Graphing data from the Compton effect

[danny20051]

Homework Statement

Not sure whether I should be posting this here or in the quantum physics thread but I felt this more of a 'homework' question.

So basically I have done an experiment in which I measure the energy of light that has been scattered through a steel rod from a radioactive source. The software used to record this saves the data as a text file with columns (energy(Kev) and impulses). There are about 3000 entries as it was required to record data for about 24 mins. The problem is I am supposed to graph this data and show the Compton effect but when ever I select the data and click insert graph it tells me "the maximum number of data series per chart is 255" and I'm unable to insert a graph.

I have tried researching this problem but I can't seem to fix it. The instructor during my lab also told me to just save the data as a text file and go home and insert it into excel. So I'm not sure what I'm doing wrong. Am I going to need some other software to do this?

My second question would be once I figure out how to graph this how would I interpret the data? From what I know the first peak is the incident wavelength and the second is the shifted wavelength. However I was under the assumption that it was the peak(maximum) energy that corresponded to the shifted wavelength as that would indicate it hit an electron that was stationary. So I'm confused as to how the impulses is used in this as this just indicated how many time that energy was recorded right? Not the maximum energy recorded.

I'll upload a screen shot of the data recorded for a 30 degree scatter angle.

Any help is greatly appreciated.
Thanks

Homework Equations

Δλ = (h/mc)(1-cos(θ))

 

[kuruman]

It looks like the 3000 data points you collected have a whole bunch of unnecessary zeroes. Couldn't you set up the experiment to fit the expected range of energies in 255 channels by widening the ΔE per channel? Anyway, if you cannot go back and repeat the experiment, your instructor's suggestion is the way to go. Use a spreadsheet to bunch up the 3000 points into, say a manageable 200 by adding every 15 channels and calling the energy the average energy of the 15.

My second question would be once I figure out how to graph this how would I interpret the data? From what I know the first peak is the incident wavelength and the second is the shifted wavelength.

How do you mean "first" and "second"? Better label these as "low energy" and "high energy" because that's what you are plotting. Is the incident photon associated with "high" or "low" energy?

 

[danny20051]

There are only about 40 unnecessary zeroes so that shouldn't be too bad. So when you say create 15 channels of 200 and adding them, calling the energy the average energy of the 15. I'm not too sure what you mean. I haven't had to work with this much data before so I don't really understand what you mean by channels. Do I desperate the data into 15 groups of 200 and create a graph for each group? If so how do I add these groups to get the final result and a final graph with all the points?

As for the second question. The scattered wavelength should be longer and thus have a lower energy which would mean it would correspond to the first peak(lower energy peak) on the graph but I'm confused as in the lectures they have the first peak as the unshifted wavelength and the second as the shifted wavelength. They have the x=axis as λ so maybe that is why it would be swapped?

http://imgur.com/a/dTQMIThanks

 

[kuruman]

So when you say create 15 channels of 200 and adding them, calling the energy the average energy of the 15. I'm not too sure what you mean.

I didn't say "create 15 channels" . I wrote

Use a spreadsheet to bunch up the 3000 points into, say a manageable 200 by adding every 15 channels and calling the energy the average energy of the 15.

This means the following procedure. Add the impulses from the first N (N could be 15, or 10 or 20 or whatever) impulses or counts. Call that number N₁. Add the corresponding energies and divide the sum by N. Call that number E₁. {E₁, N₁} is your first "massaged" data point. Put it on your new plot of "Impulses" vs. "Energy". Do the same for the next group of N points, and the next and the next until you run out of data. Note: This method assumes that your energy intervals are equally spaced which I think is true in your case. If not, you will have to do a weighted average.

As for the second question. The scattered wavelength should be longer and thus have a lower energy which would mean it would correspond to the first peak(lower energy peak) on the graph but I'm confused as in the lectures they have the first peak as the unshifted wavelength and the second as the shifted wavelength. They have the x=axis as λ so maybe that is why it would be swapped?

You are correct here. However, don't convert your energies into wavelengths when you present your plots. This is an experiment that you performed, not a theoretical lecture. Plot and present what you measured.

 

[danny20051]

Thanks for the help. I think I understand but just to confirm. I would for example take the first 200 data points and sum the total energy of the 200 points and then divide by 200 for the average. That would be E1 as you said and N1 would be the sum of the impulses for the 200 data points. Then I would do this for the next 200 and continue until I have covered all data points?

I have followed that procedure for 30 degree scatter angle and have formed this graph.

http://imgur.com/FkEeWNu

It looks correct with two peaks. However I am a bit confused with the fact it has negative energy. A lot of my data points early on have negative energy values. How does this make sense in terms of wavelength? Have I done something wrong? Which seems weird as the shape of the graph looks as expected.

Assuming it is correct in order to show the Compton effect. Would I calculate both the incident wavelength and shifted wavelength from the peak data points then find the difference and compare to the theoretical value? (However I don't know how to find the incident wavelength as the corresponding energy value is negative?)Again, thanks for the help. Really appreciate it.

 

[kuruman]

However I am a bit confused with the fact it has negative energy.

You should not have negative energies. Whether averaged or not, these energies are supposedly photon energies and cannot be negative. If the equipment you used gave negative readings, there must be an offset to the readings or these readings do not represent photon energies. Read the lab instructions/manual or consult with your instructor to figure this out.

Now for the more important part. You averaged 200 points into 1. I think that may be too many. There is no correct number of how many you average, but you have to consider that the more points you average, the less peak resolution you have. Imagine what you would get if you averaged all 3000 points into 1 ! Zero peak resolution. The optimum number is a balance between the needed resolution to tell the peaks apart and the time you have allocated to the task. Also, don't forget that you need better resolution at smaller angles because the peaks come closer together.

 

[danny20051]

The lab instructions have nothing about an offset but I did do a 3 point calibration before recording the data. Am I able to just not include the negative values and start from the first positive value? As for the averaged points would 100 be ok? That would be roughly 30 data points. I feel doing any less than 100 would take a very long time as I have to do this for 4 angles.

 

[kuruman]

Am I able to just not include the negative values and start from the first positive value?

Absolutely not. If the low-energy peak is in the "negative" values, you will be throwing the baby out with the bath water. You will have to reconsider your three-point calibration. Maybe I can help you there if you tell me exactly what you did.

I feel doing any less than 100 would take a very long time as I have to do this for 4 angles.

So be it. Welcome to experimental physics.

 

[danny20051]

I'm pretty sure the calibration was not done correctly so I am going to have to leave the data as is for now. However I'm completely stuck on how I would do error analysis on this. Apart from the uncertainty in the angle of the scatter as I had to measure it what else could I calculate?

 

[kuruman]

Apart from the uncertainty in the angle of the scatter as I had to measure it what else could I calculate?

You will also need the uncertainties in Δλ' and Δλ. Look at the sample data from the manual. How well can you determine each of the two energies? The energy uncertainties ΔE' and ΔE can be translated into wavelength uncertainties by error propagation. Note that by averaging over energies when you go from 3000 to 100 points, your uncertainty increases. Probably the uncertainty in angle is minute relative to the uncertainty in measuring the position of the peaks.

 

[danny20051]

You're finding the peak value which is the middle of the peak is that not a single point? I don't see the uncertainty in that if you have each specific data point.

 

[kuruman]

You're finding the peak value which is the middle of the peak is that not a single point?

Look at the plot you posted in #5. Where would you say the peaks are? You cannot expect them to be right smack on one of the plotted points. You have to make an educated guess that's between a low and a high limit.