Physics307L:People/Meyers/Electron Diffraction Lab Summary

Steve Koch 21:06, 21 December 2010 (EST):Nice data and presentation.

Purpose

Low Voltage Correction Device

The purpose of this lab is to become more familiar with the DeBroglie relationship. We calculated the wavelengths of the primary and secondary scattering of a beam of electrons. We showed that the length of the diameters is related to the voltage the electrons are accelerated through. We also compared the wavelengths we calculated with the accepted values.

Procedure

High Voltage and Heater Supply

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

The Diffraction Bulb

This is the Raw data from which we calculated the wavelengths:

{{#widget:Google Spreadsheet |key=0AlAK7TMhL37adFBlSzdqR3pjdGcwWExmVGJHRHBwRXc |width=775 |height=575 }}

After correcting the diameters for going from a sphere to a plane by these equations:

[math]\displaystyle{ y=R-\sqrt{R^2-\frac{D_{observed}^2}{4}}\,\! }[/math]

[math]\displaystyle{ tan(\theta)=\frac\frac{D_{observed}}{2}{L-y}\,\! }[/math]

[math]\displaystyle{ D_{corrected}=2Ltan(\theta)\,\! }[/math]

We get this graph of the inverse square root of the Voltage versus the Diameters.

^{SJK 21:05, 21 December 2010 (EST)}

21:05, 21 December 2010 (EST)
This is an excellent way of plotting the data. Wondering what accounts for the large spread between runs...

height 500

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 can use the following equation:

[math]\displaystyle{ d=\frac\frac{2hL}{\sqrt{2me}}{slope}\,\! }[/math]

to calculate d as:

[math]\displaystyle{ d1=2.59(5)*10^{-10}m=0.259(5)nm\,\! }[/math]

[math]\displaystyle{ d2=1.59(3)*10^{-10}m=0.159(3)nm\,\! }[/math]

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:

[math]\displaystyle{ %=\frac{0.259-0.213}{0.213}*100=21.59%\,\! }[/math]

[math]\displaystyle{ %=\frac{0.159-0.123}{0.123}*100=29.27%\,\! }[/math]

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

Conclusion

We showed that the wavelength follow the DeBroglie relation. We also found the wavelengths close to the accepted values. The percent errors of 21 and 29 percent are a bit troublesome but because the measuring style is primitive this is acceptable. An interesting way to get better measures would be to set up a stationary camera and take images to do a visual comparison in MATLAB. This would theoretically give better results. This was an interesting lab but the painstakingly boring measuring process takes some of the life out of the process.

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.