Electron Diffraction Notes

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^{SJK 15:03, 19 December 2009 (EST)}

15:03, 19 December 2009 (EST)
Good notebook. Graphs definitely would help in looking at the data / judging the results.

The purpose of this lab is to see experimentally how electrons act as waves. This can be done by means of electrons impacting a surface that acts as a diffraction grating. This is an example of the the de Broglie hypothesis that electrons act like waves and particles.

Safety

Went over Safety with our lab T.A. Pranav Rathi.
The major concern with this lab is again electrical personnel safety. You don't want to shock your self and get hurt. We are using equipment that has large voltages and currents.
Equipment safety is also a concern in that the bulb is breakable and you don't want to drop it and watch it shatter. Another concern is when we are connecting the equipment don't run the bias through the heater you may end up frying the bias out due to the fact that it is rated for only 500 mA and the heater is putting out a current of 3A.

Set Up

I used the following diagram from Darrell Bonn.
Circuit Diagram for the set up of the Electron Diffraction Lab
First I only used 3 different components and bnc cables. I hooked the electron diffraction machine up to the DC power supply. I had to hook up the heater on the power supply (rated at 6.3V 3A) to the F3 and F4 ports, and the high voltage supply(HV Supply) to the G7 and C5 ports with the C5 line also serving as a ground and connected this to a bias to make the whole set up work. I tried to connect the set up with out the bias but it wouldn't work for what reasons I could not tell you.

Equipment

3B DC Power Supply (0... 5kV, 6.3V AC/3Amp ,Model U3310)
TEL 2501 Universal Stand (EC UK Made)
Cabrera Precision Calipers
Electron Diffraction Tube (2555, 5 kV, 0.3 mA, EC UK Made)
DVM (digital voltmeter) (WAVETEK 85XT, Wavetek Corporation, 20A:20A/600V, min interrupt 100kA)
BNC cables

Notes

Day 1

Went through a safety brief with Pranav Rathi our lab T.A.
I then proceeded to set up the equipment.
I first turned on the power to the Power Supply and let the heater warm up the electron gun. Once this was done I checked the voltage on the heater using the voltmeter and found it to be 6.3 V. Then I turned the power up to 4.9 KV on the accelerating voltage and saw the rings produced by the electron diffraction. I then used the magnet to center the inner rings on the center of the bulb. I then proceeded to take measurements on the inner and outer diameters using the calipers (which i had to turn on due to the fact that they are digital). I then took readings of the inner and outer diameters using the calipers while i changed the accelerating voltages taking the voltage down by .25 kV for each data point. I did this until i could hardly see the diffraction patterns which ocured at approximately 2.75 kV.

Day 2

I set up the equipment again and took a measurement on the voltage going to the heater and found that it hadn't changed and was at 6.3 V
I then proceeded to let the bulb warm up and then turned the accelerating voltage to 5 kV and centered the radii on the center of the bulb again. Then i turned on the calipers and begun to take reading on the diameters of the rings. I did this starting at 5 kV and then decreasing by a factor of .2 kV until I reached the final value of 3 kV.

Data

{{#widget:Google Spreadsheet |key=0Ao8NF4FsZR3ydE4wV21uRTNRV2lQQ3pVal95czR4eHc |width=950 |height=300 }}

Calculations

Starting with [math]\displaystyle{ \lambda =\frac{h}{p} }[/math] we then need to know the spacing of the graphite lattice we use the Bragg condition [math]\displaystyle{ 2dsin\theta =2d\theta =n\lambda }[/math] where

d=the lattice spacing
n=diffraction order
[math]\displaystyle{ \lambda }[/math]=wave length of the particle
[math]\displaystyle{ \theta }[/math]=the angle that opposed the path length length difference for a matter wave

so the angle of diffraction from the incident particles is 2[math]\displaystyle{ \theta }[/math]

so [math]\displaystyle{ 2\theta =\frac{R}{2L} }[/math]

and for small angels this simplifies to [math]\displaystyle{ \frac{Rd}{L}=\lambda }[/math] where D is the spacing between the maxima on the screen at a distance L away

[math]\displaystyle{ \lambda =\frac{h}{p}=\frac{h}{\sqrt{2mE_{k}}}=\frac{h}{\sqrt{2meV_{a}}} }[/math]

substituting in [math]\displaystyle{ \frac{Rd}{l}=\lambda }[/math] gives you [math]\displaystyle{ \frac{Rd}{l}=\frac{h}{\sqrt{2meV_{a}}} }[/math]

and using the fact that [math]\displaystyle{ R=\frac{D}{2} }[/math] we can find the relationship for d [math]\displaystyle{ d=\frac{2hL}{D\sqrt{2meV_{a}}} }[/math]

so then we can take the measurements we obtained for the accelerating voltage as our y-values and our diameters to plot them or use a program to find the slope (I used linist to do this) and find D as a function of the square root of the Accelerating voltage. Then taking [math]\displaystyle{ D=\frac{2hL}{\sqrt{2me}}\frac{1}{\sqrt{V}}=\frac{\gamma }{d} }[/math] to find a value for d where [math]\displaystyle{ L=13\pm .02cm }[/math] and [math]\displaystyle{ \gamma =\frac{2hL}{\sqrt{2me}} }[/math]

So for my day one data:

the value for the inner diameter to be 0.0935 nm with a range of [math]\displaystyle{ 0.0870\geq d\geq 0.1006 nm }[/math] which had a error of 56.2%
the value for the outer diameter to be .194nm with a range of [math]\displaystyle{ .1823\geq d\geq 0.2081 nm }[/math] and an error of 58%

And for my day 2 data:

Inner diameter was .1801 nm with a range of [math]\displaystyle{ .1801\geq d\geq 0.1988 nm }[/math] with an error of 11.26%
outer diameter was .1249 nm and a range of [math]\displaystyle{ 0.1150\geq d\geq 0.1366 nm }[/math] and error of 1.54%

(error given by [math]\displaystyle{ \frac{actual-experimental}{actual}= }[/math]%error with the actual value being 0.123 nm for the outer diameter and .213 nm for the inner diameter these values can be found in Dr Golds Lab Manual)

I would like to thank Alexandra Andrego for her lab note book and her data analysis methods I took a lot from them.

Errors

^{SJK 15:02, 19 December 2009 (EST)}

15:02, 19 December 2009 (EST)
Yes, I would say that day 2 is better. The precision on day 1 is not worth it if it causes you to have so much systematic error. Graphs of the four fits (two for each day) would really help in assessing the data.

So it would seem that my day one data was off both values had an error of approximately 50% so I would say that I was making systematic errors. These errors had pretty good precision but bad accuracy due to the fact the the error was around the same for both sets of measurement (inner and outer diameters) so I would say that my methods were good but flawed in some way. For my day two data I would say that it was good and that it did not have too much error especially seeing that the error was under fifteen percent and knowing the methods for gathering the information was to put a set of calipers on the surface of light bulb so I am happy with the day 2 data.