User:Jacob R Jaramillo/Notebook/Balmer Series Rough Draft

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SJK 12:23, 14 December 2009 (EST)
12:23, 14 December 2009 (EST)Sorry I was not able to finish looking this over this weekend!  My comments below are not thorough enough, but I know you are already working in the final draft.  I recommend looking at my comments on other students pages.  Especially if they were doing the Balmer.  For example: http://openwetware.org/wiki/Physics307L:People/Andrego/FormalRoughDraft and http://openwetware.org/wiki/Physics307L:People/Ierides/The_Balmer_Series
12:23, 14 December 2009 (EST)
Sorry I was not able to finish looking this over this weekend! My comments below are not thorough enough, but I know you are already working in the final draft. I recommend looking at my comments on other students pages. Especially if they were doing the Balmer. For example: http://openwetware.org/wiki/Physics307L:People/Andrego/FormalRoughDraft and http://openwetware.org/wiki/Physics307L:People/Ierides/The_Balmer_Series

Calculating the Rydberg constant by measuring the visible spectrum lines of hydrogen and deuterium

SJK 18:34, 6 December 2009 (EST)
18:34, 6 December 2009 (EST)Good author and contact info.  You can improve the title.  One way would be to say, "...by measuring wavelength of visible spectral lines of atomic hydrogen."
18:34, 6 December 2009 (EST)
Good author and contact info. You can improve the title. One way would be to say, "...by measuring wavelength of visible spectral lines of atomic hydrogen."
}

Author/Experimentalist: Jacob R. Jaramillo

Location: University of New Mexico, Department of Physics and Astronomy, Albuquerque

E-mail: jjaramillo17@msn.com

Abstract

SJK 18:40, 6 December 2009 (EST)
18:40, 6 December 2009 (EST)You can remove the phrase "not be be confused..." (abstracts have space limits, so that's not important enough to include).  I'd also start your abstract with your sentence, "The Balmer equation can be used to calculate...."  And perhaps another sentence to say why it's important that atoms have unique spectra.  Then you can go into what you did in this experiment.  Your sentence, "I was able to calculate..." is a bit confusing, and probably can be mostly deleted.  You need uncertainty on your values!  Without uncertainty, you cannot really comment on whether your value is consistent with the accepted value.  That said, you are doing the right thing with the style of your abstract at the end.  You could add another sentence, "we present these results and discuss possible sources of systematic error."  Finally, you have to many digits on many of your numbers.  This definitely reduces the readability quite a bit.
18:40, 6 December 2009 (EST)
You can remove the phrase "not be be confused..." (abstracts have space limits, so that's not important enough to include). I'd also start your abstract with your sentence, "The Balmer equation can be used to calculate...." And perhaps another sentence to say why it's important that atoms have unique spectra. Then you can go into what you did in this experiment. Your sentence, "I was able to calculate..." is a bit confusing, and probably can be mostly deleted. You need uncertainty on your values! Without uncertainty, you cannot really comment on whether your value is consistent with the accepted value. That said, you are doing the right thing with the style of your abstract at the end. You could add another sentence, "we present these results and discuss possible sources of systematic error." Finally, you have to many digits on many of your numbers. This definitely reduces the readability quite a bit.


Balmer's equation can be used to calculate the exact wavelength of light emitted as an election drops from one energy state to another, which is commonly referred to as the quantum number (n). In this experiment I calculated Rydberg's Constant with the use of a mercury, hydrogen and deuterium tube. Hydrogen and deuterium were selected due to their slight differences in atomic mass which results in two unique visible spectrum lines as deuterium is know as heavy hydrogen and is also a stable isotope of hydrogen. My average calculated value for the Rydberg's constant for hydrogen was (RHydrogen)=1.0975\times 10^7 m^-1 (3.915\times10^3), which is consistent with the accepted value of (RHydrogen)=1.0968\times 10^7 m^-1 (6.6\times10^-12). My average calculated value for the Rydberg's constant for Deuterium was (RDeuterium)=1.0986\times 10^7 m^-1(17.525\times10^3), which is slightly off from the accepted value of (RDeuterium)=1.0965\times 10^7 m^-1 (6.6\times10^-12).

