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The Photoelectric Effect: Reconstructing the Story for the Physics Classroom

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Abstract

The photoelectric effect is commonly used as the introductory topic for the study of quantum physics. However, a literature review reveals that besides various weaknesses and errors in the presentation of the history of the photoelectric effect, textbook presentations also contain incorrect presentations of the work function and the photon concept. In this paper, I present, in story form, five key episodes of the history of the photoelectric effect that are necessary for its accurate and adequate portrayal: (a) the discovery of the photoelectric effect, (b) the characterization of and initial explanation for the photoelectric effect, (c) Einstein’s revolutionary paper on the light quantum and its explanation for the photoelectric effect, and his, eventually, receiving the Nobel Prize despite not having his hypothesis accepted, (d) Millikan’s experimental verification of Einstein’s photoelectric equation despite not accepting Einstein’s hypothesis, and (e) Compton’s measurements and his theoretical explanation which produced the ultimate acceptance of Einstein’s hypothesis. The story, entitled “The Birth of the Photon Concept,” has been tested in a classroom setting and is proposed as an essential component in the process of developing sound instructional materials.
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The Photoelectric Effect:
Reconstructing the Story
for the Physics Classroom1
Stephen Klassen2
Abstract
The photoelectric effect is commonly used as the introductory topic for the study of quan-
tum physics. However, a literature review reveals that besides various weaknesses and er-
rors in the presentation of the history of the photoelectric effect, textbook presentations
also contain incorrect presentations of the work function and the photon concept. In this
paper, I present, in story form, five key episodes of the history of the photoelectric effect
that are necessary for its accurate and adequate portrayal: (a) the discovery of the photoe-
lectric effect, (b) the characterization of and initial explanation for the photoelectric effect,
(c) Einstein’s revolutionary paper on the light quantum and its explanation for the photo-
electric effect, and his, eventually, receiving the Nobel Prize despite not having his hypoth-
esis accepted, (d) Millikan’s experimental verification of Einstein’s photoelectric equation
despite not accepting Einstein’s hypothesis, and (e) Compton’s measurements and his the-
oretical explanation which produced the ultimate acceptance of Einstein’s hypothesis. The
story, entitled “The Birth of the Photon Concept,” has been tested in a classroom setting
and is proposed as an essential component in the process of developing sound instruc-
tional materials.
Contents
1 Introduction --------------------------------------------------------------------- 2
2 Literature Review ---------------------------------------------------------------- 2
2.1 The Quasi-History of the Photoelectric Effect ---------------------------- 3
2.2 Interpretation of the Stopping Potential and Work Function ----------- 3
2.3 Interpretation of the Photon Concept ------------------------------------- 4
2.4 Student Difficulties with the Photoelectric Effect ------------------------ 5
3 Reconstructing the Story of the Photoelectric Effect --------------------------- 5
3.1 Hertz Stumbles on Something Important --------------------------------- 6
3.2 Physicists Investigate the New Phenomenon ----------------------------- 7
3.3 Einstein Has a Revolutionary Idea Which Is Rejected ------------------- 8
3.4 Millikan Fails to Disprove Einstein but Gets the Nobel Prize ------------ 9
3.5 Einstein’s Idea Is Rejected, but Compton Comes to the Rescue -------- 10
4 Concluding Remarks ------------------------------------------------------------ 11
1 Author preprint DOI: 10.1007/s11191-009-9214-6. The original publication is available at www.springerlink.com
Klassen, S. (2011). The Photoelectric Effect: Reconstructing the Story for the Physics Classroom. Science &
Education, 20(7-8), 719731.
2 e-mail: dr.s.klassengmail.com
2 S. Klassen
All these fifty years of conscious brooding have brought me no nearer to the answer
to the question, ‘What are light quanta?’ Nowadays every Tom, Dick and Harry
[jeder Lump] thinks he knows it, but he is mistaken. (Einstein 1951, p. 453)
1 Introduction
Virtually every first-year college or university
physics textbook has in its introduction to quan-
tum theory an elementary treatment of the pho-
toelectric effect. In a recent, as yet, unpublished
study, the author and colleagues (Niaz, Klassen,
McMillan, and Metz, 2009) analyzed over 100
introductory physics textbooks for their treat-
ment of historical and philosophical aspects of
the photoelectric effect. In the search for text-
books to use, only two were found that did not
include the photoelectric effect. As early as 1932,
Hughes and DuBridge wrote about Einstein’s
photoelectric equation that “[t]his equation is
perhaps the most important single equation in
the whole quantum theory” (p. 7). A few years
later, Wright wrote that “Einstein’s equation for
the photoelectric effect … is the usual starting
point for the presentation of quantum theory to
undergraduates” (1937, p. 35).
The photoelectric effect is, to this day, cited
in the textbooks as confirmation of the existence
of light-quanta or photons and this is seen as the
main reason for its importance. Physics text-
book author, Randall Knight (2004) writes
about the photoelectric effect that “[a]lthough
this discovery might seem as a minor footnote
in the history of science, it soon became a, or
maybe the, pivotal event that opened the door to
new ideas” (p. 1221, italics in original). It would
seem, then, that the textbook treatment of the
photoelectric effect, following in a long tradition
of successive presentations, each one with some
elements of improvement or new information,
is an unproblematic aspect of physics teaching.
