best thing to do if you do not want to provide the raw data as a table in the article is to put a sentence early in the results, "Raw data are available from (x)" where x is a numbered reference, and in the reference you link to the location of the data. Another alternative is to have an appendix for raw data. Any of these options would be fine in this case, since it's not a lot of data. In some other cases (such as genomics data), the amount of data is huge and too much to publish as a table in the paper.

My thinking is that this raw data should be the first table in your results section. It should be labeled (e.g. "Table 1") and referred to by number in the text and should have a caption, just like figures do.
The raw data obtained from this experiment was formatted into the table shown below.

|key=tlcu3hB5KpmJ6X9wgXnuimA |width=650 |height=305

}}

## Analysis and Results

SJK 21:50, 29 November 2009 (EST)

21:50, 29 November 2009 (EST)
The results will be improved a lot by focusing on more concise and clear presentations of the results (compared to now, there's a lot of equations with less discussion). An essential part in doing this will be creating figures to show your data and processed data. I notice now that you actually don't have any figures beyond the photos of the setup. So, you'll have to work on that. Figures in the results section are usually essential, and it's a part of a report that people will look at first or most.
The average off all values for each spectral line was used to determine the best measured wave length for each spectral color. The standard error of mean was calculated to obtain the 68% uncertainty margins for our measurements.
Once the average wavelength per spectral line was determined, a mean was taken over all spectral lines and used to compute an experimental Rydberg constant ,R, as appears in the Balmer-Rydberg equation discussed earlier.
The use of Microsoft Excel and Google Docs made the analysis of the raw data possible.

SJK 17:50, 29 November 2009 (EST)

17:50, 29 November 2009 (EST)
This first part above here is actually the missing part of "methods" section which I was talking about above. The results section can start out with your raw data table, and probably combined with the final values (mean +/- SEM) as well. Remember that the point of the formal report is to clearly show the important results. So, you can describe in the methods your methods for calculating mean +/- mean and here you can concisely report results (and link to full spreadsheet in a footnote/reference). In the results & discussion section, you can comment on any data that had to be thrown out, or were repeated and why, etc.
The spreadsheet used to perform the analysis and error propagation can be seen below.

|key=tti_lcw5NdLvkGYblz1VIxQ |width=650 |height=550

}}

From the data table above the measured experimental values of wavelengths for each spectral line observed are:

SJK 17:53, 29 November 2009 (EST)

17:53, 29 November 2009 (EST)
This whole string of results and equations is not good for the results section. Some of it should be in methods, and some of it should be cleaned up in tables (in fact, some it is repeated from the table, but with less information (no uncertainty).
$\displaystyle{ n=6\rightarrow n=2\,\! }$
$\displaystyle{ \lambda_{Hydrogen} =409.84 nm\,\! }$
$\displaystyle{ \lambda_{Deuterium} =N/A\,\! }$
$\displaystyle{ n=5\rightarrow n=2\,\! }$
$\displaystyle{ \lambda_{Hydrogen} =433.92 nm\,\! }$
$\displaystyle{ \lambda_{Deuterium} =433.3 nm\,\! }$
$\displaystyle{ n=4\rightarrow n=2\,\! }$
$\displaystyle{ \lambda_{Hydrogen} =485.96 nm\,\! }$
$\displaystyle{ \lambda_{Deuterium} =485.62 nm\,\! }$
$\displaystyle{ n=3\rightarrow n=2\,\! }$
$\displaystyle{ \lambda_{Hydrogen} =657.4 nm\,\! }$
$\displaystyle{ \lambda_{Deuterium} =655.9 nm\,\! }$
From these values a Rydberg's constant can be calculated from the Balmer-Rydberg equation as follows:
$\displaystyle{ \frac{1}{\lambda }=R(\frac{1}{2^2}-\frac{1}{n^2}), n=3,4,5,6\,\! }$
$\displaystyle{ \frac{1}{\lambda }=R(\frac{n^2-4}{4n^2})\,\! }$
$\displaystyle{ R=\frac{4n^2}{\lambda(n^2-4)}\,\! }$

