User:Arianna Pregenzer-Wenzler/Notebook/Junior Lab/Formal Report(rough draft)

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SJK 22:43, 6 December 2008 (EST)
22:43, 6 December 2008 (EST)Arianna, This is a really good first draft. Probably the most difficult thing remaining for you to do is to find and cite the original papers. There are also some other missing parts and revisions to make as I mention below. But it looks like you put in a good amount of effort building this foundation, so I think after taking more data this week you'll be able to make a very good final draft.
22:43, 6 December 2008 (EST)
Arianna, This is a really good first draft. Probably the most difficult thing remaining for you to do is to find and cite the original papers. There are also some other missing parts and revisions to make as I mention below. But it looks like you put in a good amount of effort building this foundation, so I think after taking more data this week you'll be able to make a very good final draft.

Contents

Quantum versus Wave behavior in Light, and the use of the Photo Electric Effect in the Determination of Planck's Constant

SJK 20:04, 6 December 2008 (EST)
20:04, 6 December 2008 (EST)Pretty good on the title & contact info. Typo in versus. Also, the "...and how to" is a bit informal, something like "...and determining Planck's constant from the photoelectric effect" would be better and more descriptive. Also, you should put your affiliation (Dept. Physics & Astronomy, U. New Mexico, Albuquerque)check
20:04, 6 December 2008 (EST)
Pretty good on the title & contact info. Typo in versus. Also, the "...and how to" is a bit informal, something like "...and determining Planck's constant from the photoelectric effect" would be better and more descriptive. Also, you should put your affiliation (Dept. Physics & Astronomy, U. New Mexico, Albuquerque)check
  • author: Arianna Pregenzer-Wenzler,

undergraduate student in the Department of Physics & Astronomy, University of New Mexico, Albuquerque.

  • experimentalists: Arianna Pregenzer-Wenzler, Danial Young
  • contact information:

email: arianna@umn.edu


Abstract

SJK 20:11, 6 December 2008 (EST)
20:11, 6 December 2008 (EST)This abstract flowed very well. The second time I read it I realized the first sentence must have a missing or misplace word, because it doesn't actually say anything ("determine the electromagnetic radiation?"). But it's still a pretty nice structure. Missing is a motivating statement (why is Planck's constant important, or other motivation)...in a "real" paper, your abstract should convey to the reader why your work is important. Also, the "once I knew I could interpret..." phrase makes it seem a little informal...a better phrase might be, "Having confirmed the quantum model, I..."
20:11, 6 December 2008 (EST)
This abstract flowed very well. The second time I read it I realized the first sentence must have a missing or misplace word, because it doesn't actually say anything ("determine the electromagnetic radiation?"). But it's still a pretty nice structure. Missing is a motivating statement (why is Planck's constant important, or other motivation)...in a "real" paper, your abstract should convey to the reader why your work is important. Also, the "once I knew I could interpret..." phrase makes it seem a little informal...a better phrase might be, "Having confirmed the quantum model, I..."

In this experiment I used the photoelectric effect to determine the energy of the electromagnetic radiation emitted by a mercury light source at a given frequency. By analyzing how the kinetic energy of the photo current was effected when I varied the intensity of my light source at a constant frequency, I determined that the behavior of the EM radiation is inconsistent with the wave model of light. By measuring the change in the kinetic energy of the photo current for different bands of the mercury spectrum I am able to show that there is a constant that relates the energy the EM radiation to its frequency, and by doing so I confirm that the behavior of the light is consistent with the quantum model. This constant, my experimentally determined value of Planck's constant is found by using the equation E = hν = KEmax + Wother to relate my measured values of KEmax to the known values of ν for the mercury spectrum. Using this method I determined a value for Planck's constant that contained the accepted value within a 68% confidence interval.

