User:Emran M. Qassem/Electron Diffraction

Overview

In this lab we measured the lattice spacing inside a thin sheet of graphite by using the DeBroglie relation: $\displaystyle lamda=\frac{h}{p}\,\!$ and thus proving it.

Procedure

By changing the voltage, we changed the diameter D, and were able to find a linear relation. By plotting the diameter D, that we measured from the two rings, vs the inverse of the square root of the voltage for each diameter, we were able to find a slope using the LINEST function (least squares) and then use that result to find the lattice spacing d.

Results

The values obtained for the graphite lattice spacing were:

• The values obtained for the lattice spacing d:
• $\displaystyle d = 0.183(1)nm \,\!$
• $\displaystyle d = 0.138(7)nm \,\!$

The linearity of the graphs for $\displaystyle D\,\!$ vs $\displaystyle 1/\sqrt{Voltage}\,\!$ in the lab book proves the De Broglie relation.

Error

The actual lattice spacing is 0.123nm and 0.213nm. Our results are off by over 3 sigma. This could have been caused by a few things include the following:

• It was difficult to see where the ring edge started.
• It was difficult to see the ring at all when the voltage decreased.
• It was difficult to hold the caliper still so as to see both sides of the ring at once and get an accurate measurement.
• We didn't include the curvature of the bulb in our calculations.

The reason for not including the curvature of the bulb was that we noticed there was a lot of error in our measurements and we figured it would not help much if we included the curvature.

Conclusion

In this lab, I better understood lattice spacing, as well as how important it is to be consistent with measurements. If I were to do this lab again, I would try to have a mounted caliper, so that I could take better measurements. I would also take more measurements, as this would improve the chances of getting a better result. And finally, I would include the curvature of the bulb into the calculations.