Remote Experiments for Teaching Quantum Physics
within the Integrated e-Learning Strategy
Pavel Brom, František Lustig
Charles University in Prague, Faculty of Math and Physics, Laboratory of General Physics Education (both).
Address: Ke Karlovu 3, CZ-121 16 Praha. E-mails: Pavel.Brom@mff.cuni.cz, Frantisek.Lustig@mff.cuni.cz
Abstract: In our contribution we describe two remote experiments on quantum physics
phenomena as a part of integrated e-learning. The integrated e-learning strategy involves etext with the theory, real remote experiments, and simulations or applets to demonstrate and
explain phenomena in an attractive way [1]. There are many nice applets or simulations
available [e. g. PhET.colorado.edu], but only few remote experiments providing real
experimental data concerning the topic quantum physics.
In our remote laboratory www.ises.info [2] we build up remotely controlled experiments to
support the integrated e-learning strategy. Concerning only quantum physics phenomena, we
would like to present a new remote experiment on the photoelectric effect where the voltampere characteristics of a vacuum phototube is measured. The experimental data are
discussed and compared with the virtual experiment output data (i. e. the data from
simulations or applets on the photoelectric effect). This experiment has been added to the
other remote experiment on the Heisenberg uncertainty principle using the single slit
diffraction, created earlier. One can verify the principle inequality ∆y∆py ≥ ћ/2, where ∆y is
equal to the slit and ∆py can be determined from the width of the zero-order maximum of light
intensity in the diffraction pattern. Both remote experiments that require only the Java
Runtime Environment to their control are available at www.ises.info with an overview, e-texts
and a list of links to the other real and virtual experiments. A proposal of the teachinglearning sequence is included. We recommend to use real remote experiments for the
presentation and a careful study of the phenomenon, whereas virtual experiments are suitable
for explanation of the physical background [3].
Introduction
The means of the integrated e-learning strategy we focus on here are virtual experiments (i. e.
applets, simulations) and real remote experiments [4]. They both can be regarded by students
and teachers as attractive and modern tools, aids for the physics education that help students
to start to understand difficult topics as well as to remind the phenomena anytime later thanks
to an unordinary and practical experience. We present here a proposal of the teaching-learning
sequence within the introductory course into quantum physics phenomena at the secondary
school and the university level. In the first part (A) the photoelectric effect is studied, in the
second part (B) we talk about the Heisenberg uncertainty principle. We suggest how to use
the means of integrated e-learning, and we provide typical results with an interesting
discussion and explanation. The lack of a vacuum phototube is not more an obstacle when it
can be shared in the form of a remotely controlled experiment. It can be available to anyone,
from anywhere and almost anytime (if one doesn’t need to wait in a queue usually for several
minutes), and without any registration required. It is possible to include the described means
in the class, in students‘ labworks or homework, during exams [5] (ready students may relax
while they are interacting with an applet or a remotely controlled experiment [6]). In case of
homework, a student is not limited by time like in the class. Opportunity to repeat the
measurement, to spend more time on interaction with an applet or remote experiment is the
main advantage of the integrated e-learning strategy for teaching and learning such difficult
phenomena.
Simple preparation
It is necessary only once to download (copy) and install the JAVA Runtime Environment
(JRE, available for free) on all PC stations. Then we can recommend to download the selected
applets like the „Photoelectric Effect“ [7] on the stations for a case that the Internet
connection would be slow or lost during sessions.
Proposal of the Teaching-Learning Sequence
A-1. The Presentation of the Photoelectric Effect
We suggest to present the new phenomenon during classes with the use of a real remote
experiment if the Internet connection is stable and fast. (A virtual experiment, or a screen
video should be ready, for a case.) The teacher should describe the circuit and its components
(mercury lamp with interference filters F1–F5 providing well-defined wavelengths,
picoammeter – high input impedance amplifier, voltage source, and the vacuum phototube
Phywe whose volt-ampere characteristics we are going to study). The students should try to
predict (and perhaps explain – see the quotes) the results for these cases, which should be
verified a little while afterwards.
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•
•
•
Shall we observe any current while changing the voltage with the shielded phototube
in the circuit? („No current, like with a capacitor instead of the phototube – open
circuit for DC voltage.“)
Shall we observe any current when the cathode is lit by infra-red radiation with the
peak wavelength 940 nm, for example? („Who knows, perhaps we shall.“) No
photocurrent is observed!