Introduction

SJK 20:53, 6 December 2008 (EST)
20:53, 6 December 2008 (EST)The introduction you have here is very well written and it's a great read! I see that you cite Dr. Gold's manual, which is good. However, as you note below, you also will need to find and cite some primary references (i.e. peer-reviewed scientific publications related to this background. It would be very difficult to find original references for all of these ideas, but at least a couple (e.g., Einsteins famous 1905 paper should be available).Also, even though what you have is excellent, you will need to expand it. First, since you will compare with the currently accepted Planck's constant, you will need to discuss what are the best ways of measuring Planck's constant nowadays and cite some primary research papers that have values. NIST CODATA is a great place to look. Second, you want to end your introduction with a brief explanation of what will follow--just to lead into the rest of the paper--and also any statement about the importance (impact) of your work or future work.
20:53, 6 December 2008 (EST)
The introduction you have here is very well written and it's a great read! I see that you cite Dr. Gold's manual, which is good. However, as you note below, you also will need to find and cite some primary references (i.e. peer-reviewed scientific publications related to this background. It would be very difficult to find original references for all of these ideas, but at least a couple (e.g., Einsteins famous 1905 paper should be available).

Also, even though what you have is excellent, you will need to expand it. First, since you will compare with the currently accepted Planck's constant, you will need to discuss what are the best ways of measuring Planck's constant nowadays and cite some primary research papers that have values. NIST CODATA is a great place to look. Second, you want to end your introduction with a brief explanation of what will follow--just to lead into the rest of the paper--and also any statement about the importance (impact) of your work or future work.

When light strikes a material the energy in the light is transferred to the electrons in the material, when enough energy is transferred the electrons break their bonds and are emitted from the surface of the material producing a photoelectric current, this is called the photoelectric effect. The purpose of this experiment is to use the photoelectric effect to analyze the behavior of light, and see if in this case its behavior supports the quantum or wave theory of light. If it supports quantum theory we will then determine an experimental value for Planck's constant, h. At the beginning of the last century Rayleigh and Jeans used classical theory to predict the energy density of black-body radiation as the frequency of the light was increased. Classical theory says that light will exhibit wave like behavior, which means that the value of the energy is continuous and the average total energy is constant for a given temperature; its average does not depend on its frequency. The Rayleigh-Jeans formula developed using this theory gives the energy density of a blackbody cavity and says that as the frequency of the radiation becomes large the energy density will go to infinity. Experimental physics didn't bear out the theory, in fact it showed that the energy density not only reaches a finite value at a given temperature, it then drops back toward zero. This incredible discrepancy between theory and reality, which became know as the ultraviolet catastrophe, prompted Planck to look for a theory for the behavior of light that would allow the average energy of this blackbody radiation to first increase to some finite value and then decrease again. Planck realized that for the energy to behave as suggested by experiment it could only have discrete uniformly distributed values and it had to be a function of the frequency, so he hypothesized E = hν, where h is a proportionality constant that has come to be known as Planck's Constant. The idea that light is emitted as discrete bundles of energy called photons is the basis of quantum theory.[2]

The method used by Planck to determine h was ...

Today scientists have determined Planck's constant to ... using ....

In the following sections I will outline how I arrived at my experimental value for h