Introduction

Johannes R. Rydberg, was born in 1854 in Halmstad on thet west coat of Sweden. Even though Rydberg's equation is generally presented as a function of the Balmers Series, it has been proven that Rydberg's work was independent of Balmer's research. "To begin with, Rydberg discovered that it was possible to sort the spectral lines belonging to an element in a number of different series, where the lines followed each other with a regularly decreasing difference and intensity. He put numbers n the various lines in a given series, with 1 for the next line with the longest wavelength, 2 for the next line, etc. and tried to find a formula that could express the wavelengths or frequencies as a simple formula that included integers. (1) With this finding Rydberg discovered that the relationship between wavelengths and quantum numbers resembled a hyperbola. In 1890, after numerous mathematical attempts and receiving funding from the Swedish Academy of Sciences (KVA), Rydberg concluded on the following formula and published his work thus defining the Rydberg constant.

n = noNo / (m + u)2 (2)

n is the wavenumber of the line (1/lambda) No is a constant with value of 107,921.6 while no, m and u are constants which are specific for the series.

The above formula was later re-written by Rydberg in the following, more well know method:

n / No = 1 / (m1 + u1)2 − 1 / (m2 + u2)2 (3)

With this great discovery, Rydberg was able to measure the Rydberg constant for Hydrogen (Rh = 109721.6) which he was later able critic to 109677 and officially release the value of 109737 as a value for a infinite nuclear mass. The constant No, is now known as the Rydberg's constant R(infinity) and is now most commonly written as:

R_\infty = \frac{m_e e^4}{8 \epsilon_0^2 h^3 c} = 1.0973731568525(73) \times 10^7 \,\mathrm{m}^{-1}

The Rydberg constant according to the above formula is now represented by the value 10973731.568527(73)m1 with an uncertainty of 6.6 x 10^-12 according to NIST. (4)

NIST uses an optical frequency comb for producing ultra precise colors of light that can trigger quantum energy jumps useful for accurately measuring the Rydberg constant. (5)

Image:Frequencycombjj.jpg

Figure 1: Optical Frequency Comb spectral display



SJK 12:19, 14 December 2009 (EST)
12:19, 14 December 2009 (EST)Can you add anything here about how the Rydberg constant is produced?  It it by calculating based on other factors?  Or is it measured spectroscopically?  The NIST page should say.
12:19, 14 December 2009 (EST)
Can you add anything here about how the Rydberg constant is produced? It it by calculating based on other factors? Or is it measured spectroscopically? The NIST page should say.

My purpose is to analyze my data with the above formulas and compare them to the acceptable values and tolerances to find any inconsistencies with my data.

Methods and Materials

Equipment

In this experiment I used a constant deviation spectrometer which included a Pellin-Broca prism, a spectrum tube power supply (Model SP200, 5.0KV, 10mA), and three gas tubes, Mercury, Hydrogen and Deuterium.


Image:Spectrometerjj.jpg

Figure 2: Spectrometer with Pellin Broca Prism


Image:Gastube.jpg

Figure 3: Spectrum tube power supply with Deuterium tube

Image:Pellinbroca.jpg

Figure 4: Function of the Pellin broca prism (by Jacob Jaramillo)

SJK 12:16, 14 December 2009 (EST)
12:16, 14 December 2009 (EST)It's good that you included captions on your figures and numbered them.  The captions can be improved with more detail, so that a user could understand the figures without reading the text.  For example, in Figure 1, you could explain that the prism is in the black box and not visible.
12:16, 14 December 2009 (EST)
It's good that you included captions on your figures and numbered them. The captions can be improved with more detail, so that a user could understand the figures without reading the text. For example, in Figure 1, you could explain that the prism is in the black box and not visible.

Set Up

I placed the Spectrum tube power supply with gas tube ~5-10mm away from the side of the Spectrometer with the adjustable slit (as show in Figure 3). I took caution by unplugging the Spectrum tube power supply, when placing the gas tube in the inside of it and when removing it as the power supply outputs 5.0KV's which is a large amount of voltage.

Step 1

One of the most critical steps of this experiment is to calibrate the Spectrometer. I preformed this task with the Mercury tube and the accepted wavelengths for the Mercury spectrum line found in the Mercury Calibration spreadsheet (Table 1). I chose to use the violet line and it's wavelength value to manually adjust the Pellin-Broca prism as this line was one of the brightest and sharpest lines. I adjusted the knob on the Spectrometer to 435.8nm and manually adjusted the Pellin Broca prism until the violet line was perfectly centered on the cross hairs of the Spectrometer eyepiece (I found it easiest to make minor adjustments to the Pellin-Broca prism while the tightening mechanism was almost completely tightened). Then I proceeded to turn the knob to each spectral line and insure that it matched as close to the accepted value as possible.