However, when the literature on the history and
teaching of the photoelectric effect is consulted,
a different story emerges. The purpose of this
paper is to examine the history and the scientific
facts of the photoelectric effect and, thereby,
provide a basis for the reformulation of its
presentation in textbooks and popular media.
2 Literature Review
The literature that is relevant to the teaching of
the photoelectric effect spans several areas. Sev-
eral prominent and very useful articles deal with
the history of the photoelectric effect and should
be used as a basis for historical aspects of teach-
ing materials. There are numerous articles that
deal with misconceptions relating to the inter-
pretation of the photoelectric effect. These mis-
conceptions appear mainly in textbooks and
other teaching materials. They deal with both
experimental measurements and theoretical in-
terpretations of the photoelectric effect. A major
difficulty is identified in the interpretation of the
work function in Einstein’s photoelectric equa-
tion. Closely related to it is the proper interpre-
tation of the “stopping potential” when measur-
ing the photoelectric effect. Another major
problematic issue is the interpretation of the
photon concept, which is compounded by the
progressive evolution of its understanding in
the physics community. Surprisingly, a litera-
ture search yielded only one article (Steinberg,
Oberam, and McDermott, 1996) dealing explic-
itly with the teaching of the photoelectric effect
as it relates to difficulties in student understand-
ing.
This review is designed to provide a frame-
work for the construction of an accurate and
useful story which can be used as the historical
The Story of The Photoelectric Effect 3
background to any instructional approach. Such
a presentation must not only be scientifically
and historically accurate, but engaging, and it
must qualify as a literary story (Klassen, 2009).
In addition, such a story must avoid implying
any of the several conceptual errors that have
been identified and, where possible, explicitly
portray the correct interpretation.
2.1 The Quasi-History of the Photoelectric Effect
Kragh (1992) identifies six major areas that are
a frequent part of quasi-historical presentations
of the photoelectric effect in textbooks. Quasi-
history may be defined as “a mythical history
specially prepared for the indoctrination of cer-
tain methodological and didactic viewpoints”
(Kragh 1992, p. 351). In the case of the photoe-
lectric effect, these misconceptions or “myths”
are that (a) Einstein’s 1905 theory of the photo-
electric effect relied on and was a natural exten-
sion of Planck’s theory of 1900, which Einstein
adopted and applied to the nature of light; (b)
Einstein’s 1905 paper was primarily a theory of
the photoelectric effect; (c) the main aspect of
Einstein’s theory of the photoelectric effect was
an explanation of experiments which showed
that the kinetic energy of the photoelectrons de-
pends linearly on the frequency of incident light
but is independent of its intensity; (d) the exper-
imental fact of the photoelectric effect is inexpli-
cable without the photon hypothesis; (e) since
there were no classical alternatives to Einstein’s
explanation, it was, of course, accepted; and (f)
the final verification of Einstein’s theory was
provided by Millikan in his experiments of 1916
(Kragh 1992, p. 352). Stuewer (2006) goes on to
show how Einstein’s light-quantum hypothesis
of 1905 was consistently rejected by the physics
community and that it was only with Compton’s
theoretical explanation of the effect that the
community reluctantly accepted the photon in
1925. A culmination of this early work on elec-
trons and photons was presented at the 1927
Solvay Conference in Brussels (Bacciagaluppi
and Valentini 2006). A useful summary of Ein-
stein’s paper and the circumstances surround-
ing the delay in its acceptance appears in
Rigden’s (2005) paper. Other useful historical
information is contained in the various Nobel
speeches of the era. An elaboration of the his-
tory based mainly on these resources will be pre-
sented later in this paper.
2.2 Interpretation of the Stopping Potential and
Work Function
Einstein’s photoelectric equation is normally
written in textbooks as
φυ
= heV
where e is the electronic charge, V the potential
difference across the phototube required to stop
the most energetic photoelectrons, h is Planck’s
constant,
υ
is the frequency of the incident light,
and
φ
is the work function of the cathode in the
phototube, which is assumed to be a metal.
However, Einstein (1905) did not express his
equation this way, preferring not to use Planck’s
constant explicitly, but rather expressing it in
terms of other fundamental constants. Further-
more, as a review of the relevant literature re-
veals, the equation in this form is, at best, mis-
leading, and at worst, simply incorrect.
Various authors (Keesing 1981, 2002; Rud-
nick and Tannhauser 1976; James 1973; Hodg-
son and Lambert 1975) have pointed out that
the work function in a metal is measured rela-
tive to the Fermi energy of conduction electrons
in the metal. Thus, when the photoelectric effect
is measured at room temperature, the electrons
have an energy distribution which makes it im-
possible to observe a distinct value of stopping
potential at which the most energetic photoelec-
trons are stopped. Instead, the photocurrent ap-
4 S. Klassen
proaches the voltage axis asymptotically. The di-
rect observation of a stopping potential at room
temperature along the lines predicted by Ein-
stein’s equation is thus rendered physically im-
possible according to Keesing (2002).