Methods and Materials

SJK 20:57, 6 December 2008 (EST)
20:57, 6 December 2008 (EST)some of this first paragraph, explanation of what the photoelectric effect is should go in the introduction. The actual methods and materials parts should be written in the past tense (we did) as opposed to present tense or a "how to" style. The h/e apparatus should be stated as an instrument used and the manufacturer and location of the manufacturer. e.g. "...we used a commercial h/e apparatus (Company, City) which consisted of..."
20:57, 6 December 2008 (EST)
some of this first paragraph, explanation of what the photoelectric effect is should go in the introduction. The actual methods and materials parts should be written in the past tense (we did) as opposed to present tense or a "how to" style. The h/e apparatus should be stated as an instrument used and the manufacturer and location of the manufacturer. e.g. "...we used a commercial h/e apparatus (Company, City) which consisted of..."
In this lab we used a commercial h/e apparatus (PASCO scientific, Roseville, CA) which consists of a mercury vapor light source(OS- 9286*), a mounted box containing a cathode plate in a vacuum photodiode tube which I will refer to throughout this paper as the h/e apparatus(AP-9368*), a set of filters, and the lens grating assembly (Accessory Kit, (AP-9369*)), see fig 1. The light emitted by the mercury vapor light source is broken into its spectrum and focused by a lens grating assembly, one portion of the spectrum can then be directed through a slit in the h/e apparatus and onto a photodiode which works as a cathode. Rather than measuring the photoelectric current produced by the incident light, the h/e apparatus applies a reverse potential between the cathode and the anode reversing the current to zero. The minimum voltage necessary to stop the current corresponds to the maximum value of the kinetic energy of the electrons being emitted, and can be measured with a multimeter(WavTek 85XT, WavTek Technology Systems,Woodstock, IL) connected to the h/e apparatus.
fig 1: the h/e apparatus, for a detailed schematic see the link to the PASCO manual in the refrences [4]
fig 1: the h/e apparatus, for a detailed schematic see the link to the PASCO manual in the refrences [4]


SJK 21:06, 6 December 2008 (EST)
21:06, 6 December 2008 (EST)Again for this style, you should use the past tense for your methods. This paragraph is mostly present tense...it wouldn't take much to change it to past. For example, the last sentence can be changed to "Before each measurement, we used the zeroing button to ensure that ..."
21:06, 6 December 2008 (EST)
Again for this style, you should use the past tense for your methods. This paragraph is mostly present tense...it wouldn't take much to change it to past. For example, the last sentence can be changed to "Before each measurement, we used the zeroing button to ensure that ..."
In the first portion of this experiment we focused one of the first order bands of the mercury spectrum onto the photodiode of the h/e apparatus and measured both the maximum voltage and the time it took to reach that voltage. We then inserted a filter in front of the photodiode to decrease the intensity of the incident light and repeated this process until we had measurements corresponding to intensities varying from 20% to 100%, at a constant frequency. We repeated this process for a second spectral band. Between measurements we used the zero button on the side of the h/e apparatus to discharge any accumulated potential. An initial data analysis showed that the time required to reach the maximum voltage is so short that what we were measuring with our stop watch was actually the time it took for small fluctuations around the max voltage to equilibrium, viewing the wave form on an oscilloscope (Tektronix TDS 1002 , Tetronix Test Equiptment,Long Branch, NJ) proved to be much more useful.


SJK 21:09, 6 December 2008 (EST)
21:09, 6 December 2008 (EST)I'm pretty sure this paragraph belongs in the discussion section. I'm not as accustomed to "qualitative" analysis methods like this is. But it seems more like an interpretation of data and thus would be in the discussion. Whereas quantitative methods (without interpretation) should be described in methods.
21:09, 6 December 2008 (EST)
I'm pretty sure this paragraph belongs in the discussion section. I'm not as accustomed to "qualitative" analysis methods like this is. But it seems more like an interpretation of data and thus would be in the discussion. Whereas quantitative methods (without interpretation) should be described in methods.


SJK 21:11, 6 December 2008 (EST)
21:11, 6 December 2008 (EST)This paragraph is good: in the past tense "we did this" and very easy to read.
21:11, 6 December 2008 (EST)
This paragraph is good: in the past tense "we did this" and very easy to read.
For the second part of this experiment we measured the maximum potential for each of the five bands in the mercury spectrum at maximum intensity. The bands consisted of an ultraviolet band (that shows up as dark blue on the white reflective mask that is mounted on the front of the h/e apparatus and allows you to see the UV band), two more blue bands of slightly different color, a green band and a yellow band. When we measured the green and yellow bands we placed a green or yellow colored filter in front of the photodiode to prevent higher frequency light that could have been present in the environment or from an overlap with the second order bands from interfering with our results. We measured the maximum potential of each band twice, and then repeated the procedure for the second order bands. When I went back to the lab to do some final data collection I used my RayBan polarized sunglasses as an additional filter for the second order green and yellow bands in an attempt to block out UV and other high frequency light overlapping from the third order bands.