$\displaystyle{ n=6\rightarrow n=2\,\! }$
$\displaystyle{ R_{Hydrogen}=\frac{4(6)^2}{(409.84\times10^{-9} m)((6)^2-4)}\approx1.0979895\times10^7 m^{-1}\,\! }$

$\displaystyle{ n=5\rightarrow n=2\,\! }$
$\displaystyle{ R_{Hydrogen}=\frac{4(5)^2}{(433.92\times10^{-9} m)((5)^2-4)}\approx1.0974153\times10^7 m^{-1}\,\! }$
$\displaystyle{ R_{Deuterium}=\frac{4(5)^2}{(433.3\times10^{-9} m)((5)^2-4)}\approx1.0989856\times10^7 m^{-1}\,\! }$
$\displaystyle{ n=4\rightarrow n=2\,\! }$
$\displaystyle{ R=\frac{4(4)^2}{(485.96\times10^{-9} m)((4)^2-4)}\approx1.0984840\times10^7 m^{-1}\,\! }$
$\displaystyle{ R=\frac{4(4)^2}{(485.62\times10^{-9} m)((4)^2-4)}\approx1.0982524\times10^7 m^{-1}\,\! }$

$\displaystyle{ n=3\rightarrow n=2\,\! }$
$\displaystyle{ R=\frac{4(3)^2}{(657.4\times10^{-9} m)((3)^2-4)}\approx1.0952236\times10^7 m^{-1}\,\! }$
$\displaystyle{ R=\frac{4(3)^2}{(655.9\times10^{-9} m)((3)^2-4)}\approx1.0977283\times10^7 m^{-1}\,\! }$

The average values for the measured Rydberg's constants are:
$\displaystyle{ R_{Hydrogen,average}=\frac{(1.0979895+1.0974153+1.0984840+1.0952236)\times10^7m^{-1}}{4} }$
$\displaystyle{ =\frac{4.3891124\times10^7 m^{-1}}{4}\,\! }$
$\displaystyle{ \approx1.0972781\pm 0.0025\times10^7 m^{-1}\,\! }$
$\displaystyle{ R_{Deuterium,average}=\frac{(1.0989856+1.0982524+1.0977283)\times10^7m^{-1}}{3} }$
$\displaystyle{ =\frac{3.2949663\times10^7 m^{-1}}{4}\,\! }$
$\displaystyle{ \approx1.0983221\pm 0.0007\times10^7 m^{-1}\,\! }$

SJK 18:02, 29 November 2009 (EST)

18:02, 29 November 2009 (EST)
Unless you have other ideas, I think for your "extra data" session, you should focus on the issue of whether you can discern the difference between H and D with your apparatus (I think the answer is "no"). You can approach the issue statistically (how small could you get the uncertainty with your instrument, and how does this compare with the difference between H and D. This will make your results section longer, and allow you to have more discussion. Also, you can expand your introduction to talk about difference between H and D.

## Discussion

In order to fully comprehend the results above, it is beneficial to compare the experimental results with the accepted values.
The accepted value of Rydberg's constant is calculated from the following equation found on page 30 of Professor Gold's Manual.
$\displaystyle{ R=\frac{\mu e^4}{8\epsilon _0^2ch^3}\,\! }$
Where $\displaystyle{ \mu\,\! }$ is the reduced mass
$\displaystyle{ R=1.0967758\times 10^7 m^{-1}\,\! }$

SJK 21:47, 29 November 2009 (EST)

