User:David K. O'Hara/Notebook/physics 307 lab/electron diffraction lab summary

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Electron Diffraction Lab Summary

SJK 17:33, 11 October 2009 (EDT)
17:33, 11 October 2009 (EDT)This is a very good summary, except for the lack of uncertainty on your final values (which also have a calculation error as noted) and a statistical comparison with the accepted values.  Scope of the summary is good, and I like how you point out the success in proving the wave nature of matter!
17:33, 11 October 2009 (EDT)
This is a very good summary, except for the lack of uncertainty on your final values (which also have a calculation error as noted) and a statistical comparison with the accepted values. Scope of the summary is good, and I like how you point out the success in proving the wave nature of matter!

This experiment's main intent was to demonstrate that electrons have the property of waves, by the interaction of an electron with a small slit and observing the diffraction patterns that result. In this experiment the role of small slit is played by a graphite screen, if we had been able to use a single graphite crystal and passed a single electron through it, we would have had a point diffraction pattern. With the setup we have, to insure bragg diffraction occurs, they use a graphite screen which has multiple lattice structures that the incoming electrons can interface with. [[1]]

All pertinent notes are located in the lab notebook for this experiment. [[2]]

results

SJK 17:23, 11 October 2009 (EDT)
17:23, 11 October 2009 (EDT)As mentioned in your primary notebook, I think you had an error in LINEST.  And I didn't see your calculations following that (d=2*L*h etc.).  When I quickly processed your numbers, I got a 68% confidence range of 0.122 to 0.141 nm for first spacing and 0.183 - 0.205 for the second spacing.  See excel sheet here:Image:Elecdiff2.xls
17:23, 11 October 2009 (EDT)
As mentioned in your primary notebook, I think you had an error in LINEST. And I didn't see your calculations following that (d=2*L*h etc.). When I quickly processed your numbers, I got a 68% confidence range of 0.122 to 0.141 nm for first spacing and 0.183 - 0.205 for the second spacing. See excel sheet here:Image:Elecdiff2.xls

Outer maxima results
Actual atomic spacing = .213nm
slope of outer diameter vs 1/sqrt(v) = .581625 m/sqrt(V)
Atomic spacing calculated from slope = .328nm
percent error = 32% error from accepted value

Inner maxima results
Actual atomic spacing = .123nm
slope of outer diameter vs 1/sqrt(v) = .389401 m/sqrt(V)
Atomic spacing calculated from slope = .219nm
percent error = 43% error from expected value

SJK Steve Koch 17:27, 11 October 2009 (EDT)
Steve Koch 17:27, 11 October 2009 (EDT)calculating the % error is good, though you'd want to do it relative to the accepted value, not relative to your value (usually that doesn't matter too much -- just when the error gets big).  However, even better than calculating the percent error is to compare the accepted value to your range of uncertainty and then comment on whether it's consistent.  If you see the range I obtained for your inner maxima (0.122-0.141), it's actually consistent with the accepted value!  And the out maxima isn't too far off either.  This is the kind of thing you'll want to do with your ESR data as well.
Steve Koch 17:27, 11 October 2009 (EDT)
calculating the % error is good, though you'd want to do it relative to the accepted value, not relative to your value (usually that doesn't matter too much -- just when the error gets big). However, even better than calculating the percent error is to compare the accepted value to your range of uncertainty and then comment on whether it's consistent. If you see the range I obtained for your inner maxima (0.122-0.141), it's actually consistent with the accepted value! And the out maxima isn't too far off either. This is the kind of thing you'll want to do with your ESR data as well.

conclusions

The difficulties in measurement for this experiment were substantial, the choice of where to take the measurement off the ring (either inner or outer), the visual difficulty of getting an accurate width on the vernier calipers and the idea that you are sort of ballparking the voltage reading using an analog meter which did not have a ton of precision in its readout.

The error between the true value and the calculated value I came up with is mostly due to the fact that the rings are extremely difficult to see. This creates an error that makes all the calculations and conclusions drawn from them suspect.


These difficulties aside, the experiment does a superb job of reaching the goals of verifying / demonstrating the wave aspect of the electron. The diffraction rings are generated by the multiple diffractions that occur due to the countless electron-lattice interactions as the electron beam is fired at the graphite screen.

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