SJK 21:15, 6 December 2008 (EST)
21:15, 6 December 2008 (EST)Too much "how to" in this paragraph. It's a bit contrived in this experiment to not assume that ligh is composed of photons. If that's making it too difficult to write, you can abandon that. Also, it's good how you're discussing the analysis methods (but it's too "how to."). You should change it to "we did this" statements, and then also specifically name the software (e.g. MATLAB (Mathworks, whatever city) and Excel (Microsoft, Redmond WA)) and the algorithms that were used (e.g. LINEST). As a reminder, the goal is for someone to be able to fully understand and repeat your experiment without having to ask you unpublished details.
21:15, 6 December 2008 (EST)
Too much "how to" in this paragraph. It's a bit contrived in this experiment to not assume that ligh is composed of photons. If that's making it too difficult to write, you can abandon that. Also, it's good how you're discussing the analysis methods (but it's too "how to."). You should change it to "we did this" statements, and then also specifically name the software (e.g. MATLAB (Mathworks, whatever city) and Excel (Microsoft, Redmond WA)) and the algorithms that were used (e.g. LINEST). As a reminder, the goal is for someone to be able to fully understand and repeat your experiment without having to ask you unpublished details.

Analysis of the data for the first part of this experiment was basically qualitative, leading to the assumption that the behavior of the EM radiation is in keeping with the quantum model. Using quantum theory the total energy of the light, hν, can be expressed as the sum of the amount of energy needed to overcome the binding energy of the electrons in the material of the cathode and the kinetic energy of the photoelectric current. I rewrote the equation E = hν = KEmax + W0 so that KE is expressed as a function of ν, and determined h from a least squares fit for each set of data. To calculate h, and my error in h, I used the INDEX, and LINEST functions in Excel (Microsoft Corporation, Redmond WA). I weighted each value of h (the weight is given by one divided by the square of its error), and calculated a weighted average as my best guess for h along with an appropriately weighted value of my error.[3] I used MATLAB (MathWorks Inc, Natick, MA) to display my data making use of the polyfit function to plot my linear fit curves.


SJK 21:17, 6 December 2008 (EST)
21:17, 6 December 2008 (EST)the custom is to not list materials but to put them in the text when describing the methods. This would actually be easy for you to do, since you already talk about all these items above. So, you can get rid of this list, and work it into the above text...I already gave you an example with the h/e apparatus. When you have a bunch of items from one company (such as you do w/ the h/e, filters, etc.), you can put at the beginning of the methods, "all equipment from Company (city name) unless otherwise specified."
21:17, 6 December 2008 (EST)
the custom is to not list materials but to put them in the text when describing the methods. This would actually be easy for you to do, since you already talk about all these items above. So, you can get rid of this list, and work it into the above text...I already gave you an example with the h/e apparatus. When you have a bunch of items from one company (such as you do w/ the h/e, filters, etc.), you can put at the beginning of the methods, "all equipment from Company (city name) unless otherwise specified."

Results & Discussion Part I

SJK 21:33, 6 December 2008 (EST)
21:33, 6 December 2008 (EST)I have never found it easy (or useful) to separate "results" and "discussion", though that is commonly done. So, my preference is always to put them in the same section so I don't have to worry about it. I suppose someone else would be able to explain to you the utility of separating "factual" parts of the paper form the "interprative" parts. But especially in this case, where you have two separate sorts of experiments, it's even more awkward to separate the sections, in my opinion. Thus, I'd recommend you combine them. As I'm looking at it here, it looks like you have very good results+discussion for the "wave versus photon" section. But for the "planck's constant" section, you seem to be missing quite a bit of text for results+discussion.
21:33, 6 December 2008 (EST)
I have never found it easy (or useful) to separate "results" and "discussion", though that is commonly done. So, my preference is always to put them in the same section so I don't have to worry about it. I suppose someone else would be able to explain to you the utility of separating "factual" parts of the paper form the "interprative" parts. But especially in this case, where you have two separate sorts of experiments, it's even more awkward to separate the sections, in my opinion. Thus, I'd recommend you combine them. As I'm looking at it here, it looks like you have very good results+discussion for the "wave versus photon" section. But for the "planck's constant" section, you seem to be missing quite a bit of text for results+discussion.

