Webexperiment – Electron diffraction
Text and images by Karl Sarnow
Table of contents
Introduction................................................................................................................................................1
What is it about?........................................................................................................................................1
Pedagogic background of the experiment..................................................................................................2
How to use it?............................................................................................................................................3
Tools needed for students lab work ..........................................................................................................3
Conducting the experiment .......................................................................................................................4
Analysing a screen shot..............................................................................................................................4
Global cooperation.....................................................................................................................................9
Students notes............................................................................................................................................9
References..................................................................................................................................................9
Introduction
At the URL
http://www.xplora.org/ww/en/pub/xplora/megalab/web_experiments/web_experiments_examples.htm
a user can reach a webexperiment called “Electron diffraction”, set up by the AG Jodl of the physics
department at Kaiserslautern university [1]. This article highlights how to use the webexperiment in a
physics lesson.
What is it about?
The experiment is about the Debye-Scherrer diffraction of an electron beam in a vacuum tube, hitting a
graphite foil. The experiments hardware is available for school use, so schools could use the hardware
in their school laboratory (http://www.leybold-didactic.de/phk/a.asp?a=555626&L=1). A schematic
setup is shown in figure 1.
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Figure 1: Schematic setup of the diffraction tube.
Pedagogic background of the experiment
During his physics lesson a student normally perceives the concept of light as a wave. Many
experiments in the school lab are easily available to be used in the school lab since the availability of
cheap lasers, which demonstrate the wave nature of light.
With the photo effect the didactic necessary interruption of a linear learning process arrives in the
classroom and makes students revise their image of the nature of light. We now face a combination of
the old Newtonian corpuscular theory of light with the Huygens wave theory of light into the
Einstein/Planck quantum concept.
The next interruption of linear knowledge acquisition arrives by De Broglies prolongation of the
quantum concept to matter, which causes particles having wave properties. As ateacher you can get
students really excited having them think about the interference of a car at a garden fence. The idea
that matter can interfere seems very strange to students and this is where the webexperiment hooks in.
Students can measure the interference of electrons at a grid. The motivation for having this experiment
run by students is normally very high and should not be underestimated as an overall physics interest
booster.
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How to use it?
In an ideal learning environment, the teacher would show the experimental setup in the school lab and
explain the details. Then the teacher would probably run a sample experiment, showing the influence
of the accelerating voltage. And finally he/she would give each student his diffraction tube for lab
work. The student gets the task to measure the diffraction ring diameters for one voltage in the school
lab.
In a real school the physics teacher will be happy to have one working diffraction tube. He/She will not
give away the tube for students experiments. Even worse: There will be too many schools around in
Europe, where the teacher can not even use a single diffraction tube. For all these cases the
webexperiment is created.
Whether the experimental setup is available in the school lab or not, the teacher will first explain either
using the lab setup or the explanations in the web page to prepare the students exercise. In any case,
the web site is visited, so every student can examine the web page. The teacher explains the measuring
procedure, including the procedure for preparing the notes of the experiment. Then each student gets
the task to conduct an experiment for one voltage with 3 repetitions in total. The teacher will take care
of a useful distribution of voltages (for example 2.0kV, 2.5kV,...,5.0kV). The task should have a time
slot of some days, depending on the number of pupils. The students task includes the creation of a
report of the experiment, which contains three parts:
1. The experimental setup (figure 1 is contained in the student folder without text and might be handed
out to the students).
2. The description of the experimental procedure.
3. The description of calculating the results from the experimental data.
Three scenarios are possible:
● Calculate the wavelength of an electron based on the tube and crystal geometry and accelearation
h
voltage and compare it with the value from the DeBroglie equation =
. From this
m∗v
calcujlation the student will get a verification of DeBroglies concept as well insight into which of
the interplanar distances of the graphite crystal is responsible for a specific interference pattern.
This scenario is the basis for Table 1.
● Use the wavelength to determine the interplanar distance of graphite. If DeBroglies equation has
been accepted, the interplanar distances can be calculated.