Furthermore, as soon as the phototube is
connected into a real circuit, it is no longer the
stopping potential which is being measured, but
the stopping potential plus the difference in
contact potentials of the various metallic junc-
tions in the circuit. The net effect is that the
work function in the photoelectric equation is
not that of the cathode, but rather that of the an-
ode! So, a more correct photoelectric equation
would read
A
h
eV
φ
υ
=
where
φ
A is the work function of the anode or
collector, which is not an intuitive result. Strictly
speaking, if the photoelectric equation were to
be formulated in the least problematic manner,
assuming non-relativistic photoelectrons, it
would read
φυ
= hmv
2
2
1
where m is the mass of a photoelectron, v is the
non-relativistic velocity of the most energetic
electron, and
φ
is the minimum energy required
to remove an electron from the surface of the
metal in question. Even in this formulation, a
temperature of 0K is assumed, otherwise a
Fermi energy distribution for the velocities of
the photoelectrons must be taken into account.
Keesing remarks, in this context, that “[s]everal
generations of undergraduate textbooks have
made claims about the photoelectric effect
which are not borne out by direct experiments
and are incompatible with other branches of
physics” (1981, p. 148). James (1973) suggests
that “[i]t is possible to discuss all the qualitative
features of the photoelectric effect that lead to
the idea of energy quanta without the detailed
discussion of work functions … . If one merely
demands that removing an electron from a
metal … uses up a certain energy … then pho-
tons have to be at least as energetic as this before
the photoelectric effect releases electrons” (p.
384). Any elementary treatment of the photoe-
lectric effect should, hence, not raise the issue of
the work function but, simply, talk in general
terms about the energy required to remove an
electron from the metal.
2.3 Interpretation of the Photon Concept
Einstein used the term “light quantum” in his
1905 paper and the term “photon” was only in-
vented in 1926 by the chemist Gilbert Lewis and
used in his presentation of an incorrect theory
of light quanta in which he proposed that pho-
tons were conserved and could be neither cre-
ated or destroyed (Lewis 1926). The term was
immediately adopted by the physics community
when Compton began to use it in 1927. A num-
ber of authors (Strnad 1986; Kidd, Ardini, and
Anton 1989; Jones 1991; Milonni 1997; Free-
man 1984; Armstrong 1983; Berger 1981; Stan-
ley 1996) have pointed out that the concept of
the photon has evolved since its initial proposal
and that its interpretation, even today, is rather
murky and even difficult. Twenty-five years ago,
Freeman (1984) wrote that “[t]he nature of the
photon is an unresolved problem” (p. 11) and
varying viewpoints still persist (Zeilinger,
Weihs, Jennewein, and Aspelmeyer 2005; Roy-
choudhuri and Tirfessa 2006; Sulcs 2003; Gun-
ther and Beretta 2005). Today, it would be un-
controversial to say that photons “are not parti-
cles like baseballs or shot; and the photon is not
a return to Newton’s corpuscular theory of
light” (Armstrong 1983, p. 104) contrary to
what is stated in some textbooks. Zeilinger,
Weihs, Jennewein, and Aspelmeyer, (2005) who
are proponents of the photon, portray an instru-
mentalist account of the photon when they
write:
One might be tempted, as was Einstein, to con-
sider the photon as being localized at some place
with us just not knowing the place. But whenever
The Story of The Photoelectric Effect 5
we talk about a particle, or more specifically, a
photon, we should only mean that which a ‘click
in the detector’ refers to. (p. 233)
Whether one takes an instrumentalist or re-
alist position, the interpretation of the photon is
challenging; moreover, it is held by many that it
is not necessary to have photons in order to ex-
plain the photoelectric effect successfully
(Strnad 1986; Milonnni 1997). In my conversa-
tions with colleagues who teach advanced un-
dergraduate physics, I have learned that, even
today, they use a semi-classical model to derive
the photoelectric effect in their classes. How-
ever, the photon per se, can only be understood,
and only partially at that, by a thorough under-
standing of quantum electrodynamics.
What, then, is one to say to students when
they are being introduced to quantum mechan-
ics? It should be made clear that the behavior of
photons between the emitter and detector is not
known but that we only know their quantum
mechanical behavior when they are detected.
Strnad recommends that
At the introductory level it is best to consider
photons in the discussion of the photoelectric ef-
fect as energy quanta and in the discussion of the
Compton effect as energy and momentum
quanta, to say nothing about their position and
avoiding as far as possible the analogy with elec-
trons. (1986, p. 650)
The dominant picture of photons as “parti-
cles of light” is misleading, as it implies the lo-
calization and motion of particles of light be-
tween the emitter and detector of the light, even
though such motion is not defined. What
should be emphasized, rather, is the quantum
mechanical nature of the interaction of light
with matter.
The situation vis-à-vis the concept of the
photon is much more complex than can be por-
trayed in a short summary such as this, and a
thorough discussion of the various aspects
would surely require a large volume. However,
the few main points that have been discussed
here will serve to guide the writing of introduc-
tory materials.
2.4 Student Difficulties with the Photoelectric Effect
It would seem that with the complexities men-
tioned here and given the misleading nature of
much of the existing instructional material, stu-
dents would be expected to experience difficul-
ties in understanding the photoelectric effect.
Surprisingly, not much has been written about
the matter. Only Steinberg, Oberam, and
McDermott (1996) outline a study in which stu-
dents had difficulty interpreting the photoelec-
tric experiment in terms of the photon model
for light. In the study a tutorial was designed to
address the problem. However, this study does
not address the difficulties with the concepts
themselves.