21:47, 29 November 2009 (EST)
You can also calculate these from the accepted value of Rydberg constant, right? It would be a nice table to compare the predicted wavelengths for H versus D (along with your final measurements), which would then support your discussion of whether you should be able to measure H versus D. Also, below, you say systematic error has been minimized, but is that true, based on statistical comparison with accepted value and the value you measure?
The following accepted values for the four visible wavelengths of the Balmer Series were taken from the hyperphysics website
$\displaystyle{ n=6\rightarrow n=2\,\! }$
$\displaystyle{ \lambda =410.174 nm\,\! }$
$\displaystyle{ n=5\rightarrow n=2\,\! }$
$\displaystyle{ \lambda =434.047 nm\,\! }$
$\displaystyle{ n=4\rightarrow n=2\,\! }$
$\displaystyle{ \lambda =486.133 nm\,\! }$
$\displaystyle{ n=3\rightarrow n=2\,\! }$
$\displaystyle{ \lambda =656.272 nm\,\! }$
Through comparison it is evident that the measured values attained through this experiment were successfully close to the accepted values listed above. It is evident from results such as these that the systematic error was successfully minimized for this experiment. When comparing the results from the hydrogen bulb and the deuterium bulb, it can be noticed that both results have significantly different true means for each wavelength and the Rydberg constant. According to the theory behind the Balmer series, and Rydberg constant, this is due to the difference in mass that exists between the two atoms. This should therefore be true for all atoms of varying mass.

### Uncertainty and Error

SJK 21:52, 29 November 2009 (EST)

21:52, 29 November 2009 (EST)
This is not a typical section heading in a formal report. It should be worked into the discussion. A paper would be more likely to end with a "conclusions" section.
Though this experiment proves to have minimized major sources of systematic error, there were still some areas of which could have been improved on.
This experiment was conducted over the course of two non-consecutive days, where it is known that the spectrometer was used by other members of the facility between data taking. This caused a source of systematic error in that the spectrometer had to be recalibrated for a second day's worth of experimentation. Precise and consistent calibration is very important for this lab because it allows better comparison of results and more accurate measurements.
Our error percentiles for the calculations made in this experiment for the Rydberg's Constant can be calculated as:
$\displaystyle{ \% error=\frac{R_{accepted}-R_{measured}}{R_{accepted}} }$
$\displaystyle{ \% error_{Hydrogen}=\frac{1.0967758\times 10^7 m^{-1}-1.0972781\times10^7 m^{-1}}{1.0967758\times 10^7 m^{-1}} }$
$\displaystyle{ \approx0.046%\,\! }$
$\displaystyle{ \% error_{Deuterium}=\frac{1.0967758\times 10^7 m^{-1}-1.0983221\times10^7 m^{-1}}{1.0967758\times 10^7 m^{-1}} }$
$\displaystyle{ \approx0.141%\,\! }$

## Acknowledgments

SJK Steve Koch 21:53, 29 November 2009 (EST)

Steve Koch 21:53, 29 November 2009 (EST)
A formal publication would almost surely have more formally worded acknowledgements. I like the way you have it, but to make it more formal, something like "I extend my greatest gratitude for Anastasia's enthusiasm and work ethic as my lab partner for this project." etc.
I would like to take the time now to extend my greatest gratitude for Anastasia Ierides who was my lab partner for this lab. Her enthusiasm and work ethic made this experiment one of my favorites.
Google Docs and Microsoft Excel were used to format and post our raw data and error analysis to our wiki lab notebook
I would also like to thank Professor Koch and Pranav for asking all the hard questions and never loosing patience with us during the long lab hours.

## References

SJK 18:57, 29 November 2009 (EST)

18:57, 29 November 2009 (EST)
You will need more references, and especially to peer-reviewed research. Most of these will end up in the introduction and methods probably. For the citations to peer-reviewed research, you'll want to use a standard reference format (such as Author list, title, year, journal, volume, pages, and a hyperlink.

[1] Hydrogen Energies and Spectrum http://hyperphysics.phy-astr.gsu.edu/Hbase/hyde.html#c4
[2] The University of New Mexico Dept. of Physics and Astronomy PHYSICS 307L: Junior Laboratory Manual Fall 2006 By Professor Michael Gold http://www-hep.phys.unm.edu/~gold/phys307L/manual.pdf