Shall we observe any current when the cathode is lit by light of any other
wavelength? („We don’t know now, let’s try it.“) We repeat preferably the automatic
measurement for any more selected filter positions F1-F5 (see the fig. 1), meanwhile
the students should note the differences, changes and give hypotheses. We do observe
some photocurrent and some kind of its dependence on the wavelength.
More possible questions: Why there was no photocurrent with the LED 940 nm?
What is the dependence on the wavelength like?
Fig. 1.: The view of the main part of the user interface: Measurement of the volt-ampere
characteristics of the Phywe vacuum phototube can be remotely controlled by buttons in the
right panel, with data acquisition. Additional control buttons are available in the left panel.
A-2. Explanation of the Photoelectric Effect
For the explanation we strongly recommend to use simplified visualisation of the
phenomenon, provided e. g. by the applet in the fig. 2-a from the PhET project ([3], [7]). With
this applet we can simulate the similar behaviour observed in the real remote laboratory and to
present the Einstein’s explanation of the photoelectric effect using the quantum (photon)
hypothesis. The PhET applet is very well designed, various dependences may be plotted, the
origin of the photocurrent and the observed threshold character can be illustrated. The teacher
may switch between the wave and the corpuscular visualisation. In order to compare the
dependences, the set of three graphs can be stored as a screen shot before some of the graphs
are cleared due to any change of free parameters. See the fig. 2-b.
Fig. 2: a) View of the user interface of the virtual laboratory „Photoelectric Effect“ [7] from
the PhET project ([3], [7]), b) example screen shot of the set of graphs for the comparison.
After the teacher has explained the background of the photoelectric effect and its threshold
behaviour, the work function W can be introduced and by the application of the energy
conservation law one can derive the Einstein’s formula for the photoelectric effect
hf = W + Ek where h is the Planck constant, f is the frequency of the elmg. radiation, and the
kinetic energy Ek of electrons emitted from the photocathode is usually determined by the
stopping voltage method, which should have been illustrated in the applet. The stopping
voltage U0 determines the kinetic energy of electrons Ek = e |U0| where e is the charge of
electron in the absolute value.
A-3. Labworks
There are three usual ways for students how to get practical experience with the photoelectric
effect: a) traditional hands-on (when a vacuum phototube is available), b) measurement in
a real remote laboratory (real data with noise, more contributions to the photocurrent, and
perhaps systematic errors to be discussed), and c) measurement in a virtual laboratory
(simplified case with results corresponding to the literature values). The teacher’s choice
should consider many aspects like the school curriculum, students‘ skills and knowledge,
goals, etc.
The most important goals and tasks are the determination of the experimental value of the
Planck constant h and the work function W. We assume that the stopping voltage U0(λ) is
equal to the zero-photocurrent voltage determined from the volt-ampere characteristics (for
details see the discussion).
Secondary school students should be able to read the experimental values of U0(λ) from the
graphs (the V-A characteristics) with some estimation of the errors. University students
should apply some advanced methods of data processing like fitting/smoothing the data to
consider the noise, and perhaps to consider the offset of the photocurrent amplifier (that is
almost zero). We share the results for a very simple method – linear fits in small, almost linear
intervals with the centres at U0(λ) as tangents (see the graph 1). The linear fits were performed
by the scientific freeware gnuplot [8] that determined errors of the fit – see the table 1 and the
graph 2.
Table 1: Results of the linear fits
with errors of the fits
Wavelength Stopping Voltage
λ [nm]
U0 [V]
365
1,46 ± 0.07
405
1,14 ± 0.07
436
0,95 ± 0,07
546
0.44 ± 0,05
568
0,33 ± 0,04
–34
hfit [10 J·s]
6,12 ± 0,08
W [eV]
1,68 ± 0,04
Iph [nA]
Graph 1:
U [V]
The volt-ampere characteristics of the Phywe vacuum phototube for certain
wavelengths λ. Linear fits (tangents) at zero photocurrents (Iph = 0 nA)
to determine the stopping voltages U0(λ).
Finally from the dependence U0(f) where the frequency f, the wavelength λ, and the vacuum
light velocity c are in the relation f = c/λ, we can determine the experimental value of the
Planck constant and the work function. Secondary school students may use the lowest and the
highest measured point U0(f) to be the most precise, perhaps they may use MS-Excel-like
software for the linear fit. University students should perform linear fit via parameters A, B:
U0 ( f ) =
h c W h
W
⋅ − = ⋅ f − = A⋅ f + B
e λ e e
e
⇒
h[ Js ] =
10 -12 THz
⋅ e[ C] ⋅ A[ V/THz] ,
Hz
W[ J ] = −eB ,
W[ eV ] ≡ − B .