The results of the first part of this experiment are essentially the qualitative analysis of the behavior of the light at constant frequency. If our light is behaving as would be predicted by classical theory then we should see a decrease in the maximum voltage as the intensity of the light decreases. This is because higher intensity means a greater wave amplitude (higher energy light), which would allow a for a larger amount of energy to transfer to the individual electrons. If, on the other hand, the behavior of our light is being governed by quantum theory, the amount of energy being transferred to the electrons is a function of the frequency of the light. According to the quantum model, in the first part of this experiment where we are keeping the frequency constant by using the same spectral band, the only effect the we should see as the intensity decreases is that the time it takes to reach the maximum voltage should increase.

My experimental data showed that the intensity of light, at a constant frequency, incident on the photodiode did not significantly effect the value of the maximum potential (Fig 2)
(Figure 2) This is a graph of Vmax for the ultra violet band, and the first blue band of the mercury spectrum. In this portion of the experiment the frequency was kept constant while the intensity of the light was decreased. The average value of Vmax for these frequencies is in black along with its error bar, notice the small size of the error bar indicating only a small change in Vmax over the range of intensity varying from 20% to 100%.
(Figure 2) This is a graph of Vmax for the ultra violet band, and the first blue band of the mercury spectrum. In this portion of the experiment the frequency was kept constant while the intensity of the light was decreased. The average value of Vmax for these frequencies is in black along with its error bar, notice the small size of the error bar indicating only a small change in Vmax over the range of intensity varying from 20% to 100%.
. Notice that while Vmax does vary from one intensity to the next those variations are small and do not appear to be correlated to the intensity. Though you cannot draw any conclusions from this data as to the effect of intensity compared to time required to reach Vmax, it is clear that Vmax does not increase significantly with increasing intensity, supporting the quantum model for light. When I was trying to measure the time required to the maximum potential, I found that even at a very low intensity the maximum voltage was reached so quickly that I was not able to directly measure the time it took to reach Vmax using a stopwatch. It was possible to draw some conclusions about the time required to reach the maximum potential at various intensity by viewing the wave form of the voltage going from zero to Vmax on the oscilloscope (Fig 3).
(Figure 3) Oscilloscope image of voltage vs time, the sharp spike in the wave form corresponds to the release of the discharge switch after which the voltage drops, then climbs towards its maximum in the expected fashion. (Steve Koch:Good start with the caption, but you should add more detail so the reader can understand the figure from the picture and caption alone. E.g., tell them, "The switch was released at the point where the trace begins to rise..." etc.)
(Figure 3) Oscilloscope image of voltage vs time, the sharp spike in the wave form corresponds to the release of the discharge switch after which the voltage drops, then climbs towards its maximum in the expected fashion. (Steve Koch:Good start with the caption, but you should add more detail so the reader can understand the figure from the picture and caption alone. E.g., tell them, "The switch was released at the point where the trace begins to rise..." etc.)
SJK 21:35, 6 December 2008 (EST)
21:35, 6 December 2008 (EST)Your figures need to be numbered and every figure should be referred to in the text somewhere (that is, there are no "standalone" figures that aren't also mentioned in parts of the text of the paper.
21:35, 6 December 2008 (EST)
Your figures need to be numbered and every figure should be referred to in the text somewhere (that is, there are no "standalone" figures that aren't also mentioned in parts of the text of the paper.
You can see there is an initial spike in voltage greater in height to Vmax that corresponds with the release of the discharge (zero) switch on the h/e apparatus that allows the apparatus to begin building up charge, then the voltage dips and grows again in the expected exponential fashion, something like 1-e-x until it reaches Vmax. Though I couldn't directly measure the time required to reach Vmax I could see on the oscilloscope, that the time to reach Vmax does indeed decrease as the intensity of the light is diminished.

