User:Randy Jay Lafler/Notebook/Physics 307L/Electron Diffraction Summary

Purpose/Procedure
The purpose of the Electron Diffraction lab was to measure the lattice spacing inside a thin sheet of graphite, and to prove the De Broglie relation: $$lamda=\frac{h}{p}\,\!$$ We proved the De Broglie relation by plotting the diameter D that we measured as a function of one over the square root of the voltage we applied, and determining that the relationship is linear. We then solved for d using the two slopes we obtained from our two Excel plots. My Electron Difraction lab notebook

Data overview
The values that we obtained for d were:
 * We calculated the value of the lattice spacings d from the slope of the graphs of the D verse one over the squareroot of the voltage. We also had to use an equation derived in the book and solved for the slope.
 * $$d=0.183(10)nm\,\!$$

and
 * $$d=0.138(7)nm\,\!$$


 * Since the graphs of D verse one over the squareroot of the voltage are linear this proves the De Broglie relation.

Error
The actual values for the lattice spacing d are 0.123nm and 0.213nm. The values we obtained are more than three Standard Diviation away. The reason for this is probably due to the difficulty we had in measuring the diameters. It was hard to steady the calipers, and it was hard to tell exactly when a diffraction ring started and ended. We also did not incorporate the curvature of the glass bulb in our measurements, because we know that the error in measuring the diameters with the calipers was larger than neglecting the error due to the curvature of the bolb. Therefore, I believe the large error in our measurements are due to the human error in using the calipers to measure the diameters.

Acknowledgements
Emran my lab partner. Professor Koch for helping us to better understand why the diffraction patter of the electron is a ring. Emran for the help with the Excel sheet and the pictures.