Results of the fit (A ≈ 0,00382 V/THz) can be seen in the graph 2 and the table 1 (see the
value hfit with the error of the fit determined by gnuplot [8]). The relative errors of the results
correspond to the small relative errors of A and B.
U0 [V] ,
Ek [eV]
Graph 2:
f [THz]
The linear fit through experimental points U0(f). Their errorbars are equal to the
errors of the fit (see the graph 1 and the table 1). For the comparison, theoretical
dependence for the literature value of h and the work function 1,87 eV is added.
A-4. Discussion
The accuracy of determination of stopping voltages U0(f) from the volt-ampere characteristics
is limited by noise. Our experience is that all five experimental points (measured by automatic
scans for F1–F5) always follow a line with respect to their errorbars, which might be a good
verification of the Einstein’s formula. Moreover, the temperature (e. g. due to the temperature
dependence of the work function), geometry of the experiment, the state and the runtime of
the mercury lamp with luminophore may influence the slope (deviations up to 4 %).
Comparing the result experimental value hexp = (6,1 ± 0,1)·10–34 J·s to the literature value
6,63·10–34 J·s, the presence of the source of systematic error is clear. We can speculate about
its origin, e. g. unwanted contributions to the photocurrent, leakage of electrons, which causes
the stopping voltages (and hexp, and W as well, see the graph 2) to be smaller than expected
values. When we consider the errorbars in graph 2 determining the possible error of the
results, we can measure the Planck constant and the work function with the relative error up to
10 %, which can be regarded as a success for such simple measurements of very low
photocurrents. Then we can rather present results hexp = (6,1 ± 0,6)·10–34 J·s and
W = (1,7±0,2) eV.
Furthermore, we can observe negative photocurrent and its saturation for higher negative
voltages (the beginnings of V-A characteristics usually show capacitor discharging). The
explanation and its verification is very complicated but we can answer students‘ questions
simply by the photoelectric effect on the anode (especially on some impurities there) because
a very small amount of light is reflected from the large photocathode to the anode although
the anodes in Phywe vacuum phototubes are well shielded and the leakage current that can be
also determined (at the filter position F6) is very low. The saturation of photocurrent from the
cathode could be observed up around 20 V, the qualitative differences before saturation may
be caused by different electric fields around the anode (a straight wire, greater gradient) and
around the large half-circle photocathode (lower gradient), the quantitative differences by
their areas and geometry. This is another kind of source of the systematic error because we
always measure the sum of contributions to the photocurrent. All these V-A characteristics
measured by the Keithley picoammeter 6487 with internal voltage source had very similar
properties and behaviour and they produced the same results.
B. Heisenberg Uncertainty Principle
Another real remote experiment on the „Diffraction on microobjects“ (created in 2007 by F.
Schauer, F. Lustig and M. Ožvoldová) can be used for an illustration and interesting
application of the Heisenberg uncertainty principle where the common inequality ∆x∆px ≥ ћ/2
is rewritten for y-axis. Theory is explained in details in the e-text [9]. When a slit d can be
determined from the positions of minima (or maxima) of the light intensity in the diffraction
pattern and is assumed to be equal to the uncertainty ∆y of the photon position while passing
through the slit, then the uncertainty ∆py must increase after the slit gets narrower – for sure:
the width of the zero-order maximum (the position of the first minimum in the direction αmin1
– see the angle in the fig. 3) in the light intensity pattern becomes wider, which might have
been predicted by students so that the principle inequality would remain valid. Thus using the
formula for the momentum p = h / λ, its uncertainty ∆py can be examined in this way:
∆py = 2 p sin αmin1 = 2 h sin αmin1 / λ. Considering ћ = h/(2π), we have:
∆y∆p y ≥
d ⋅ sin α min 1
λ
≥
h
,
4π
1
.
8π
Fig. 3: Geometry of the remote experiment for the verification
of the Heisenberg uncertainty principle (F. Schauer, [9]).
For red laser beam (λ = 632 nm) and the narrow slit (d = 0.231 mm as a fit parameter, see the
result fit in the graph 3), we have the inequality approx. 1.00 ≥ 0.04, therefore we have
succeeded to verify the Heisenberg uncertainty principle in this case.
