User:Richard T. Meyers/Notebook/Phys307l/Electron Diffraction Lab

Procedure


Along with the Lab Manual the procedure for this experiment is primarily just adjusting the high voltage and measuring the associated diameters of the projected diffraction pattern. We used a micrometer to measure the diameters of the rings of the diffraction pattern. The wiring diagram for the set up is shown Here.

Data
Unfortunately I analyzed the data in EXCEL and I forgot how to export the spreadsheet to openwetware, however I did use a conversion site the results are below the raw data. The raw data is shown below:

Analysis


For the correction of the diameter I had to use the trigonometric functions stated in the manual and a bit of reading on the subject, thank you Kirsten. The relations are as follows:

$$y=R-\sqrt{R^2-\frac{D_{observed}^2}{4}}\,\!$$

$$tan(\theta)=\frac\frac{D_{observed}}{2}{L-y}\,\!$$

$$D_{corrected}=2Ltan(\theta)\,\!$$

With the corrected diameters I was able to calculate the $$d$$ using the following equations:

$$d=\frac{2hLc}{{D}\sqrt{2eV_{accelerated}c^2}}=\frac{2hL}{{D}\sqrt{2eV_{accelerated}}}\,\!$$

further this becomes:

$$d=\frac\frac{2hL}{\sqrt{2me}}{slope}\,\!$$

Using the experimentally found slopes and h being Plank's constant, e being the elementary charge, m being the mass of an electron and L and R being defined in the manual as 13cm and 66mm respectively. we calculated d as follows:

$$d1=2.59(5)*10^{-10}m=0.259(5)nm\,\!$$

$$d2=1.59(3)*10^{-10}m=0.159(3)nm\,\!$$

Error
The error I calculated using STDEV in EXCEL is 2.272 and 3.696 for the inner and outer ring respectively. From there I put these into the above equations to get the reported diameters. To calculate the percent error see below:

$$%=\frac{0.259-0.213}{0.213}*100=21.59%\,\!$$

$$%=\frac{0.159-0.123}{0.123}*100=29.27%\,\!$$

For how unsteady we were at taking the data with the calipers I think to have 30% error is fair.

Thanks
1)To exce2wiki.net for the conversion of an excel doc to wiki code converter. It saved me for hours of menial data input.

2)To Kirstin from who I got the relations for the diameter correction.

3)To Nathan for being a great lab partner.