3 Reconstructing the Story of the Photoelectric Effect
As has been outlined in the literature review,
many of the portrayals of the photoelectric effect
suffer from inclusion of quasi-history and a par-
tially wrong portrayal of the concepts, them-
selves. In order to facilitate the teaching of the
introduction to quantum mechanics in a first-
year university class, the author developed an
accurate story to weave through the instruction.
The historical and scientific sources for the story
are contained in the literature review, above.
Additional sources are cited, below. The story
consists of five episodes that correspond to nat-
ural divisions in the development of the photo-
electric effect. Usually, historical treatments of
the photoelectric effect do not make a strong
connection to the Compton Effect, but this is
necessary, since the photon concept was not ac-
cepted until Compton formulated his explana-
tion for the effect. The five episodes as presented
6 S. Klassen
here are (a) the discovery of the photoelectric ef-
fect, (b) the characterization of and initial expla-
nation for the photoelectric effect, (c) Einstein’s
revolutionary paper on the light quantum and
its explanation for the photoelectric effect, and
his, eventually, receiving the Nobel Prize despite
not having his hypothesis accepted, (d) Milli-
kan’s experimental verification of Einstein’s
photoelectric equation despite not accepting
Einstein’s hypothesis, and (e) Compton’s meas-
urements and his theoretical explanation which
produced the ultimate acceptance of Einstein’s
hypothesis. I have entitled the story “The Birth
of the Photon Concept”.
This story has been presented four times to
the author’s first-year university physics class
where it was well-received. In practice, the story
is integrated with instruction, which includes
live demonstrations, whole-class concept quiz-
zes, chalkboard illustrations, and worked exam-
ples. In the presentation of the story below,
commentary has been inserted in italics to sep-
arate it from the text of the story as it should be
presented to students.
3.1 Hertz Stumbles On Something Important
The story of the photoelectric effect must begin
with the discovery of the effect. In the story, the
relationships among the protagonists should be
featured in order to re-introduce the humanistic
element, which is, for the most part, not present
in textbook presentations. Some relevant details
can be found in Bryant (1998) and Acolyte Sci-
ence (2008). Stories should, where possible, con-
tain elements of suspense. At the beginning, I
have chosen to withhold the identity of Hertz,
naming him only when he makes the important
discovery of radio waves.
The story begins in the 1880’s with a 30-
year-old physics professor in GermanyHein-
rich, or Heinz as we shall call himwho had just
been appointed Professor at the University of
Karlsruhe. Heinz’s doctoral supervisor had been
the famous physicist, Helmholtz. Although
Heinz was no longer his student, Helmholtz had
ambitions for him. There was a problem prize in
physics to be won from the Berlin Academy of
Science, which Helmholtz wished that Heinz
would tackle. The problem dealt with the exper-
imental verification of an aspect of Maxwell’s
proposals on electromagnetism. Heinz was not
much interested in winning the prize, but he was
fascinated by Maxwell’s theory, wondering
whether the equations could be interpreted to
yield electromagnetic waves that traveled
through space. So, he took up Helmholtz’s prob-
lem, but not his challenge, and developed an
idea which resulted in an experimental demon-
stration of what was soon to be called “radio
waves”.
Heinz’s demonstration worked essentially
by connecting an oscillating high-voltage coil to
a circuit in which it produced a series of sparks
across a gap so as to cause the voltage to switch
rapidly across an antenna. At the other end of
the room, he placed a copper wire loop inter-
rupted with a small copper sphere close to a
pointed end of the wire. To everyone’s amaze-
ment, small sparks jumped across the gap in the
loop even though there was no physical connec-
tion between the antenna and the loop, located
at opposite ends of a large room. And this is
how, at the age of 31, Heinrich Hertz instantly
became famous as the discoverer of radio waves.
Hertz might have had a long and distinguished
career, but, sadly, his life was cut short when at
the age of 36 he died of a blood disease.
During his first series of experiments with
radio waves, Hertz ran into a most curious phe-
nomenon. He noticed that when he placed a
shield over the detector coil to see the spark bet-
ter in the dark, the size of the spark decreased.
Even if he placed a plate of glass in front of the
detector coil, the size of the spark still decreased.
Knowing that, unlike ordinary glass, quartz
transmits ultraviolet light, Hertz substituted a
quartz plate for the glass. Now the spark re-
tained its original size. It was a curious phenom-
enon, indeed!
The Story of The Photoelectric Effect 7
In all his work, Hertz was assisted by his stu-
dents. One student, in particular, Wilhelm Hall-
wachs, had an idea for transforming Hertz’s cu-
rious result into a systematic experiment. He
took a piece of pure zinc and attached it to an
electrometer. Then he … but instead of describ-
ing what he did, let’s do it ourselves and see if we
can figure out what is going on.
A live demonstration of the photoelectric ef-
fect similar to what was done by Hallwachs fol-
lows. Questions that should be raised as a result
of the demonstration are (a) What properties of
the phenomenon demonstrated did you observe?
and (b) Do you [the students] have any (tenta-
tive) explanations (with reasons) for what you
observe? The story should be concluded with a
summary of Hallwach’s observations, as follows.