Light
Intensity
[rel. units]
Graph 3:
Position [mm]
The theoretical fit of the diffraction pattern to determine the slit and the
width of the zero-order maximum as well.
The main pedagogical goals are:
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Opportunity for interactive teaching and learning, for students‘ predictions followed
by verification with the use of remotely controlled experiments.
Using simplified visualisation (PhET applets) to explain the physical background.
Students should determine one of the universal constants, with the error.
Students will learn how to consider noise (data fitting or smoothing, estimation of the
error).
Students will try to solve a complex problem (perhaps considering the offset).
Students learn about typical problems with low photocurrent measurements (noise,
offset of the amplifier, leakage current, …).
Students test themselves whether they understand the theory well when they have to
determine h and W from real or virtual experimental data.
Students practise calculations with the usage of correct units.
Students learn and progress in the basics of graphical data processing (data fitting),
reading from graphs, verifying theoretical models (e.g. Einstein‘s formula), etc.
Students have opportunity to discuss their experimental results that almost correspond
to the literature value (systematic error, etc.).
The modern means of integrated e-learning help students to start to understand more
difficult topics and complex problems.
Conclusion
We have suggested a teaching-learning sequence within the integrated e-learning strategy for
teaching introductory topics of quantum physics in an attractive way. Remote measurements
with data acquisition can be done as a homework with no time limitations (each student needs
different time to start to understand).
We managed to build up real remote experiment to study the photoelectric effect where the
new phenomenon can be interactively presented and later studied carefully with many
interesting advantages and possible goals described in the text. For the explanation of the
photoelectric effect, its threshold character, its measurement method (stopping voltage), etc.
we strongly recommend to use the simplified applet from the PhET project. The teacher can
change settings for the best visualisation; moreover, the applet can be used for data
acquisition where the result Planck constant corresponds to the literature value. From the real
experimental data we have the result Planck constant and the work function
h = (6,1 ± 0,6)·10–34 J·s , W = (1,7 ± 0,2) eV.
It is possible to verify the Einstein’s formula for the photoelectric effect with the relative error
around 10 %. Furthermore, one can verify the Heisenberg uncertainty principle in another real
remote experiment studying the diffraction on a single slit.
Acknowledgment
The presented e-laboratory park was supported by grant of the Ministry of Education, Youth,
and Sport of the Czech Republic: Development of the Hardware and Software Equipment for
ICT at the Charles University in Prague, Fac. of Math and Physics – E-laboratory of Real
Remote and Interactive Physics Experiments.
Literature:
[1] Schauer, F., Ožvoldová, M., Lustig, F.: Integrated e-Learning – New Strategy of Cognition of Real World in
Teaching Physics. In Aung, W. et al. (eds.): INNOVATIONS 2009: World Innovations in Engineering
Education and Research, iNEER, USA, 2009, 119–135.
[2] Schauer, F., Lustig, F., Ožvoldová, M.: ISES – Internet School Experimental System for ComputerBased Laboratories in Physics. In Aung, W. et al. (eds.): INNOVATIONS 2009: World Innovations in
Engineering Education and Research, iNEER, USA, 2009, 109–118.
[3] Wieman, C. E., Adams, W. K., Perkins, K. K.: PhET: Simulations That Enhance Learning. Science 322,
682 (2008).
[4] Eckert, B., Gröber, S., Jodl, H. J.: Distance Education in Physics via Internet. Am. J. Dist. Edu 23 (2009), 3,
125–138.
[5] Thomsen, C., Scheel, H., Morgner, S.: Remote Experiments in Experimental Physics. Proceedings of the
ISPRS E-Learning 2005, June 1-3, Potsdam/Germany, June 2005.
[6] Ožvoldová, M., Schauer, F., Lustig, F., Dekar, M.: Real Remote Mass-Spring Laboratory Experiments
across Internet-Inherent Part of Integrated E-Learning of Oscillations. iJOE, Vol. 4, No. 1 (2008).
[7] Applets and metodical materials available at http://PhET.colorado.edu. (Cited 1. 9. 2010.)
[8] Kelley, C., Williams, T. et al.: gnuplot, http://www.gnuplot.info. (Cited 1. 9. 2010.)
[9] Schauer, F., Lustig, F., Ožvoldová, M.: Remote laboratory on the Heisenberg uncertainty principle,
Physical Background, http://www.ises.info. (Cited 1. 9. 2010.)