● Determine Planck's constant h from the experimental data using the DeBroglie equation. This
scenario is of minor didactic importance and reflects more accuracy aspects of the experiment.
Tools needed for students lab work
The students will need the following resources to successful finish his task:
● Internet access from home or from the school library, where he/she can work in his/her spare time.
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●
●
A graphics software to take a screen shot (GIMP).
An image interpretation software to measure the diameter of the diffraction ring from the screenshot
(GIMP).
● A spreadsheet program to calculate the results and have a little statistics of the results
(OpenOffice.org, Excel).
● A word processor to write the notes of the experiment. If the school is using e-portfolios, it might be
useful to have the result in HTML-form for the school web as well as in printable form for the
classroom. The word processor should have a good formula editor (LyX. OpenOffice.org, Word).
GIMP, OpenOffice.org and LyX are Open Source products and can therefore freely distributed by the
teacher. A complete ready to run solution, with all software installed is the GI-Knoppix CDROM,
which a teacher or a student may freely download, distribute and use from the Xplora repository
(Search for Knoppix). Insert the CDROM into the bootable CDROM drive at boot time and start the
software without installation issues.
Conducting the experiment
The student visits the web page http://131.246.237.97/rlab/web/eindex.shtml [2] and selects the
Laboratory tag. Then he/she will click on the “Change Acceleration Voltage” link to set the voltage for
his experiment. After filling the form with his data and sending it, the voltage is shown and the video
window shows the actual diffraction pattern for this voltage. He/She will now overlay a scale to the
image. Now the student starts the image software (GIMP) and creates a screen shot. Then he/she saves
the image with a meaningful name, for example diffr1_5_0.gif for the first image of the diffraction
pattern at 5.0kV. This procedure is repeated three times.
Analysing a screen shot
Once the screen shots are done, the student will be able to analyse it with a image software, that has the
feature of measuring the length of a line in the image. We will explain here the steps for analysing an
image with the GIMP software [2], which is available free of charge for all major operating systems
and hardware platforms.
After loading the image, the display is set to a zoom factor of 2 (2:1) and the measuring tool is selected
(figure 2).
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Figure 2: The pattern is shown with zoom factor 2 and the measuring tool is selected.
With the measuring tool (the pair of compasses symbol) the student clicks on a position of the
diffraction ring, holds the mouse button pressed, moves to the opposite position of the same diffraction
ring (the line must pass the centre of origin) and releases the mouse button. In the status line of the
image, the length and angle (not used here) of the line is shown (figure 3).
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Figure 3: The measuring tool indicates a diameter of 197 pixels.
As the length of the line is given in pixels, a calibration procedure is needed to calculate the diameter
in cm. For this task, the same measuring tool is used to measure the length of the axis scale. It is useful
to measure the length of the full 6cm scale in pixels. These data are then transferred into the
spreadsheet “Diffraction tube” (diffr_calc.sxc). Figure 4 shows where in the spreadsheet to put the
numbers.
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Figure 4: Data needed to calibrate the image.
The measured diameter of the diffraction pattern is put into a different location of the spreadsheet
together with the acceleration voltage. Figure 5 shows where the data have to go. The student should
not touch the rest of the spreadsheet, as there reside the formulas used to calculate the results.
Figure 5: The data fields for input of
experimental results.
When a student has input his data, The calculated fields of the spreadsheet fill up with numbers. Some
columns use the geometry data of the diffraction pattern and graphite foil to calculate the wavelength
according to equation 1:
=
D∗d
2∗l
Equation 1
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Herein D is the diameter of the diffraction pattern on the screen, d is the interplanar spacing of graphite
and l is the distance of the graphite foil from the screen. As according to [3] graphite has two
interplanar distances, the student can calculate two wavelengths for the same diffraction ring. As a
teacher, you know that the inner ring is caused by the planes with large interplanar distances, while the
outer ring is caused by the planes with small interplanar distances. This knowledge is not availablefor
the average student. The correct selection will be proofed in the results section of table 1. There the
student will compare the calculated wavelength with the DeBroglie wavelength and find that only one
calculation matches the DeBroglie wavelength with good precision.