Results & Discussion Part II

After eliminating the wave model of light as a means of predicting the behavior of our light, and seeing that at a constant frequency our light behaved as predicted by the quantum model, I went on to confirm the correlation between the energy of our light and its frequency by measuring Vmax for different frequencies. Taking measurements of Vmax for both the first and second order bands of the mercury spectrum showed that an increase in frequency always resulted in an increase in Vmax. My first set of data clearly shows this relation between the frequency and Vmax for the first and second order bands (Fig 4)
(Figure 4) My first set of data for Vmax measured at the different frequencies that make up the mercury spectrum. The maximum potential increases as the frequency of the light increases, supporting the quantum model of light. Notice how the 2nd order point corresponding to 5.5Hz is way out of line from all the other points of both 1st and 2nd order.
(Figure 4) My first set of data for Vmax measured at the different frequencies that make up the mercury spectrum. The maximum potential increases as the frequency of the light increases, supporting the quantum model of light. Notice how the 2nd order point corresponding to 5.5Hz is way out of line from all the other points of both 1st and 2nd order.
. With closer analysis it was clear that my data supported the quantum model, and that I would be able to determine an experimental value for Planck's constant from it, but a mystery had emerged as well. The value of the maximum potential corresponding to the green spectral band in the 2nd order was much greater than predicted by the general trend (see Fig 4). Some investigation showed that the cause of this discrepancy is an overlap of the high frequency 3rd bands with the 2nd order bands. In my second data set I was able to reduce the effect of this overlap by using my sunglasses as an UV filter when measuring the values of Vmax for the 2nd order green and yellow bands (Fig 5).
Image:Planck,voltage2.jpg.
(Figure 5) My second data set for Vmax vs intensity. Using a makeshift UV filter, I was able to bring the values of Vmax for the 2nd order green and yellow bands into the expected range.

(Steve Koch:Unlike most people, in this case you actually probably have too much information in your figure legend (and correspondingly very little in the text of the paper. It's good for figures to have lots of description so the reader knows what they're looking at...you do well with this with the beginning and end of your caption. The middle of your caption is more interpretation and conclusions drawn from the data and that can go in your results and discussion section. I would say a figure caption almost always doesn't have this much discussion (it's more "here're the results, see text for discussion")...though you can sometimes point out something important, (such as "note very little change in Vmax").]]


My experimental data in this experiment definitely supports the quantum model of light.


Using the method described above I calculated h using a least squares fit for each trial (two trials for both first and second order). My final experimental values for h and W0 are the weighted averages for these four calculations.


  • experimental value of h: h = 4.08(64)E-15 eV
  • experimental value of W0: W0 = 1.5916(13) eV

Further Discussion

While there was not a strong correlation between a decrease in intensity and a decrease in Vmax, I did on average see a slightly smaller Vmax at lower intensity's. This slight drop in Vmax corresponds to a systematic error. According to section 5.6 (technical information on the h/e apparatus) in the Planck's Constant lab (see lab manual [1]), the h/e apparatus has a high impedance amplifier that allows us to measure Vmax with a voltmeter. The high impedance means that the voltage coming in equals the voltage going out, ie. a photoelectric current comes in, goes out unchanged and gets measured by the voltmeter and we record Vmax. While the apparatus is good it is not perfect and as the amount of time necessary to charge the capacitor increases there is some current drain which leads to a decrease in Vmax as intensity decreases.