View/Edit Spreadsheet

Step 2

Next I removed the Mercury tube and replaced it with the Hydrogen tube. Once the hydrogen tube was stabilized/warm (generally takes 2 minutes), I proceeded to take measurements of each spectral line, as illustrated in the Hydrogen Spectrum spreadsheet (Table 2). As noted in the Hydrogen Spectrum spreadsheet, the Hydrogen Spectrum consisted of the following lines, two violet, one teal and one red line.

Hydrogen Spectrum Data Analysis Table 2

My average calculated value for the Rydberg's constant for hydrogen was (RHydrogen)=1.0975\times 10^7 m^-1 (3.915\times10^3), which is consistent with the accepted value of (RHydrogen)=1.0968\times 10^7 m^-1 (6.6\times10^-12).

Image:Hydrogen_spectrumjj.jpg

Figure 5: (Hydrogen Spectrum, slope of Rydberg constant)


Step 3

Same as step two; however, I used the Deuterium tube. Measurements can be found in the Deuterium Spectrum spreadsheet (Table 3). As noted in the Deuterium Spectrum spreadsheet, the Deuterium Spectrum consisted of the following lines, two violet, one teal and one red line.

Deuterium Spectrum Data Analysis Table 3

My average calculated value for the Rydberg's constant for Deuterium was (RDeuterium)=1.0986\times 10^7 m^-1(17.525\times10^3), which is 3.475\times 10^7 m^-1 off from the accepted value of (RDeuterium)=1.0965\times 10^7 m^-1 (6.6\times10^-12).

Image:Deuritiumspectrumjj.jpg

Figure 6: (Deuterium Spectrum, slope of Rydberg constant)


Formulas

\frac{1}{\lambda }=R(\frac{1}{2^2}-\frac{1}{n^2}) n=3,4,5,...\,\!

Calculating percent error

\% error=\frac{R_{accepted}-R_{measured}}{R_{accepted}}

Results and Discussion

As shown above my Rhydrogen value was within the accepted value while my Rdeuterium value was 3.475x10^7 off from the accepted value. Although my values were not 6.6x10^-12 within the accepted value, based on the equipment used and the fact that I didn't have an optical frequency comb, I feel that my measurements were still fairly precise.

SJK 12:20, 14 December 2009 (EST)
12:20, 14 December 2009 (EST)OK good, charts will be great!
12:20, 14 December 2009 (EST)
OK good, charts will be great!

Conclusion

As explained above, my values were either within the accepted value or extremely close. I believe the reason for my error is due to the error I found when calibrating the Spectrometer as my red spectrum was off by ~3nm. Also, although I was aware of backlash in the Spectrometer, a few times I did turn the knob the wrong way and even though I completed a full revolution before changing directions to try to reduce backlash, I feel it may have contributed.

SJK 12:21, 14 December 2009 (EST)
12:21, 14 December 2009 (EST)Make sure to have an acknowledgments section!
12:21, 14 December 2009 (EST)
Make sure to have an acknowledgments section!

Acknowledgments

I would like to thank my lab partner Johnny Gonzalez whom I conducted my initial data with, as well as Prof Koch who helped me with data analysis.

References

(1) Janne Rydberg-his life and work, I. Martinson, L.J. Curtis, www.sciencedirect.com, 2005.

(2) J.J. Balmer, Annalen der Physik und Chemie, N.F.25 (1895)80.

(3) J.R. Rydberg, Den Kungliga Svenska Ventenskapsakademiens Handlingar 23 (11)(1889).

(4) CODATA, Peter J. Mohr, Barry N. Taylor, David B. Newell, CODATA Recommended Values of the Fundamental Physical Constants: 2007 (95), (http://physics.nist.gov/cuu/Constants/codata.pdf).

(5) U.D. Jentschura, P.J. Mohr, J.N. Tan and B.J. Wundt, Fundamental constants and tests of theory in Rydberg states of hydrogen-like ions, Physical Review Letters, 100, 160404 (2008), posted online April 22, 2008 http://www.nist.gov/public_affairs/techbeat/tb2008_0429.htm

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