Hallwachs concluded that when the electro-
scope is negatively charged, then this charge dis-
sipates immediately and quickly under the in-
fluence of light on the zinc plate and that the
light only has this effect if it has a strong ultra-
violet component. However, when the electro-
scope is positively charged, then this charge dis-
sipates very slowly, even under the influence of
light shining on the zinc plate.
3.2 Physicists Investigate the New Phenomenon
During the period between the initial discovery of
the photoelectric effect and Einstein’s 1905 paper,
the phenomenon was investigated by prominent
physicists. Students should realize that good ex-
perimental work was done at this early stage and
that satisfactory theoretical explanations were
put forward. These investigations established the
main features of the photoelectric effect which
should serve to help students understand the phe-
nomenological aspects quite thoroughly.
The new phenomenon, which became
known as the photoelectric effect, generated
much interest in the physics community, but
was seen as only one of the many new phenom-
ena which needed to be explained by the theo-
ries of physics of the day.
Two prominent physicists, in particular,
paid attention to the new effect. One was Sir J. J.
Thomson of England and the other was Philipp
von Lenard of Germany. Thomson was trying to
establish the nature of the fundamental negative
charge of electricity which he called “corpus-
cles”, but which were commonly known as
“cathode rays” and which we now know as the
electron. Beams of the negative “rays” had been
studied by physicists for some time. Many phys-
icists did not believe that cathode rays were par-
ticulate in nature, but Thomson was certain that
they were. In 1899, Thomson subjected the
negative electricityemitted from metal plates
under the influence of ultraviolet light to the
same analysis as cathode rays. His conclusion
was that these, too, were “corpuscles” or, as they
were soon to become known, electrons.
Lenard set out to investigate the nature of
the photoelectric effect even more thoroughly.
By 1902, he had found, to his surprise, that only
the number of electrons given off, but not their
energy, was affected by the intensity of the light.
But, most surprising of all, Lenard found that
the energy of the electrons depended on the
wavelength of the light and that shorter wave-
length light tended to yield faster electrons.
However, Lenard was unable to develop ade-
quate experimental conditions to determine in
what way this effect varied. In 1905, Lenard was
awarded the Nobel Prize for his work on cath-
ode rays. The next year, Thomson received the
prize for his work on the electron. Although the
photoelectric effect was, to some degree, puz-
zling, Lenard and other physicists used existing
theories of physics to devise good explanations
for it. Basically, they reasoned that since the
electrons are ejected immediately when the light
hits and since they have energy which does not
depend on the intensity of the light, their energy
must originate inside the atom. All that the light
does is trigger the release of the electrons. Since
the structure of the atom was not known at the
time, their explanation was quite reasonable alt-
hough not very detailed.
8 S. Klassen
At this point, diagrams should be employed to
explain in greater detail Lenard’s experiments
and what it was that he observed. Questions that
students should address are (a) What further
characteristics of the photoelectric effect (beyond
those uncovered by Hallwachs) were revealed by
Lenard’s work? And (b) Does Lenard’s explana-
tion for the photoelectric effect seem reasonable?
3.3 Einstein Has a Revolutionary Idea Which Is Rejected
The next episode is the important story surround-
ing Einstein’s 1905 paper. Following the advice
gathered from the literature review, I have taken
the liberty of removing several words from Ein-
stein’s revolutionary statement, namely, that
light quanta “are localized points in space, which
move without dividing” (Einstein 1905, p. 2).
This aspect, according to the literature cited, cre-
ates a picture of photons which is not consistent
with what is currently believed. Furthermore, it
must be explained that when a circuit is con-
structed to illustrate Einstein’s equation that the
quantity usually identified with the work func-
tion is no longer the actual work function de-
scribed by Einstein. Lastly, it should be pointed
out that Einstein received virtually no support for
his light quantum hypothesis for about 20 years
and that even his being awarded the Nobel Prize
was controversial.
In the next few years, much work was done
on the photoelectric effect. The youthful Albert
Einstein read about it, but his mind was on other
things. He wondered how it could be that light,
which is considered a wave, can interact with an
atom which exists at only a point. His thoughts
along these lines culminated in his famous pa-
per of 1905, “On a Heuristic Point of View Con-
cerning the Production and Transformation of
Light”. In it, he makes one of the most revolu-
tionary statements in the history of physics:
“…the energy of a light ray spreading out from
a point source is not continuously distributed
over an increasing space but consists of a finite
number of energy quanta which … can only be
produced and absorbed as complete units” (Ein-
stein 1905, p. 2). These “energy quanta” eventu-
ally became known as photons. Einstein pre-
dicted that his light quanta each had energy that
was a multiple of the frequency,
ν
(the Greek let-
ter, nhu). The constant could easily be worked
out to be equal to Planck’s constant, h, but Ein-
stein chose not to use that notation. Einstein
borrowed the concept of h, from Planck’s re-
cently-published concept of a collection of oscil-
lators inside a heated body, but applied it, in-
stead, to individual oscillators, in this case light
quanta. Einstein listed three ways in which his
hypothesis could be tested. One was a model of
the photoelectric effect. Einstein claimed that it
was possible for one light quantum to be ab-
sorbed by a single electron, imparting to it all its
energy. If the electron is near the surface, some
of its new-found energy will be lost in moving to
the surface and escaping any electrical forces at
the surface, requiring a quantity of energy,
φ
(designated by the Greek letter, phi), which is a
property of the metal itself. The remaining en-
ergy, E, is observed as the kinetic energy, ½ mv2
of the electron as it is ejected from the surface of
the metal. The energies of the electrons so
ejected will have a maximum value, since some
may originate from beneath the surface and oth-
ers (with maximum energy) originate exactly at
the surface. The governing relationship is, then,
very simply
E = h
ν
φ ,
where it is understood that E is the maximum
energy of ejected electrons. If the electrons
(which have a charge, e) are stopped by applying
a negative repelling or stopping voltage of value
V to the collector, then the relation becomes
eV = h
ν
φ
C .
