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Contents 1 Coments from Helio 1.1 Data Analysis 1.2 Results 2 Coments from Marx

Coments from Helio

This is a nice lab report. The hypothesis prior to measurements are well founded. The tricky part are the experimental measurements.

Data Analysis

With the great risk of being a pain in the neck:

1. Graphs or plots should show data very clearly and in an understanble manner. They all should have captions and figures as well.
2. Plot 1 - Do not include the point (0,0) it is not a measurements. Lines joining points should only be present if it is a theoretical prediction or a "fit".
3. Plot 2 - The axis are reversed. Usually the parameter we vary (independent parameter) should go in the X-Axis and the parameter we measure on the Y-Axis. Again the line should not be there.
4. Plot 3 - I would not include this plot in the report. The table contain all the necessary information.
5. Plot 4 - same comment as plot 2.
6. Plot 5 - This one is difficult to understand. It is better if you plot physical quantities. The Y axis is in box units. It should be in nanoseconds, as you know the calibration factor. It is also best to show this type of data as a histogram. Excel can produce histograms.

On another issue. It is general better to have the same number of counts at each distance rather than a fixed time. Suppose you have a very well know process that happens in average at a rate of 1 per minute. So in the first minute, I could have zero counts, and in the second minute 2 counts - and I lucked out. But, for some reason, I could have, zero in my first minute and 1 in the second minute, and I would conclude that I have 0.5 events/minute. At this point I should point out my statistical uncertainty. I could also reduce my statistical uncertainty by measuring for a longer time interval, say 30 minutes. When you did the experiment, rather than counting for 4 minutes and stop it would be better if you have similar number of counts. You only had 270 counts when the counters were at 120 cm apart, but you concluded that 1 minute counting was not adequate on the basis of 662 counts!

Results

As correctly stated the rate diminishes because (at some level) cosmic rays come from different directions. However, they they come predominantly from above. So what is the dependence or rate with distance? is it simply 1 / d or 1 / d²? Or is it an exponential??

Can you say anything about how fast cosmic rays are traveling? What would you do to circumvent the problem of time spent by light in the scintillator paddle?

Coments from Marx

There is a lot of very nice work that has been accomplished here in a very short time. It is apparent that you have understood the main goals of using the equipment on hand to "discover" the nature of cosmic rays. You have also had insights into the actual difficulty of doing precise and unambiguous measurements - cosmic rays are notorious for thsi problem, and is quite amazing that they provided us with many early discoveries of subatomic particles.
I agree with all the comments made by Helio above. The biggest issue to improve is to understand how to deal with your measurements and treatment of the experimental errors. Because you can calculate a number to 3 deciaml places does not mean that is th eprecision you actually attained. I suggest you look at the SLAC Cosmic Ray page. This site also has a cosmic ray array that can be used interactively to make measurements of the flux and also shows how to present data and treat the statistical issues. Click on the SLAC's Online Cosmic Ray Detector, and then go to Tour Stop 1. Here you will find a nice discussion of the treatment of data and how to present it so that it reflects the actual uncertainties (and how to improve that by counting longer as you already have discovered) I also had troubles with Plot 5 and agree you should "histogram" your data- simply the number of counts in time bins whose width you choose appropriately. This would then immediately allow you to determine the mean and variance directly from the plot. You should also convert your answer for the speed into units that are recognized ,i.e. convert "This means that it takes an average of one nanosecond for a cosmic ray to travel 25.7362 centimeters." into meters/second - and then compare to the accepted value and see how well you did. The insight that rays can hit at different places in the paddles is important and has an effect on many of your measurements - you spend a lot of time in one lab aligning the paddles - you might want to think whether that was abig help given this problem. This issue also effects the solid angle discussion of how the rate depends on separation. Can you suggest how it could be improved next time? Overall, well done and I can't wait to read the rest of the reports. Thanks Mike