  • SJK 22:33, 6 December 2008 (EST)
    22:33, 6 December 2008 (EST)This is a good thing to look into...plus, when you retake data, you should solve the "mystery of the 2nd order green band".
    22:33, 6 December 2008 (EST)
    This is a good thing to look into...plus, when you retake data, you should solve the "mystery of the 2nd order green band".
    I want to note in this section how I saw yellow and green second order bands, I would like to recheck this in lab, and I also need to do some research in this area. The lab manual indicated that any band in the second order past the three blue bands were overlap from third order. It is interesting that in the Pasco lab manual [4] it both states that you can see five spectral band for mercury in the first and second order and shows that there is an overlap from the third order bands with the yellow and green second order bands.

note for final

I would also like to include a plot of my best guess for h for each trial along with my final value, all with error bars. I tried to do this but for some reason Excel would not display the axis values for h. Also is there a way to get my figures a little larger?

Conclusions

SJK 02:19, 8 December 2008 (EST)
02:19, 8 December 2008 (EST)I think I forgot to question you on this: do you think it is fair to do a weighted average of the first and second order results? Or to fit them all at once? Or do you think there's a systematic problem?
02:19, 8 December 2008 (EST)
I think I forgot to question you on this: do you think it is fair to do a weighted average of the first and second order results? Or to fit them all at once? Or do you think there's a systematic problem?

The accepted value of Planck's Constant:

h = 4.13566E-15 eV

My experimental value for h compares well to the accepted value, which my value includes in a 68% confidence interval.

SJK 22:35, 6 December 2008 (EST)
22:35, 6 December 2008 (EST)I agree with you on these conclusions. But, since we're practicing a formal report, this probably is too informal. I suppose it would be reasonable in some context to comment on the accessibility of this experiment to undergraduates.
22:35, 6 December 2008 (EST)
I agree with you on these conclusions. But, since we're practicing a formal report, this probably is too informal. I suppose it would be reasonable in some context to comment on the accessibility of this experiment to undergraduates.
It was fascinating that I could conduct such a simple experiment in my junior lab class, and come up with such a good value for such an important constant! It was also interesting that the difference between the quantum and wave models of light can be used to analyze the way that light is behaving in a given situation. SJK 22:36, 6 December 2008 (EST)
22:36, 6 December 2008 (EST)Another part of your conclusion could be further experiments (or "next steps") that you'd like to take.
22:36, 6 December 2008 (EST)
Another part of your conclusion could be further experiments (or "next steps") that you'd like to take.


Acknowledgments

SJK 22:38, 6 December 2008 (EST)
22:38, 6 December 2008 (EST)Good acknowledgments. The formal style is almost always complete sentences in one paragraph, and usually a mention of what was provided (technical assistance, money, supplies, etc.). If you received any advice from students who's work you didn't cite in your reference, you can thank them here too.
22:38, 6 December 2008 (EST)
Good acknowledgments. The formal style is almost always complete sentences in one paragraph, and usually a mention of what was provided (technical assistance, money, supplies, etc.). If you received any advice from students who's work you didn't cite in your reference, you can thank them here too.

Thanks to those who helped me during this lab;

Dr. Steve Koch, my lab professor,

Aram Gragossian, the teacher assistant in our lab, and

Daniel Young ,my lab partner.

References

  • [1]: Michael Gold, "The UNM Dept. of Physics and Astronomy PHYSICS 307L: Junior Laboratory"(Fall 2006),experiment 5 (page 31-40)
  • [2]: Eisberg and Resnick, "Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd edition" (1985, Wiley and Sons, Inc), Chapter 1 and Chapter 2, sec 2
  • [3]: Taylor, "An Introduction to Error Analysis, 2nd edition" (1997, University Science Books): The details of the weighted average are in chapter 7.2, and the method of least-squares fitting is explained in detail in chapter 8
  • obviously I need to do some research, it will be done! I do not intend the listed sources to be my only sources.
    • Steve Koch 22:38, 6 December 2008 (EST): I totally agree and I think I mentioned this above along with suggestions where to find primary "peer reviewed" reports.
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