In this relationship the energy to remove the
electron from the metal,
φ
, is replaced by a com-
posite value,
φ
C , which is a property of the cir-
The Story of The Photoelectric Effect 9
cuit as a whole. Einstein wrote, in his 1905 pa-
per, that “[i]f the derived formula is correct,
then [the stopping potential], when represented
in Cartesian coordinates as a function of the fre-
quency of the incident light, must be a straight
line whose slope is independent of the nature of
the emitting substance(Einstein 1905, p. 14).
Einstein’s light quantum was disdainfully re-
jected by the physics community. Max Planck,
when nominating Einstein for membership in
the Prussian Academy of Science in Berlin in
1913, felt that he had to defend Einstein in his
nomination letter by writing “[t]hat [Einstein]
sometimes, as for instance in his hypothesis on
light quanta, … may have gone overboard in his
speculations should not be held too much
against him” (Kirsten and Körber, p. 201). Even
though Einstein’s hypothesis was almost univer-
sally rejected, he wrote to his friend, Michelle
Besso, that the existence of “the light quantum
is practically certain” (Einstein 1916). In 1921,
when Einstein was to receive his Nobel Prize,
the Royal Swedish Academy of Sciences, which
awards the prize, was caught in a dilemma, as
they did not believe in Einstein’s special theory
of relativity, so they included the photoelectric
effect in the prize when they awarded it the next
year. However, they did not believe in the quan-
tization of light either! In his Nobel Prize
speech, also in the next year, Niels Bohr, who
had formulated the first quantized theory of the
atom, expressed his disregard for the light quan-
tum concept by saying, “The hypothesis of light
quanta ... is not able to throw light on the nature
of radiation” (Bohr 1922, p. 14).
At this point, Einstein’s equation should be
discussed by plotting it on a graph. Questions that
students should address are (a) What fundamen-
tal quantities can be determined from the graph?
and (b) What are the main practical problems in
measuring the photoelectric effect? The problem
of surface contamination and oxidation may be
raised. It would help to remind students that in
the demonstration of the photoelectric effect in
class, the sample had to be cleaned with emery
cloth before using it.
3.4 Millikan Fails to Disprove Einstein but Gets the Nobel Prize
In discussing the contribution of Millikan to the
understanding of the photoelectric effect, it
should be made clear that Millikan set out to dis-
prove Einstein, and even when he confirmed Ein-
stein’s equation exactly, he did not accept Ein-
stein’s light quantum hypothesis. In addition,
Millikan’s restatement of the trigger hypothesis in
his 1916 paper can be used to show students that
viable theories for the photoelectric effect other
than Einstein’s hypothesis existed.
Chicago physicist, Robert Millikan, did not
accept Einstein’s light quantum hypothesis ei-
ther. He saw it as an attack on the wave theory
of light. From 1912 to 1915 Millikan put all his
efforts into measuring the photoelectric effect.
A major difficulty was posed by the rapid oxida-
tion of the metallic surfaces. To solve that prob-
lem, Millikan devised a technique for scraping
clean the metal surfaces inside the vacuum tube
which he described as a small “machine shop in
vacuo(Millikan 1950, p. 103). By 1915 it had
become clear to Millikan that he had verified
Einstein’s equation exactly. He published his re-
sults in 1916, describing Einstein’s light quan-
tum hypothesis as a “bold, not to say reckless,
hypothesis of an electro-magnetic light corpus-
cle of energy h
ν
which flies in the face of thor-
oughly established facts of interference” and
which “now has been pretty generally aban-
doned” (Millikan 1916, p. 355). Millikan, who
was not a theorist, paraphrased the theories ex-
plaining the photoelectric effect in his paper. He
wrote that the photosensitive metal must con-
tain oscillators of all frequencies that are at all
times loading up to the energy value h
ν
. A few
of them will be in tune with the frequency
ν
0 of
the incident radiation and thus will absorb en-
ergy until it reaches the critical value h
ν
0 at
which time an explosion will occur and the elec-
tron will be shot out from the atom. Millikan’s
10 S. Klassen
theoretical explanation was known as the trigger
hypothesis and had been popular since Lenard.
For a discussion of another theory of the photo-
electric effect, that of Richardson, see Katzir,
2006. By this time, everyone was beginning to
realize that the trigger hypothesis was not a very
satisfactory explanation, but they chose to live
with it rather than accept Einstein’s hypothesis.
So, Millikan, albeit failing to disprove Einstein’s
equation, was able to measure h to within 0.5%
of the value proposed by Planck. His consola-
tion was that he received the Nobel Prize for his
work on both the photoelectric effect and on de-
termining the value of the electronic charge, in
1923.