From the accelerating voltage U the electrons speed is caluclated according to equation 2:
v=

2∗e∗U
me
Equation 2
Herein e is the charge of the electron, U the acceleration voltage and me the mass of the electron. This
calculation does not pay attention to relativistic effects. A teacher might let the students argument
about this.
From the speed of the electron, equation 3 might be used to calculate the DeBroglie wavelength of the
electron:
=
h
me∗v
Equation 3
This wavelength is caluclated in a separate column of the spreadsheet and then compared with the two
possible wavelength calculated with the two graphite interplane distances (table 1).
Ua[kV]
2.5
2.5
3
3
D[pixel]
106
175
102
161
D[cm]
3.21
5.3
3.09
4.88
Calculated according equation 1
λ1[m]
λ2[m]
2.53E-011
1.46E-011
4.18E-011
2.42E-011
2.44E-011
1.41E-011
3.85E-011
2.22E-011
v [m/s] λ_DeBroglie[m]
2.97E+007
2.45E-011
2.97E+007
2.45E-011
3.25E+007
2.24E-011
3.25E+007
2.24E-011
Δλ1
-3.20%
-41.36%
-8.17%
-41.82%
Δλ2
67.64%
1.54%
59.03%
0.75%
Table 1: Results of one conduct of the web experiment electron diffraction.
The first two columns contain the experiments result (yellow background). In table 1 are the results for
two experiments: One with 2.5kV and one with 3kV accelerating voltage. For both experiments the
diameters of the inner and outer diffraction ring are measured in pixels. The calibration data from the
previous calibration procedure are used to calculate the diameter in cm in column three. In columns
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four and five contain the calculation results of equation 1 applied to the data in column three. From the
acceleration voltage in column one, the speed of the electrons is calculated in column six. This result
is used to calculate the DeBrogle wavelength according to equation 3 in column seven. Comparing the
relative difference of the DeBroglie wavelength in column seven with the two geometrical wavelength
in column four and five, a student can easily see two things:
1. The small rings results from diffraction at the planes with the large interplanar distances (d1=2.13Å),
while the big rings result from diffraction at the planes with small interplanar distances (d2=1.23Å).
2. The good precision of the results proofs the validity of DeBroglies assumption of matter having
wave properties.
Global cooperation
Not every student might have found a good correlation between the geometrical calculation (equation
1) of the wavelength and the DeBroglie calculation (equation 3) of the wavelength. It is also of interest
to see how other students performed conducting the experiment. It is therefore recommended, that the
student inserts his results into the Xplora database for the webexperiment electron diffraction. The
student may input his data into the database and look for the results of others. In case he is unable to
use a spreadsheet program, he will even be able to use the output of the database for creating his notes.
Students notes
Finally the student has to prepare his notes. The teacher might point to the Xplora resources to
download the whole package of information (schematic setup without text, spreadsheet without data
and this text as PDF file) in a zipped archive, in order to save time. But the teacher should insist, that
the student fills in missing text in the graphics, data in the spreadsheet and explains in the 3 standard
sections of a laboratory note (Setup, Procedure, Result) the calculation contained in the spreadsheet
and procedures they followed. It must be clear to a student, that simple cut&paste procedures are
known to the teacher and are rated bad.
References
[1]Informationen about AG Jodl: http://pen.physik.uni-kl.de/w_jodl/
[2]The webexperiment „Elektron diffraction“:
http://www.xplora.org/ww/en/pub/xplora/megalab/web_experiments/web_experiments_examples.htm
[3]The Hardware of the experiment: http://www.leybold-didactic.de/phk/a.asp?a=555626&L=1
[4]The GIMP: http://www.gimp.org
[5]OpenOffice.org: http://www.openoffice.org
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[6]LyX: http://www.lyx.org
[7]Xplora: http://www.xplora.org
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