User:Emran M. Qassem/Notebook/Physics 307L/2010/11/01

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=Electron Diffraction=

Purpose
Use the De Broglie relation "wavelength = planks constant / momentum" to measure the inner lattice spacing of the crystalline structure of graphite by sending an electron beam through a thin layer of the material and analyzing the diffraction pattern that it produces on a phosphorus Bulb surface.

Equipment

 * Carrera Precision 6 inch digital caliper alloy # CP8806-T
 * DC Power Supply 0-5 kV 3B U33010 6.3V AC/3A
 * HP6216B Power Supply
 * Electron Diffraction Bulb 5kV .3mA 3B 0185712309003

Safety

 * 5kV of power is very dangerous. We must be careful not to shock ourselves.
 * We should not exceed 15 volts for the biasing voltage.
 * Make sure the heater doesn't overheat the graphite, it will glow dull red if it is.

Setup
Golds Lab manual explains how to setup. Basically do the following:
 * Match up the banana wires with the leads described in the lab manual on P24.
 * Turn on both power supplies
 * Turn up Voltage to 5kV.
 * Center the rings using the magnet on the neck of the bulb.

Procedure
You will notice that there are two rings glowing green on the white surface of the bulb (see image). Measure the ring diameter by measuring from the inside edge, as it is unclear where the edge ends on the outside one. 
 * Note the voltage
 * Measure the inner diameter of the Inner ring using the caliper.
 * Measure the inner diameter of the Outer ring using the caliper.
 * Adjust the voltage down by 200V and repeat.

Data
Electron Diffraction XL Doc



Calculations
We plotted the Diameter of the inner and outer ring vs one over the square root of the voltage and found a linear relationship. We then calculated the two different lattice spacings "d" by using the slope of the plots and the equation:
 * $$d=\frac{2Lh}{D\sqrt{2emV_A}}\,\!$$
 * $$D=\frac{2Lh}{d\sqrt{2emV_A}}\,\!$$
 * $$slope=\frac{2Lh}{d\sqrt{2em}}\,\!$$

The values that we obtained for d were:
 * $$d=0.183(1)nm\,\!$$

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

This standard error is the average standard error (column SE in the Excel sheet) calculated by the SE divided by the slope, multiplied by the value we obtained for d. The range of values of d we obtained are:
 * $$0.173 nm < d < 0.193 nm\,\!$$

and
 * $$0.131 nm < d < 0.145 nm\,\!$$

The actual values of d are:
 * $$ d = 0.123nm\,\!$$

and
 * $$ d = 0.213nm\,\!$$.

Error
Our results are more than 3 standard errors away from the actual accepted value for both spacings. I would attribute this to our inability to take accurate measurements as it was difficult to hold the calipers steady against the glass bulb as well as systematic error from the curvature of the bulb, which we did not account for. We decided not to include the curvature of the bulb into our calculations as we were having such difficulty getting accurate readings in the first place.

Acknowledgments/Citations
I thank Randy for calculations. I thank Dr. Koch and Randy for helping me understand the what was happening with the electron as it passed through the graphite lattice spacing and why it produced diffraction rings.


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