At this point, students should be ready to
work textbook type problems on the photoelectric
effect. However, the instructor should take the
student through some typical problems so as to
relate them to relevant aspects of what has been
discussed about the photoelectric effect, so far.
3.5 Einstein’s Idea Is Rejected, but Compton Comes to the
Rescue
Students will be entering into a state of disequi-
librium by now, as Einstein’s hypothesis has still
not been accepted by the physics community. At
this point, the story of Compton’s contribution, as
portrayed in Stuewer (2006), can be used to bring
a satisfactory resolution to the story.
Even though Einstein had received the No-
bel Prize in 1922, physicists did not accept his
photon concept. Almost the only one believing
Einstein was his friend, Paul Ehrenfest. It was at
this time that Arthur Compton began his exper-
imental work in physics, first in St. Louis in 1920
and then in Chicago in 1923. Compton began to
investigate the curious behavior of X-rays when
projected at an aluminum target. Physicists had
noticed that the absorption factor of the X-rays
was lower than it should be. Compton began to
consider various explanations for the anoma-
lous absorption, including the speculation that
the X-rays were being diffracted like light by the
electrons in the aluminum atoms. The problem
with Compton’s explanation was that it re-
quired the electron to be almost as large as the
atom itself. Other physicists were not impressed
with the explanation, and Compton began to
look for other reasons for the X-ray behavior.
For one thing, he began to look more closely at
the energies of the X-rays after they left the alu-
minum target. The energy of the X-rays de-
creased (or their wavelength increased) with the
angle of emergence from the target. Finally, in
1923, Compton began to formulate a revolu-
tionary explanation that worked. He observed
with ever greater precision how the X-ray en-
ergy varied as it emerged from the target.
Compton explained the change in wavelength
(or energy) as the result of a billiard-ball-like
collision of an X-ray quantum with a nearly-free
electron in the target. In Compton’s picture,
both energy and momentum were perfectly
conserved in the collision. At any given angle of
emergence of the X-ray, only one wavelength
was observed and the value shifted downward as
the angle increased. Compton’s billiard-ball ex-
planation was somewhat complicated by the ra-
ther high energy of the electrons after their col-
lision with the X-rays, which necessitated using
a relativistic expression for the electron momen-
tum. When Compton put it all together, how-
ever, the resulting expression was amazingly
simple:
)cos1(
0
θλλ
=
cm
h
e
where
λ
' is the wavelength of the X-ray emerg-
ing at an angle
θ
,
λ
0 is the incident wavelength,
h is Planck’s constant, me the mass of the elec-
tron, and c is the speed of light in a vacuum.
Niels Bohr, who had recently received the Nobel
Prize for his work on the structure of the atom,
would not accept Compton’s explanation. He
The Story of The Photoelectric Effect 11
devised experiments to attempt to disprove
Compton’s theory by trying to show that the
Compton Effect was only an average over many
X-ray-electron interactions. However, by 1925
several experiments had been done that proved
fairly conclusively that energy and momentum
were conserved for each X-ray and electron pair
separately. When Bohr learned of these results,
he wrote to his friend, “It seems … that there is
nothing else to do than to give our … efforts as
honorable a funeral as possible” (Bohr 1925, p.
82).
In 1926 the word “photon” was invented for
the light quantum. Compton’s experiment and
his theory to explain it served to provide con-
vincing support for Einstein’s photon hypothe-
sis, and physicists generally accepted it at that
time. Einstein wrote to his friend, Ehrenfest,
“We both had no doubts about it (Einstein
1925, p. 35). Some would say that Compton’s
experiment and theory was the definitive factor
in the movement to the new physics of quantum
mechanics. It was, certainly, the definitive factor
in the acceptance of the photon concept.
At this point, students should be invited to
discuss the importance of Compton’s work both
for the acceptance of Einstein’s photon hypothesis
and the movement to the new quantum mechan-
ics. The stage has been set for moving to the next
topic in the course, which is, commonly, the wave
nature of matter.
4 Concluding Remarks
As an example of the pervasiveness of pseudo or
mythical histories of science, I refer to the pop-
ular and widely-used video series, The Mechan-
ical Universe and Beyond. In episode 24, the
topic “Particles and Waves” is introduced. In
interpreting Robert Millikan’s experiments per-
formed up to 1916 to measure the photoelectric
effect, the narrator of the video states:
When he measured the energies of electrons
ejected from various metals by different frequen-
cies of light, Millikan verified that while each
metal has a different work function, Planck’s con-
stant has the same universal value for all of them.
But this explanation of the photoelectric effect
not only confirmed Planck’s theory, it showed di-
rectly that bundles of energy already exist in the
electromagnetic field. (California Institute of
Technology 1987)
However, as we have already established, this
popular presentation misrepresents Millikan’s
motivation and his contribution. Initially, Mil-
likan did not set out to verify, even indirectly,
Planck’s radiation formula or Einstein’s light
quantum hypothesis, which he did not accept
until some time later. He simply sought to es-
tablish the mathematical form of the relation-
ship between ejected electron maximum energy
and incident light frequency, not any particular
theory behind the relationship (Kragh 1992).
Helge Kragh agrees with Thomas Kuhn that
such quasi-histories of science are intended to
“make students believe that they are participants
in a grand historical tradition which has pro-
gressed cumulatively and according to definite
methodological norms” (Kragh 1992, p. 359).
My recounting of the story and raising prob-
ing questions as the problematic aspects emerge
highlights the weakness of teaching science in a
decontextualized and predictable fashion. In
presenting the science story as it evolved histor-
ically, I have shown that science does not pro-
gress in the fashion in which it is stereotypically
presented in science curricula and textbooks. I
have shown that scientific discoveries are messy
and that scientific theories do not arise in a neat
and orderly sequence or even, necessarily, lead
to better theories. By simplifying and misrepre-
senting the nature of scientific discoveries in
isolation, we may, in fact, produce the very thing
that we, as science teachers, want to avoid. Pre-
tending that the answers to big questions were
resolved in an uncomplicated, problem-free
progression destroys or prevents the very en-
gagement and questioning of students that we
12 S. Klassen
hope to stimulate. As American satirist H. L.
Mencken once wrote, “[t]here is always an easy
solution to every human problemneat, plausi-
ble, and wrong” (Mencken 1917, p. 443).
Acknowledgements The researching, writing, and presenting of this paper was made possible, in
part, through funding provided by NSERC CRYSTAL at the University of Manitoba, the Maurice
Price Foundation, and the University of Winnipeg.
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14 S. Klassen
About the Author
Stephen Klassen is a Senior Scholar at The University of Winnipeg.
His Ph.D. (University of Manitoba) is in Science Education, and his
background is in experimental physics. Dr. Klassen’s current research
is in the writing, analysis, and use of history-of-science stories in sci-
ence teaching. His work, in part, is published in Science & Education,
Science Education, Interchange, and Physics Education. Since 1997, he
has presented papers regularly at the periodic International Confer-
ence on History of Science in Science Education (ICHSSE) and has
contributed significantly to its organization, especially in co-chairing
the Planning Committee. As of 2001, he has been actively involved in
the International History, Philosophy, and Science Teaching Group
(IHPST) in various capacities: presenting at most of its conferences,
assuming the role of Program Chair in 2003, and serving on its governing Council from 2010 through 2014 and
the Editorial Committee of Science & Education from 2011 through 2013.
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An investigation conducted after standard lecture instruction in a sophomore-level modern physics course revealed that many students were unable to interpret the photoelectric experiment in terms of the photon model for light. Findings from this research were used to guide the development of an interactive computer-based tutorial to address the conceptual and reasoning difficulties that were identified. The primary instructional strategy used in the tutorial is the drawing and interpretation of graphs of current versus voltage for the circuit in the experiment. The program has been used both as an aid to instruction and as a probe to obtain additional information about the nature, prevalence, and persistence of specific difficulties. Analysis of student performance on examination problems on the photoelectric experiment indicates that those who have worked through the tutorial make fewer errors and give better explanations than those who have not had this experience. This result suggests that the intellectual engagement required by the program helps students improve their understanding of the photoelectric effect.
Conference Paper
Albert Einstein's light-quantum paper was the only one of his great papers of 1905 that he himself called "very revolutionary". I sketch his arguments for light quanta, his analysis of the photoelectric effect. and his introduction of the wave-particle duality into physics ill 1909. 1 show that Robert Andrews Millikan, in common with almost all physicists at the time, rejected Einstein's light-quantum hypothesis as an interpretation of his photoelectric-effect experiments of 1915. I then trace the complex experimental and theoretical route that Arthur Holly Compton followed between 1916 and 1922 that led to his discovery of the Compton effect, a discovery that Peter Debye also made virtually simultaneously and independendy. Compton's discovery, however, wits challenged oil experimental grounds by William Duane and oil theoretical grounds by Niels Bohr in the, Bohr-Kramers-Slater theory of 1924, and only after that theory was disproved experimentally the following year by Walther Bothe and Hans Geiger in Berlin and by Compton and Alfred W. Simon in Chicago was Einstein's light-quantum hypothesis generally accepted by physicists.
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The theory proposed by Einstein's which stated that light consists of discrete quantum particles, was analyzed. Einstein suggested that light consists of individual, discrete, localized and indivisible quantum particles. He demonstrated the efficacy of light quanta by applying them to three different phenomena of photoelectric effects, ionization of gases and Stoke's rule. Einstein's concept of light particle is said to have changed the physics by transforming Planck's quantum from a mathematical convenience to a basic physical concept.
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Christa Kirsten and Hans-Günther Körber Berlin: Akademie-Verlag 1915 pp 299 price 38DM The editors remark that these proposals are often as revealing about their authors as about the nominee; thus Planck on Einstein in 1913: 'Dass er in seinen Spekulationen gelegentlich auch einmal über das Ziel hinausgeschossen haben mag, wie z. B. in seiner Hypothese der Lichtquanten, wird man ihm nicht allzuschwer anrechnen dürfen; derm ohne einmal ein Risiko zu wagen, lässt sichauch in der exaktesten Naturwissenschaft keine wirkliche Neuerung einfuhren.'
Chapter
At the Heinrich Hertz Conference at the University of South Carolina in March 1994, I gave demonstrations of several replicas of Hertz’s experimental apparatus; described my search for and discovery of three identifying photographs, and a set of exact replicas; and gave some of my interpretations of Hertz’s work in electromagnetics.
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The history of the photoelectric effect is described. An analysis that field quantization is not required for an explaination of the photoelectric effiect is also given. (AIP)